Chapter 13, Problem 38PS

The owners of a chain of ice cream stores have the business objective of improving the forecast of daily sales so that staffing shortages can be minimized during the summer season. As a starting point, the owners decide to develop a simple linear regression model to predict daily sales based on atmospheric temperature. They select a sample of 21 consecutive days and store the results in IceCream.

a. Assuming a linear relationship, use the least-squares method to compute the regression coefficients $b_0$ and $b_1.$

b. Predict the sales for a day in which the temperature is ${83}^{\circ }\text{F}\text{.}$

c. Plot the residuals versus the time period.

d. Compute the Durbin-Watson statistic. At the 0.05 level of significance, is there evidence of positive autocorrelation among the residuals?

e. Based on the results of (c) and (d), is there reason to question the validity of the model?

f. What conclusions can you reach concerning the relationship between sales and atmospheric temperature?