Linear Regression

1. Introduction:

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









2. Prediction with an imperfect relationship

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?







R2 = rYX12 + rYX22 - 2 rYX1 rYX2 rX1X2

1-rX1X22