# Difference between revisions of "AP Statistics Curriculum 2007 GLM MultLin"

## General Advance-Placement (AP) Statistics Curriculum - Multiple Linear Regression

In the previous sections we saw how to study the relations in bivariate designs. Now we extend that to any finite number of varaibles (mulitvariate case).

### Multiple Linear Regression

We are interested in determining the linear regression, as a model, of the relationship between one dependent variable Y and many independent variables Xi, i = 1, ..., p. The multilinear regression model can be written as

$Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots +\beta_p X_p + \varepsilon$, where $$\varepsilon$$ is the error term.

The coefficient $$\beta_0$$ is the intercept ("constant" term) and $$\beta_i$$s are the respective parameters of the p independent variables. There are p+1 parameters to be estimated in the multilinear regression.

• Multilinear vs. non-linear regression: This multilinear regression method is "linear" because the relation of the response (the dependent variable $$Y$$) to the independent variables is assumed to be a linear function of the parameters $$\beta_i$$. Note that multilinear regression is a linear modeling technique not because is that the graph of $$Y = \beta_{0}+\beta x$$ is a straight line nor because $$Y$$ is a linear function of the X variables. But the "linear" terms refers to the fact that $$Y$$ can be considered a linear function of the parameters ( $$\beta_i$$), even though it is not a linear function of $$X$$. Thus, any model like

$Y = \beta_o + \beta_1 x + \beta_2 x^2 + \varepsilon$

is still one of linear regression, that is, linear in $$x$$ and $$x^2$$ respectively, even though the graph on $$x$$ by itself is not a straight line.

### Approach

Models & strategies for solving the problem, data understanding & inference.

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### Model Validation

Checking/affirming underlying assumptions.

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### Examples

Computer simulations and real observed data.

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### Hands-on activities

Step-by-step practice problems.

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