Weather News broadcasts use weather forecasts to attract viewers to their station. These data give the observed daily high temperature for 137 consecutive days in Philadelphia along with the broadcast forecasts of high temperature produced one day before, two days before and three days before.

(a) Examine plots of the association between these variables. Is the associated correlation matrix a good summary of the association, or do correlations omit important aspects of the data that are only seen in plots?

(b) Consider the correlations between the actual temperature and the forecast temperatures. Which are more correlated, and is the pattern in the correlations what you would expect?

(c) Fit the multiple regression of the observed high temperature on the one-day ahead forecast and two-days-ahead forecasts. Show a summary of the fitted model.

(d) Does the estimated model in (c) meet the conditions of the MRM? Explain the consequences of any deviations from the MRM.

(e) Compare the estimated partial slopes of the fitted model to the marginal slopes for these variables. Why are these different, and does the difference make substantive sense?