SOCR - User contributions [en]

Multiple Linear Regression Tutorial

2011-07-29T06:21:56Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Multiple Linear Regression Tutorial==

'''Multiple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using multiple explanatory variables by using SOCR. In this example, we will predict median income using age, proportion of homeowners, and proportion of whites in population.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:MReg1.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab. This is where we define our dependent and independent variables. The dependent variable is the one we want to make a prediction on, and the independent variables are the ones which we will use to make the prediction. In this example, we add “Income” to the dependent variables list and “Age”, “Homes” and “White” to the independent variables list.[[File:MReg2.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. Here you can see the regression equation and <math>R^2</math>, among others. [[File:MReg3.png|center|800px]]

''Step 6:'' Click “GRAPH”. Here you will see scatterplots of the Income variable against each of the three chosen explanatory variables, [[File:MReg4.png|center|800px]] as well as the residual plots [[File:MReg5.png|center|800px]] and the Normal QQ Plot. [[File:MReg6.png|center|800px]]

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent and dependent variables.
* How to check: Make a scatter plot of the variables
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Linear model fits the data moderately well'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values. Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase in residuals at the top range of exploratory variables'''''

Assumption 3: Errors are normally distributed.
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the "Results" tab that the regression equation is:
[[File:MReg7.png|center|800px]]

Income = -21139.729 +1347.656*Age +49806.135*White +53726.649*Homes + E

The “E” is the error term. “Income” is the predicted value, and “Homes”, “Age”, and “White” are the explanatory variables.

This model states that for every 100 percent increase in homeowner proportion, and everything else held constant, the median household income will increase by $53726.65. For every 1 year increase in median age, and everything else held constant, the median household income will increase by $1,347.66. For every 100 percent increase in the proportion of whites in the population, with everything else held constant, the median household income will increase by $49806.14.

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Multiple_Linear_Regression_Tutorial}}

Multiple Linear Regression Tutorial

2011-07-29T06:20:16Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Multiple Linear Regression Tutorial==

'''Multiple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using multiple explanatory variables by using SOCR. In this example, we will predict median income using age, proportion of homeowners, and proportion of whites in population.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:MReg1.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab. This is where we define our dependent and independent variables. The dependent variable is the one we want to make a prediction on, and the independent variables are the ones which we will use to make the prediction. In this example, we add “Income” to the dependent variables list and “Age”, “Homes” and “White” to the independent variables list.[[File:MReg2.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. Here you can see the regression equation and <math>R^2</math>, among others. [[File:MReg3.png|center|800px]]

''Step 6:'' Click “GRAPH”. Here you will see scatterplots of the Income variable against each of the three chosen explanatory variables, [[File:MReg4.png|center|800px]] as well as the residual plots [[File:MReg5.png|center|800px]] and the Normal QQ Plot. [[File:MReg6.png|center|800px]]

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income).
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Linear model fits the data moderately well'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values ( ). Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase in residuals at the top range of exploratory variables'''''

Assumption 3: Errors are normally distributed.
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the "Results" tab that the regression equation is:
[[File:MReg7.png|center|800px]]

Income = -21139.729 +1347.656*Age +49806.135*White +53726.649*Homes + E

The “E” is the error term. “Income” is the predicted value, and “Homes”, “Age”, and “White” are the explanatory variables.

This model states that for every 100 percent increase in homeowner proportion, and everything else held constant, the median household income will increase by $53726.65. For every 1 year increase in median age, and everything else held constant, the median household income will increase by $1,347.66. For every 100 percent increase in the proportion of whites in the population, with everything else held constant, the median household income will increase by $49806.14.

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Multiple_Linear_Regression_Tutorial}}

Multiple Linear Regression Tutorial

2011-07-29T06:18:31Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Multiple Linear Regression Tutorial==

'''Multiple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using multiple explanatory variables by using SOCR. In this example, we will predict median income using age, proportion of homeowners, and proportion of whites in population.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:MReg1.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab. This is where we define our dependent and independent variables. The dependent variable is the one we want to make a prediction on, and the independent variables are the ones which we will use to make the prediction. In this example, we add “Income” to the dependent variables list and “Age”, “Homes” and “White” to the independent variables list.[[File:MReg2.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. Here you can see the regression equation and <math>R^2</math>, among others. [[File:MReg3.png|center|800px]]

''Step 6:'' Click “GRAPH”. Here you will see scatterplots of the Income variable against each of the three chosen explanatory variables, [[File:MReg4.png|center|800px]] as well as the residual plots [[File:MReg5.png|center|800px]] and the Normal QQ Plot. [[File:MReg6.png|center|800px]]

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income).
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Linear model fits the data moderately well'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values ( ). Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase in residuals at the top range of exploratory variables'''''

Assumption 3: Errors are normally distributed.
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumptions met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the "Results" tab that the regression equation is:
[[File:MReg7.png|center|800px]]

Income = -21139.729 +1347.656*Age +49806.135*White +53726.649*Homes + E

The “E” is the error term. “Income” is the predicted value, and “Homes”, “Age”, and “White” are the explanatory variables.

