# AP Statistics Curriculum 2007 GLM MultLin

### From Socr

## Contents |

## 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 *X*_{i}, *i* = 1, ..., *p*. The multilinear regression model can be written as

- , where is the error term.

The coefficient β_{0} is the intercept ("constant" term) and β_{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 β_{i}. Note that multilinear regression is a linear modeling technique**not**because is that the graph of*Y*= β_{0}+ β*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 ( β_{i}), even though it is not a linear function of*X*. Thus, any model like

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.

- TBD

### Model Validation

Checking/affirming underlying assumptions.

- TBD

### Computational Resources: Internet-based SOCR Tools

- TBD

### Examples

Computer simulations and real observed data.

- TBD

### Hands-on activities

Step-by-step practice problems.

- TBD

### References

- TBD

- SOCR Home page: http://www.socr.ucla.edu

Translate this page: