Predicting tropical storms. The picture above gives data on William Gray's predictions of the number of named tropical storms in Atlantic hurricane...

Predicting tropical storms. The picture above gives data on William Gray's predictions of the number of named tropical storms in Atlantic hurricane seasons from 1984 to 2013. Use these data for regression inference as follows.

(a) Does Professor Gray do better than random guessing? That is, is there a significantly positive correlation between his forecasts and the actual number of storms? (Report a t statistic from regression output, and give the one-sided P-value.)

(b) Give a 95% confidence interval for the mean number of storms in years when Professor Gray forecasts 16 storms.

(c) Make a stemplot of the residuals (round to the nearest tenth) from your regression. Explain why your plot suggests that we should not use these data to get a prediction interval for the number of storms in a single year.