This model states that for every 100 percent increase in homeowner proportion, and everything else held constant, the median household income will increase by $53726.65. For every 1 year increase in median age, and everything else held constant, the median household income will increase by $1,347.66. For every 100 percent increase in the proportion of whites in the population, with everything else held constant, the median household income will increase by $49806.14.

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Multiple_Linear_Regression_Tutorial}}

Multiple Linear Regression Tutorial

2011-07-29T06:17:59Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Multiple Linear Regression Tutorial==

'''Multiple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using multiple explanatory variables by using SOCR. In this example, we will predict median income using age, proportion of homeowners, and proportion of whites in population.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:MReg1.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' You should now see the data in the window. Click on the “MAPPING” tab. This is where we define our dependent and independent variables. The dependent variable is the one we want to make a prediction on, and the independent variables are the ones which we will use to make the prediction. In this example, we add “Income” to the dependent variables list and “Age”, “Homes” and “White” to the independent variables list.[[File:MReg2.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. Here you can see the regression equation and <math>R^2</math>, among others. [[File:MReg3.png|center|800px]]

''Step 6:'' Click “GRAPH”. Here you will see scatterplots of the Income variable against each of the three chosen explanatory variables, [[File:MReg4.png|center|800px]] as well as the residual plots [[File:MReg5.png|center|800px]] and the Normal QQ Plot. [[File:MReg6.png|center|800px]]

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income).
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Linear model fits the data moderately well'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values ( ). Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase in residuals at the top range of exploratory variables'''''

Assumption 3: Errors are normally distributed.
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumptions met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the "Results" tab that the regression equation is:
[[File:MReg7.png|center|800px]]

Income = -21139.729 +1347.656*Age +49806.135*White +53726.649*Homes + E

The “E” is the error term. “Income” is the predicted value, and “Homes”, “Age”, and “White” are the explanatory variables.

This model states that for every 100 percent increase in homeowner proportion, and everything else held constant, the median household income will increase by $53726.65. For every 1 year increase in median age, and everything else held constant, the median household income will increase by $1,347.66. For every 100 percent increase in the proportion of whites in the population, with everything else held constant, the median household income will increase by $49806.14.

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Multiple_Linear_Regression_Tutorial}}

Multiple Linear Regression Tutorial

2011-07-29T02:39:03Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Multiple Linear Regression Tutorial==

'''Multiple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using multiple explanatory variables by using SOCR. In this example, we will predict median income using age, proportion of homeowners, and proportion white in population.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:MReg1.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' You should now see the data in the window. Click on the “MAPPING” tab. This is where we define our dependent and independent variables. The dependent variable is the one we want to make a prediction on, and the independent variables are the ones which we will use to make the prediction. In this example, we add “Income” to the dependent variables list and “Age”, “Homes” and “White” to the independent variables list.[[File:MReg2.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. Here you can see the regression equation and <math>R^2</math>, among others. [[File:MReg3.png|center|800px]]

''Step 6:'' Click “GRAPH”. Here you will see scatterplots of the Income variable against each of the three chosen explanatory variables, [[File:MReg4.png|center|800px]] as well as the residual plots [[File:MReg5.png|center|800px]] and the Normal QQ Plot. [[File:MReg6.png|center|800px]]

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income).
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Linear model fits the data moderately well'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values ( ). Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase in residuals at the top range of exploratory variables'''''

Assumption 3: Errors are normally distributed.
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumptions met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the "Results" tab that the regression equation is:
[[File:MReg7.png|center|800px]]

Income = -21139.729 +1347.656*Age +49806.135*White +53726.649*Homes + E

The “E” is the error term. “Income” is the predicted value, and “Homes”, “Age”, and “White” are the explanatory variables.

This model states that for every 100 percent increase in homeowner proportion, and everything else held constant, the median household income will increase by $53726.65. For every 1 year increase in median age, and everything else held constant, the median household income will increase by $1,347.66. For every 100 percent increase in the proportion of whites in the population, with everything else held constant, the median household income will increase by $49806.14.

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Multiple_Linear_Regression_Tutorial}}

Multiple Linear Regression Tutorial

2011-07-29T02:38:48Z

JayZzz: Created page with '==SOCR_EduMaterials_AnalysesActivities - Multiple Linear Regression Tutorial== '''Multiple Linear Regression Tutorial Using LA Neighborhoods Data''' '''Data:''' We will be …'

==[[SOCR_EduMaterials_AnalysesActivities]] - Multiple Linear Regression Tutorial==

