SOCR EduMaterials AnalysisActivities SLR

This SOCR Activity demonstrates the utilization of the SOCR Analyses package for statistical Computing. In particular, it shows how to use Simple Linear Regression and how to interpret the results

• Simple Linear Regression Background:

Simple Linear Regression is a class of statistical analysis models and procedures, which takes one indepdent variable and one dependent variable, both being quantitative, and models the relationship between them.

The model form is: y = intercept + slope * x + error, where x denotes the independent variable and y denotes the dependent variable. The error is assumed to follow a standard normal distribution.

The goal of the Simple Linear Regression computing procedure is to estimate the intercept and the slope, based on the data. Least Squares Fitting is used.

In this activity, the students can learn about:

A. Reading results of Simple Linear Regression;

B. Making interpretation of the slope and intercept;

C. Observing the scatter plots of dependent variable vs. independent variable, and diagnostic plots such as the Residual on Fit plot and the Normal QQ plot, etc.

Read more about Simple Linear Regression

• SOCR Simple Linear Regression: Go to SOCR Analyses and select Simple Linear Regression from the drop-down list of SOCR analyses, in the left panel. There are three ways to enter data in the SOCR Simple Linear Regressionapplet:

• • Click on the Example button on the top of the right panel.
  • Generate random data by clicking on the Random Example button
  • Pasting your own data from a spreadsheet into SOCR ANOVA data table.

• We will demonstrate a SOCR built-in example. This example is based on the data taken from "An Introduction to Computational Statistics: Regression Analyses" by Robert Jennrich, Prentice Hall, 1995. (Page 4)

1. As you start the SOCR Analyes Applet, click on "Simple Linear Regression" from the combo box in the left panel.

Here's what the screen shoud look like.

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The left part of the panel looks like this. Make sure that the "Simple Linear Regression" is showing during this activity but not something else, otherwise you won't be able to find the correct dataset to get the correct results.

Then click on the "Example" button and then "Data" button in the right panel. You should see the data displayed in two columns. They are named as VarA and VarB here.

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2. We'd like to use VarA as the regressor (that is, 'x', the independent variable); and use VarB as the response (that is, 'y', the dependent variable). To tell the computer which variables are assigned to be the regressor and response, we have to do a "Mapping." This is done by clicking on the "Mapping" button first to get to the Mapping Panel, and then map the variables.

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(Note that, since the columns C3 through C10 do not have data and they are not used, just ignore them.)

3. After we do the "Mapping" to assign variables, now we can let the computer calculate the regression results by click on the "Calculate" button. Then clikc on the "Result" button to see the output.

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The text in the Result Panel summarize the results of this simple linear regression analysis.

4. If you'd like to see graphical analyses, click on the "Graph" button. You'll then see the graph panel that displays scatter plot, as well as diagnostic plots of "residual on fit", "Normal QQ" plots, etc. The plot titles indicate plot types.

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Note: if you happen to click on the "Clear" button in the middle of the procedure, all the data will be cleared out. Simply start over from step 1.