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 β0 is the intercept ("constant" term) and βis 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 βi. Note that multilinear regression is a linear modeling technique not because is that the graph of Y = β0 + βx 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 ( βi), 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 x2 respectively, even though the graph on x by itself is not a straight line.

Approach

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

• TBD

Model Validation

Checking/affirming underlying assumptions.

• TBD

• TBD

Examples

Computer simulations and real observed data.

• TBD

Hands-on activities

Step-by-step practice problems.

• TBD

• TBD