'''Multiple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using multiple explanatory variables by using SOCR. In this example, we will predict median income using age, proportion of homeowners, and proportion white in population.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:MReg1.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' You should now see the data in the window. Click on the “MAPPING” tab. This is where we define our dependent and independent variables. The dependent variable is the one we want to make a prediction on, and the independent variables are the ones which we will use to make the prediction. In this example, we add “Income” to the dependent variables list and “Age”, “Homes” and “White” to the independent variables list.[[File:MReg2.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. Here you can see the regression equation and <math>R^2</math>, among others. [[File:MReg3.png|center|800px]]

''Step 6:'' Click “GRAPH”. Here you will see scatterplots of the Income variable against each of the three chosen explanatory variables, [[File:MReg4.png|center|800px]] as well as the residual plots [[File:MReg5.png|center|800px]] and the Normal QQ Plot. [[File:MReg6.png|center|800px]]

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income).
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Linear model fits the data moderately well'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values ( ). Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase in residuals at the top range of exploratory variables'''''

Assumption 3: Errors are normally distributed.
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumptions met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the "Results" tab that the regression equation is:
[[File:MReg7.png|center|800px]]

Income = -21139.729 +1347.656*Age +49806.135*White +53726.649*Homes + E

The “E” is the error term. “Income” is the predicted value, and “Homes”, “Age”, and “White” are the explanatory variables.

This model states that for every 100 percent increase in homeowner proportion, and everything else held constant, the median household income will increase by $53726.65. For every 1 year increase in median age, and everything else held constant, the median household income will increase by $1,347.66. For every 100 percent increase in the proportion of whites in the population, with everything else held constant, the median household income will increase by $49806.14.

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Simple_Linear_Regression_Tutorial}}

Simple Linear Regression Tutorial

2011-07-29T02:37:42Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Simple Linear Regression Tutorial==

'''Simple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using one explanatory variable by using SOCR. In this example, we will use the age variable.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:SReg2.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab. This is where we define our dependent and independent variables. The dependent variable is the one we want to make a prediction on, and the independent variable is the one which we will use to make the prediction. In this example, we add Income to the dependent variable list and Age to the independent variable list. [[File:SReg4.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. [[File:SReg5.png|center|800px]] Here you can see the regression equation, <math>R^2</math>, individual residuals, and also mean and standard deviation for both variables.

''Step 6:'' Click “GRAPH”. Here is the scatterplot of Income vs Age. We see the upward trend: As median age increases, so does median household income. [[File:SReg6.png|center|800px]] There are also residual plots [[File:SReg7.png|center|800px]]and the Normal-QQ Plot.[[File:SReg8.png|center|800px]]

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income)
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Assumption Met'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values. Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase of residuals at the high end of age'''''

Assumption 3: Errors are normally distributed
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption Met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the results tab that the regression equation is: [[File:SReg9.png|center|800px]]

Income = -74549.596 + 4096.055 age

Income is the predicted value, -74549.596 is the intercept, 4096.055 is the slope, and age is the independent variable.

'''The linear model states that for every 1 year increase in median age, the median household income will increase by $4,096.06.'''

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Simple_Linear_Regression_Tutorial}}

SOCR EduMaterials AnalysesActivities Others

2011-07-29T02:19:08Z

JayZzz:

== [[SOCR_EduMaterials_AnalysesActivities| SOCR Analysis Activities]] - Additional Analysis Activities ==
* [[Simple Linear Regression Tutorial]]
* [[Multiple Linear Regression Tutorial]]

===See also===
* [[SOCR_EduMaterials_AnalysesActivities| Main SOCR Analysis Activities]].

<hr>
* [[SOCR_EduMaterials_AnalysesCommandLine | Command-line SOCR Analysis executions]]
* [[SOCR_Videos_Analyses | SOCR Analyses Video Tutorial]]
* SOCR Home page: http://www.socr.ucla.edu

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Simple Linear Regression Tutorial

2011-07-25T22:41:50Z

JayZzz: /* SOCR_EduMaterials_AnalysesActivities - Simple Linear Regression Tutorial */

==[[SOCR_EduMaterials_AnalysesActivities]] - Simple Linear Regression Tutorial==

'''Simple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using one explanatory variable by using SOCR. In this example, we will use the age variable.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:SReg2.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab, and add Income to the dependent variable list and Age to the independent variable list. [[File:SReg4.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. [[File:SReg5.png|center|800px]] Here you can see the regression equation, <math>R^2</math>, individual residuals, and also mean and standard deviation for both variables.

''Step 6:'' Click “GRAPH”. Here is the scatterplot of Income vs Age. We see the upward trend: As median age increases, so does median household income. [[File:SReg6.png|center|800px]] There are also residual plots [[File:SReg7.png|center|800px]]and the Normal-QQ Plot.[[File:SReg8.png|center|800px]]

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income)
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Assumption Met'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values. Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase of residuals at the high end of age'''''

Assumption 3: Errors are normally distributed
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption Met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the results tab that the regression equation is: [[File:SReg9.png|center|800px]]

Income = -74549.596 + 4096.055 age

Income is the predicted value, -74549.596 is the intercept, 4096.055 is the slope, and age is the independent variable.

