11.23 Multiple linear regression model. Refer to the previous two exercises. Let’s now consider a linear regression using all three explanatory variables.

a. Write out the statistical model for this analysis, making sure to specify all assumptions.

b. Run the multiple regression model and specify the fitted regression equation.

c. Obtain the residuals and check the conditions needed for inference.

d. Generate a 95% confidence interval for each coefficient. Explain what these intervals tell you.

e. What percent of the variation in total score is explained by this model? What is the estimate for

σ ?