Television news programs attempt to attract viewers in local markets by claiming to offer the “best” local weather forecasts. The particular station in this exercise claims to offer more accurate predictions of the next day’s weather. In particular, it claims to predict rainfall and temperature more precisely than others. This example focuses specifically on a claim for predicting the following day’s high temperature. The data for this question give actual high temperatures for a sequence of 137 consecutive days in Philadelphia and the predicted high temperatures offered the day before on a prominent local news station. Motivation

(a) How precise would you expect the prediction of the local high temperature tomorrow to be? What degree of precision would it take to impress you?

(b) Express your answer to part (a) as a range and a probability, such as “within x degrees with 95% probability.”

Method
(c) Explain how to use regression analysis to measure the performance of the predictions of a weather forecast. In particular, what characteristic of the estimated regression of the actual high temperature on the forecast high temperature would be critical to meeting a claimed precision?

(d) Inspect the scatterplot of actual temperature on the predicted temperature. Do these data appear to meet the conditions of the SRM?

Mechanics
(e) Summarize the estimated least squares equation.

(f) Explain why the least squares slope is substantially less than one. (You may want to refer back to ideas introduced in Chapter 6 related to correlation.)

(g) With the benefit of residual analysis, do these data meet the conditions of the SRM? Explain why or why not.

Message
(h) Compared to what it would take to impress you stated in (a), are you impressed by the predictions offered by this television station?