Chapter 15, Problem 3PS

A national chain of consumer electronics stores had the business objective of determining the effectiveness of newspaper advertising. To promote sales, the chain relies heavily on local newspaper advertising to support its modest exposure in nationwide television commercials. A sample of 20 cities with similar populations and monthly sales totals were assigned different newspaper advertising budgets for one month. The following table, stored in Advertising, summarizes the sales (in $\text{\$}$ millions) and the newspaper advertising budgets (in $\text{\$}$ thousands) observed during the study:

a. Construct a scatter plot for newspaper advertising and sales.

b. Fit a quadratic regression model and state the quadratic regression equation.

c. Predict the mean monthly sales for a city with newspaper advertising of $\text{\$20,000}\text{.}$

d. Perform a residual analysis on the results and determine whether the regression assumptions are valid.

e. At the 0.05 level of significance, is there a significant quadratic relationship between monthly sales and newspaper advertising?

f. At the 0.05 level of significance, determine whether the quadratic model is a better fit than the linear model.

g. Interpret the meaning of the coefficient of multiple determination.

h. Compute the adjusted $r^2.$

i. What conclusions can you reach concerning the relationship between newspaper advertising and sales?