'''The linear model states that for every 1 year increase in median age, the median household income will increase by $4,096.06.'''

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Simple_Linear_Regression_Tutorial}}

Simple Linear Regression Tutorial

2011-07-25T22:39:58Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Simple Linear Regression Tutorial==

'''Simple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using one explanatory variable by using SOCR. In this example, we will use the age variable.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:SReg2.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab, and add Income to the dependent variable list and Age to the independent variable list. [[File:SReg4.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. [[File:SReg5.png|center|800px]] Here you can see the regression equation, <math>R^2</math>, individual residuals, and also mean and standard deviation for both variables.

''Step 6:'' Click “GRAPH”. Here is the scatterplot of Income vs Age. We see the upward trend: As median age increases, so does median household income [[File:SReg6.png|center|800px]]. There are also residual plots [[File:SReg7.png|center|800px]]and the Normal-QQ Plot[[File:SReg8.png|center|800px]].

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income)
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Assumption Met'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values. Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase of residuals at the high end of age'''''

Assumption 3: Errors are normally distributed
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption Met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the results tab that the regression equation is: [[File:SReg9.png|center|800px]]

Income = -74549.596 + 4096.055 age

Income is the predicted value, -74549.596 is the intercept, 4096.055 is the slope, and age is the independent variable.

'''The linear model states that for every 1 year increase in median age, the median household income will increase by $4,096.06.'''

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Simple_Linear_Regression_Tutorial}}

SOCR MotionCharts Earthquakes

2011-07-25T22:15:26Z

JayZzz:

==[[SOCR_MotionCharts| SOCR MotionCharts Activities]] - California Earthquakes Data Activity==

'''Goal:''' Illustrate the use of SOCR Motion Charts using the California Earthquakes Data by visualizing relationships between multiple variables, including time variables.

'''Data:''' [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_Dinov_021708_Earthquakes California Earthquakes Data]. Data with earthquake locations, magnitudes, depths, and various other variables.

'''Activity'''

* Go to the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_Dinov_021708_Earthquakes California Earthquakes Data] and find the table with the dataset. Select all of the data, including the headers, and copy it (Ctrl+C on Windows and Command+C on Mac).

* Go to the SOCR Motion Charts: http://socr.ucla.edu/SOCR_MotionCharts/

* Select the "Data" tab, click on the first white cell of the table and paste in the data that we have just copied (Ctrl+V on Windows and Command+V on Mac).

[[File:EData.png|center|800px]]

* On the right side of the page, there will be a panel called “mappings” with drop-down menus.
** Key should be your time variable. We can first put in the “Date_(YYYY/MM/DD)” variable. If you want to see all of the data on the chart at the same time, leave this blank.
** X-axis and Y-axis should be the Longitude and Latitude variables, respectively. Earthquakes will show up as bubbles on the chart, in the correct geographical locations relative to each other.
** Size is the variable which will govern the size of the bubbles on the chart. We will choose “Mag” as the size variable. This way, earthquakes with larger magnitudes will be represented by a bigger bubble.
** Color is the variable which will govern the color of the bubbles on the chart. We will choose “Depth” as the color variable. Earthquakes with greater depths will be red.
** Category is the variable that differentiates the bubbles. We want each bubble to be a different earthquake, so we choose “EventID” for this option.

Our selections for our mappings are as follows:

[[File:Mappings2.png|center|200px]]

* Now click on the "Chart" tab:

[[File:Motion3.png|center|800px]]
**Each bubble represents one earthquake. Because we have longitude and latitude data, these bubbles are in the correct geographical locations relative to each other. The larger the bubble, the larger the magnitude for that earthquake. Red bubbles are earthquakes with high values for their depth. You can mouse over a bubble to see the Event ID of the earthquake. Notice that because we have included a time variable, we can use the scroll bar at the bottom or the play button to cycle through each earthquake, ordered by the time that it occurred.
** Make sure the seeker button is at the very left side, and press play. Each bubble that pops up represents a single earthquake. The size and color of the bubble represents the magnitude and depth of the earthquake, respectively.

* Now leave the Key dropdown menu blank. All of the earthquakes will now be displayed at the same time:

[[File:Motion4.png|center|800px]]

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/SOCR_MotionCharts_Earthquakes}}

SOCR MotionCharts Earthquakes

2011-07-25T22:15:11Z

JayZzz: Created page with '== SOCR MotionCharts Activities - California Earthquakes Data Activity== '''Goal:''' Illustrate the use of SOCR Motion Charts using the California Earthqua…'

File:Mappings2.png

2011-07-25T22:11:18Z

JayZzz:

File:EData.png

2011-07-25T22:07:51Z

JayZzz:

SOCR MotionCharts

2011-07-25T05:50:18Z

JayZzz: /* Under Construction */

== [[SOCR_EduMaterials_ChartsActivities |SOCR Charts Activities]] - SOCR Motion Charts ==
[[Image:SOCR_Activities_MotionCharts_HPI_070109_Fig6_9_Animation.gif|250px|thumbnail|right| [http://www.socr.ucla.edu/SOCR_MotionCharts/ SOCR MotionCharts] ]]

===Description===
[http://www.socr.ucla.edu/SOCR_MotionCharts/ SOCR Motion Charts] can be used to provide interactive and dynamic display of longitudinal or temporal [[SOCR Data]].

