We looked at data from the National Oceanic and Atmospheric Administration about their success in predicting hurricane

Question:

We looked at data from the National Oceanic and Atmospheric Administration about their success in predicting hurricane tracks. On the following page is a scatter plot of the error (in nautical miles) for predicting hurricane locations 24 hours in the future vs. the year in which the prediction (and the hurricane) occurred.

In Chapter 6, we could describe this relationship only in general terms. Now we can learn more. Here is the regression analysis:
Response variable is 24 Error
R-squared = 72.5% R-squared (adjusted) = 71.8%
s = 16.13 with 43 - 2 = 41 degrees of freedom
Variable Coefficient SE (Coeff) t-Ratio P-Value
Intercept 133.024 4.835 27.5 ‰¤0.0001
Years Since 1970 -2.06016 0.1982 -10.4 ‰¤0.0001
a) Explain in words and numbers what the regression says.
b) State the hypothesis about the slope (both numerically and in words) that describes how hurricane prediction quality has changed.
c) Assuming that the assumptions for inference are satisfied, perform the hypothesis test and state your conclusion. Be sure to state it in terms of prediction errors and years.
d) Explain what the /^-squared means in terms of this regression.