Forecasting daily admission of a water park (cont’d). Refer to Exercise 12.165. The owners of the water adventure park are advised that the prediction model could probably be improved if interaction terms were added. In particular, it is thought that the rate at which mean attendance increases as predicted high temperature increases will be greater on weekends than on weekdays. The following model is therefore proposed: E1y2 = b0 + b1x1 + b2x2 + b3x3 + b4x1x3 The same 30 days of data used in Exercise 12.165 are again used to obtain the least squares model yn = 250 - 700x1 + 100x2 + 5x3 + 15x1x3 with sbn 4 = 3.0 R2 = .96

a. Graph the predicted day’s attendance, y, against the day’s predicted high temperature, x3, for a sunny weekday and for a sunny weekend day. Plot both on the same graph for x3 between 70°F and 100°F. Note the increase in slope for the weekend day. Interpret this.

b. Do the data indicate that the interaction term is a useful addition to the model? Use a = .05

c. Use this model to predict the attendance for a sunny weekday with a predicted high temperature of 95°F.

d. Suppose the 90% prediction interval for part c is (800, 850). Compare this result with the prediction interval for the model without interaction in Exercise 12.165, part

e. Do the relative widths of the confidence intervals support or refute your conclusion about the utility of the interaction term (part b)?

e. The owners, noting that the coefficient bn 1 = -700, conclude the model is ridiculous because it seems to imply that the mean attendance will be 700 less on weekends than on weekdays. Explain why this is not the case.