== Activities==
* [[SOCR_MotionCharts_HousingPriceIndex | MotionChart: Housing Price Index Activity]]
* [[SOCR_MotionCharts_CAOzoneData | MotionChart: California Ozone Data]]

==Under Construction==
* [[SOCR MotionCharts_LAPopulation | MotionChart: LA Population Data Activity]]
* [[SOCR MotionCharts_Earthquakes | MotionChart: Earthquakes Data Activity]]

===See also===
* [[SOCR_Videos_MotionCharts|Motion Charts Videos]]
* [http://www.gapminder.org/data/ Gapminder data] for motion charts (e.g., by country per capita income 1800-2015)
* [http://www.duckware.com/pmvr/howtoincreaseappletmemory.html Browser/Java memory usage] requirements: The [http://www.socr.ucla.edu/SOCR_MotionCharts/ SOCR MotionCharts] require at least 200MB of RAM memory. This requirement increases quadratically with the size of the data.
* [[About pages for SOCR Motion Charts]]
* [[Help pages for SOCR Motion Charts]]
* [[Google Motion Charts]]
* [[SOCR_Data | SOCR Datasets]]
* [[SOCR_MotionCharts_Test | Can these Motion Charts Work on Wiki pages?]]
* [[SOCR_Videos_Charts | SOCR Charts Video Tutorial]]
* SOCR Home page: http://www.socr.ucla.edu

==References==
* Al-Aziz, J, Christou, N, Dinov, ID. (2010). [http://www.amstat.org/publications/jse/v18n3/dinov.pdf SOCR Motion Charts: An Efficient, Open-Source, Interactive and Dynamic Applet for Visualizing Longitudinal Multivariate Data], [http://www.amstat.org/publications/jse/contents_2010.htm JSE, 18(3)], 1-29.
* Dinov, ID, Christou, N. (2011) [http://www.informaworld.com/smpp/content%7Edb=all?content=10.1080/0020739X.2011.562315 Web-based tools for modelling and analysis of multivariate data: California ozone pollution activity], [http://www.informaworld.com/smpp/title%7Edb=all%7Econtent=t713736815 International Journal of Mathematical Education in Science and Technology (JMEST)], iFIRST:1-17, [http://www.informaworld.com/smpp/content%7Edb=all?content=10.1080/0020739X.2011.562315 DOI: 10.1080/0020739X.2011.562315].

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_MotionCharts}}

Simple Linear Regression Tutorial

2011-07-25T00:50:24Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Simple Linear Regression Tutorial==

'''Simple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using one explanatory variable by using SOCR. In this example, we will use the age variable.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:SReg2.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab, and add Income to the dependent variable list and Age to the independent variable list. [[File:SReg4.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. [[File:SReg5.png|center|800px]] Here you can see the regression equation, <math>R^2</math>, individual residuals, and also mean and standard deviation for both variables.

''Step 6:'' Click “GRAPH”. Here is the scatterplot of Income vs Age. We see the upward trend: As median age increases, so does median household income [[File:SReg6.png|center|800px]]. There are also residual plots [[File:SReg7.png|center|800px]]and the Normal-QQ Plot[[File:SReg8.png|center|800px]].

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income)
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Assumption Met'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values. Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase of residuals at the high end of age'''''

Assumption 3: Errors are normally distributed
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption Met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the results tab that the regression equation is: [[File:SReg9.png|center|800px]]

Income = -74549.596 + 4096.055 age

Income is the predicted value, -74549.596 is the intercept, 4096.055 is the slope, and age is the independent variable.

'''The linear model states that for every 1 year increase in median age, the median household income will increase by $4,096.06.'''

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/Simple_Linear_Regression_Tutorial}}

Simple Linear Regression Tutorial

2011-07-25T00:50:04Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Simple Linear Regression Tutorial==

'''Simple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using one explanatory variable by using SOCR. In this example, we will use the age variable.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:SReg2.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab, and add Income to the dependent variable list and Age to the independent variable list. [[File:SReg4.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. [[File:SReg5.png|center|800px]] Here you can see the regression equation, <math>R^2</math>, individual residuals, and also mean and standard deviation for both variables.

''Step 6:'' Click “GRAPH”. Here is the scatterplot of Income vs Age. We see the upward trend: As median age increases, so does median household income [[File:SReg6.png|center|800px]]. There are also residual plots [[File:SReg7.png|center|800px]]and the Normal-QQ Plot[[File:SReg8.png|center|800px]].

