1. Chapter 14 Introduction to Multiple Regression Sections 1, 2, 3, 4, 6

2. 14.1: Developing the Multiple Regression Model Often, a better-fitting model of the dependent variable results from using multiple independent variables. Multiple independent variables means multiple regression. The “omni-power” example models sales as a function of price and promotion.

3. Software Output Be able to construct the model from the output. The technique is still “least squares” because we are assuming a linear relationship between each independent variable and the dependent variable.

4. Notes on Mechanics We refer to “k” explanatory or independent variables. A slope coefficient is interpreted as the change in the mean of Y for every change in X 1, taking into account the effect of other X (sometimes said “holding all other X constant”). In multiple regression, this “slope” called a “net regression coefficient.”

5. 14.2: r 2, adjusted r 2, and the overall F test R-squared, R 2, the proportion of variation in Y explained by the set of explanatory variables in the data set. R 2 will increase every time a new independent variable is added to the regression model, EVEN if the new independent variable is NOT useful. Use adjusted R 2 to compare models.

6. Overall F test Is there a significant relationship between the dependent variable and the set of explanatory variables? H 0 : β 1 = β 2 = … = β k = 0. H 1 : at least one of the β s ≠ 0. F calc = MSR/MSE (formula 14.6) Table 14.2 defines the test constituents. Use p.

7. 14.3: Residual Analysis for the Multiple Regression Model Page 580 lists the useful plots. Note that they are the same plots used in Chapter 13. What are the assumptions?

8. 14.4: Inferences Concerning the Population Regression Coefficients The hypothesis test for a single slope is the same “t test” used in Chapter 13. H 0 : β i = 0 and H 1 : β i ≠ 0. 1 tailed tests are possible. Recommend using the observed significance, i.e. the “p-value.” Important note on page 583.

9. 14.6: Using Dummy Variables and Interaction Terms in Regression Models Dummy: Use categorical independent variables. Interaction: Use products of independent variables.