Researchers have asked whether there is a relationship between nutrition and cancer, and many studies have shown that there is. In fact, one of the conclusions of a study by B. Reddy et al., “Nutrition and Its Relationship to Cancer” (Advances in Cancer Research, Vol. 32, pp. 237–345), was that “. . . none of the risk factors for cancer is probably more significant than diet and nutrition.” One dietary factor that has been studied for its relationship with prostate cancer is fat consumption. On the WeissStats CD, you will find data on per capita fat consumption (in grams per day) and prostate cancer death rate (per 100,000 males) for nations of the world. The data were obtained from a graph—adapted from information in the article mentioned—in J. Robbins’s classic book Diet for a New America (Walpole, NH: Stillpoint, 1987, p. 271).
• For the estimations and predictions, use a per capita fat consumption of 92 grams per day.
• For the correlation test, decide whether per capita fat consumption and prostate cancer death rate are positively 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.