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income)
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Assumption Met'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values. Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase of residuals at the high end of age'''''

Assumption 3: Errors are normally distributed
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption Met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the results tab that the regression equation is: [[File:SReg9.png|center|800px]]

Income = -74549.596 + 4096.055 age

Income is the predicted value, -74549.596 is the intercept, 4096.055 is the slope, and age is the independent variable.

'''The linear model states that for every 1 year increase in median age, the median household income will increase by $4,096.06.'''

<hr>
{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/SOCR_MotionCharts_LAPopulation}}

SOCR MotionCharts LAPopulation

2011-07-25T00:49:19Z

JayZzz:

==[[SOCR_MotionCharts| SOCR MotionCharts Activities]] - LA Neighborhoods Population Data Activity==

'''Goal:''' Illustrate the use of SOCR Motion Charts using the LA Neighborhoods Data by visualizing relationships between multiple variables.

'''Data:''' [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]. Data with various geographic and demographics variables including longitude, latitude, median income, and population breakdowns for Los Angeles Neighborhoods.

'''Activity:'''

* Go to the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] and find the table with the dataset. Select all of the data, including the headers, and copy it (Ctrl+C on Windows and Command+C on Mac).

* Go to the SOCR Motion Charts: http://socr.ucla.edu/SOCR_MotionCharts/

* Select the "Data" tab, click on the first white cell of the table and paste in the data that we have just copied (Ctrl+V on Windows and Command+V on Mac).

[[File:LAData.png|center|800px]]

* On the right side of the page, there will be a panel called “mappings” with drop-down menus.
** Key should be your time variable. If you want to see all of the data on the chart at the same time, leave this blank.
** X-axis and Y-axis should be the Longitude and Latitude variables, respectively. Neighborhoods will show up as bubbles on the chart, in the correct geographical locations relative to each other.
** Size is the variable which will govern the size of the bubbles on the chart. We will choose “income” as the size variable. This way, neighborhoods with higher incomes will be represented by a bigger bubble.
** Color is the variable which will govern the color of the bubbles on the chart. We will choose “white” as the color variable. Neighborhoods with high percentages of whites will be red.
** Category is the variable that differentiates the bubbles. We want each bubble to be a different neighborhood, so we choose “LA_Nbhd” for this option.

Our selections for our mappings are as follows:

[[File:Mappings.png|center|200px]]

* Now click on the "Chart" tab:

[[File:Motion1.png|center|800px]]
**Each bubble represents one neighborhood. Because we have longitude and latitude data, these bubbles are in the correct geographical locations relative to each other. The larger the bubble, the larger the median income for that neighborhood. Red bubbles are neighborhoods with high percentage of whites. You can mouse over a bubble to see the name of the neighborhood.
** With this Motion Chart we can note some interesting relationships between the variables. Notice that the Westwood bubble is very small, meaning a low median income. This is most likely due to the high percentage of students living there. Also, the three largest red bubbles are the three neighborhoods with the largest median incomes, and they also happen to have the highest percentages of whites. These three neighborhoods are Pacific Palisades, Bel-Air, and Beverly Crest.

* We can also experiment with other variables. For example, the population could govern the bubble sizes and diversity of the neighborhood could govern the bubble color:

[[File:Motion2.png|center|800px]]

<hr>
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SOCR MotionCharts LAPopulation

2011-07-25T00:49:08Z

JayZzz:

File:Mappings.png

2011-07-25T00:38:57Z

JayZzz: uploaded a new version of "File:Mappings.png"

File:Mappings.png

2011-07-25T00:37:46Z

JayZzz:

File:LAData.png

2011-07-25T00:33:01Z

JayZzz:

SOCR MotionCharts LAPopulation

2011-07-25T00:08:15Z

JayZzz: Created page with '== SOCR MotionCharts Activities - LA Neighborhoods Population Data Activity== '''Goal:''' Illustrate the use of SOCR Motion Charts using the LA Neighborhoo…'

==[[SOCR_MotionCharts| SOCR MotionCharts Activities]] - LA Neighborhoods Population Data Activity==

'''Goal:''' Illustrate the use of SOCR Motion Charts using the LA Neighborhoods Data.

'''Data:''' [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data]. Data with various geographic and demographics variables including longitude, latitude, median income, and population breakdowns for Los Angeles Neighborhoods

SOCR MotionCharts

2011-07-24T23:55:54Z

JayZzz: /* Activities */

== [[SOCR_EduMaterials_ChartsActivities |SOCR Charts Activities]] - SOCR Motion Charts ==
[[Image:SOCR_Activities_MotionCharts_HPI_070109_Fig6_9_Animation.gif|250px|thumbnail|right| [http://www.socr.ucla.edu/SOCR_MotionCharts/ SOCR MotionCharts] ]]

===Description===
[http://www.socr.ucla.edu/SOCR_MotionCharts/ SOCR Motion Charts] can be used to provide interactive and dynamic display of longitudinal or temporal [[SOCR Data]].

