Linear Regression

1. Introduction:

- a. Uses: Prediction

e.g., predicting stats grades from math anxiety.

2. Prediction with an imperfect relationship

- a. need "line of best fit", or "least squares regression line"

3. Constructing the Least Squares Regression Line

where

so,

and

4. Errors in prediction

a. need to know how much

b. homoscedasticity

c. standard error of the estimate

i. Conceptually:

ii. Computationally:

5. Multiple Correlation/Regression

A. Are two variables better than one?

R^{2} = __r _{YX1}^{2} + r_{YX2}^{2} - 2 r_{YX1} r_{YX2} r_{X1X2}__

1-__r _{X1X2}__