The National Oceanic and Atmospheric Administration publishes temperature and precipitation information for cities around the world in Climates of the World. Data on average high temperature (in degrees Fahrenheit) in July and average precipitation (in inches) in July for 48 cities are on the WeissStats CD.
• For the estimations and predictions, use an average July temperature of 83◦F.
• For the correlation test, decide whether average high temperature in July and average precipitation in July are linearly correlated.
a. determine the sample regression equation.
b. find and interpret the standard error of the estimate.
c. decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.
d. determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
e. find and interpret a 95% confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
f. determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
g. find and interpret a 95% prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
h. compare and discuss the differences between the confidence interval that you obtained in part (e) and the prediction interval that you obtained in part (g).
i. perform and interpret the required correlation t-test at the 5% significance level.
j. perform a residual analysis to decide whether making the preceding inferences is reasonable. Explain your answer.