== Activities==
* [[SOCR_MotionCharts_HousingPriceIndex | MotionChart: Housing Price Index Activity]]
* [[SOCR_MotionCharts_CAOzoneData | MotionChart: California Ozone Data]]

==Under Construction==
* [[SOCR MotionCharts_LAPopulation | MotionChart: LA Population Data Activity]]

===See also===
* [[SOCR_Videos_MotionCharts|Motion Charts Videos]]
* [http://www.gapminder.org/data/ Gapminder data] for motion charts (e.g., by country per capita income 1800-2015)
* [http://www.duckware.com/pmvr/howtoincreaseappletmemory.html Browser/Java memory usage] requirements: The [http://www.socr.ucla.edu/SOCR_MotionCharts/ SOCR MotionCharts] require at least 200MB of RAM memory. This requirement increases quadratically with the size of the data.
* [[About pages for SOCR Motion Charts]]
* [[Help pages for SOCR Motion Charts]]
* [[Google Motion Charts]]
* [[SOCR_Data | SOCR Datasets]]
* [[SOCR_MotionCharts_Test | Can these Motion Charts Work on Wiki pages?]]
* [[SOCR_Videos_Charts | SOCR Charts Video Tutorial]]
* SOCR Home page: http://www.socr.ucla.edu

==References==
* Al-Aziz, J, Christou, N, Dinov, ID. (2010). [http://www.amstat.org/publications/jse/v18n3/dinov.pdf SOCR Motion Charts: An Efficient, Open-Source, Interactive and Dynamic Applet for Visualizing Longitudinal Multivariate Data], [http://www.amstat.org/publications/jse/contents_2010.htm JSE, 18(3)], 1-29.
* Dinov, ID, Christou, N. (2011) [http://www.informaworld.com/smpp/content%7Edb=all?content=10.1080/0020739X.2011.562315 Web-based tools for modelling and analysis of multivariate data: California ozone pollution activity], [http://www.informaworld.com/smpp/title%7Edb=all%7Econtent=t713736815 International Journal of Mathematical Education in Science and Technology (JMEST)], iFIRST:1-17, [http://www.informaworld.com/smpp/content%7Edb=all?content=10.1080/0020739X.2011.562315 DOI: 10.1080/0020739X.2011.562315].

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_MotionCharts}}

SOCR EduMaterials AnalysesActivities Others

2011-07-24T23:54:49Z

JayZzz:

== [[SOCR_EduMaterials_AnalysesActivities| SOCR Analysis Activities]] - Additional Analysis Activities ==
* [[Simple Linear Regression Tutorial]]

===See also===
* [[SOCR_EduMaterials_AnalysesActivities| Main SOCR Analysis Activities]].

<hr>
* [[SOCR_EduMaterials_AnalysesCommandLine | Command-line SOCR Analysis executions]]
* [[SOCR_Videos_Analyses | SOCR Analyses Video Tutorial]]
* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_AnalysesActivities_Others}}

SOCR EduMaterials AnalysesActivities Others

2011-07-24T23:53:46Z

JayZzz:

== [[SOCR_EduMaterials_AnalysesActivities| SOCR Analysis Activities]] - Additional Analysis Activities ==
* [[Simple Linear Regression Tutorial]]
* [[Motion Charts Activity]]

===See also===
* [[SOCR_EduMaterials_AnalysesActivities| Main SOCR Analysis Activities]].

<hr>
* [[SOCR_EduMaterials_AnalysesCommandLine | Command-line SOCR Analysis executions]]
* [[SOCR_Videos_Analyses | SOCR Analyses Video Tutorial]]
* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_AnalysesActivities_Others}}

Simple Linear Regression Tutorial

2011-07-24T07:08:13Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Simple Linear Regression Tutorial==

'''Simple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using one explanatory variable by using SOCR. In this example, we will use the age variable.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:SReg2.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab, and add Income to the dependent variable list and Age to the independent variable list. [[File:SReg4.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. [[File:SReg5.png|center|800px]] Here you can see the regression equation, <math>R^2</math>, individual residuals, and also mean and standard deviation for both variables.

''Step 6:'' Click “GRAPH”. Here is the scatterplot of Income vs Age. We see the upward trend: As median age increases, so does median household income [[File:SReg6.png|center|800px]]. There are also residual plots [[File:SReg7.png|center|800px]]and the Normal-QQ Plot[[File:SReg8.png|center|800px]].

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income)
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Assumption Met'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values. Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase of residuals at the high end of age'''''

Assumption 3: Errors are normally distributed
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption Met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the results tab that the regression equation is: [[File:SReg9.png|center|800px]]

Income = -74549.596 + 4096.055 age

Income is the predicted value, -74549.596 is the intercept, 4096.055 is the slope, and age is the independent variable.

'''The linear model states that for every 1 year increase in median age, the median household income will increase by $4,096.06.'''

