QA 8. Regression with Multiple Explanatory Variables

Learning Objectives

1) Distinguish between the relative assumptions of single and multiple regression.

2) Interpret regression coefficients in a multiple regression.

3) Interpret goodness of fit measures for single and multiple regressions, including $R^2$ and adjusted-$R^2$.

4) Construct, apply and interpret joint hypothesis tests and confidence intervals for multiple coefficients in a regression.

5) Calculate the regression $R^2$ using the three components of the decomposed variation of the dependent variable data: the explained sum of squares, the total sum of squares, and the residual sum of squares.