Simple Linear Regression Tutorial

2011-07-24T07:06:48Z

JayZzz: /* SOCR_EduMaterials_AnalysesActivities - Simple Linear Regression Tutorial */

==[[SOCR_EduMaterials_AnalysesActivities]] - Simple Linear Regression Tutorial==

'''Simple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using one explanatory variable by using SOCR. In this example, we will use the age variable.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source and find the table with the data. Select all of the data, and press Ctrl+C (Command+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:SReg2.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab, and add Income to the dependent variable list and Age to the independent variable list. [[File:SReg4.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. [[File:SReg5.png|center|800px]] Here you can see the regression equation, <math>R^2</math>, individual residuals, and also mean and standard deviation for both variables.

''Step 6:'' Click “GRAPH”. Here is the scatterplot of Income vs Age. We see the upward trend: As median age increases, so does median household income [[File:SReg6.png|center|800px]]. There are also residual plots [[File:SReg7.png|center|800px]]and the Normal-QQ Plot[[File:SReg8.png|center|800px]].

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income)
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Assumption Met'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values ( ). Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase of residuals at the high end of age'''''

Assumption 3: Errors are normally distributed
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption Met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the results tab that the regression equation is: [[File:SReg9.png|center|800px]]

Income = -74549.596 + 4096.055 age

Income is the predicted value, -74549.596 is the intercept, 4096.055 is the slope, and age is the independent variable.

'''The linear model states that for every 1 year increase in median age, the median household income will increase by $4,096.06.'''

Simple Linear Regression Tutorial

2011-07-24T07:04:31Z

JayZzz:

==[[SOCR_EduMaterials_AnalysesActivities]] - Simple Linear Regression Tutorial==

'''Simple Linear Regression Tutorial Using LA Neighborhoods Data'''

'''Data:''' We will be using the [http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source LA Neighborhoods Data] for this tutorial.

'''Goal:''' Our goal is to predict the median income using one explanatory variable by using SOCR. In this example, we will use the age variable.

''Step 1:'' First, we will import the data into the SOCR Simple Regression Analysis Activity. Head to http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_LA_Neighborhoods_Data#Data_Source and find the table with the data. Select all of the data, and press Ctrl+C (Apple+C on Macs) to copy it.

''Step 2:'' Next, head to http://socr.ucla.edu/htmls/SOCR_Analyses.html, and find the Simple Regression Analysis Activity in the drop-down menu. [[File:SReg2.png|center|800px]]

''Step 3:'' Now Click the “PASTE” button under the drop down menu. You should now see the data in the window. [[File:SReg3.png|center|800px]]

''Step 4:'' Click on the “MAPPING” tab, and add Income to the dependent variable list and Age to the independent variable list. [[File:SReg4.png|center|800px]]

''Step 5:'' Click “CALCULATE”. You will now be taken to the “RESULTS” tab. [[File:SReg5.png|center|800px]] Here you can see the regression equation, <math>R^2</math>, individual residuals, and also mean and standard deviation for both variables.

''Step 6:'' Click “GRAPH”. Here is the scatterplot of Income vs Age. We see the upward trend: As median age increases, so does median household income [[File:SReg6.png|center|800px]]. There are also residual plots [[File:SReg7.png|center|800px]]and the Normal-QQ Plot[[File:SReg8.png|center|800px]].

''Step 7:'' We want to check that the assumptions of linear regression, and make sure that they are met.

Assumption 1: There is a linear relationship between the independent (age) and dependent variable (income)
* How to check: Make a scatter plot of income and age
* How to fix: Transformations (for example Log(y) vs x), or the relationship is not linear.
'''''Assumption Met'''''

Assumption 2: The variance is constant
* How to check: Look at plot of residuals vs. predicted values ( ). Make sure there is not a pattern, such as the residuals getting larger as the predicted values increase.
* How to fix: Logging of variables, fixing underlying independence or linearity causes.
'''''Slight increase of residuals at the high end of age'''''

Assumption 3: Errors are normally distributed
* How to check: Normal QQ Plot (Should lie close to straight line)
* How to fix: Take out outliers, if applicable. Non-linear transformation may be needed
'''''Assumption Met'''''

'''Conclusions'''

No major violation of linear regression assumptions, we proceed with our analysis:

We can see from the results tab that the regression equation is: [[File:SReg9.png|center|800px]]

Income = -74549.596 + 4096.055 age

Income is the predicted value, -74549.596 is the intercept, 4096.055 is the slope, and age is the independent variable.

'''The linear model states that for every 1 year increase in median age, the median household income will increase by $4,096.06.'''

Simple Linear Regression Tutorial

2011-07-24T06:52:16Z

JayZzz: Created page with '==SOCR_EduMaterials_AnalysesActivities - Simple Linear Regression Tutorial== '''Simple Linear Regression Tutorial Using LA Neighborhoods Data''' '''Data:''' We will be usin…'

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2011-07-24T06:47:06Z

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