91Ó°ÊÓ

The figure shows three residual plots and a normal probability plot of residuals. For each part, decide whether the graph suggests a violation of one or more of the assumptions for regression inferences. Explain your answers.

(a) Decide, at the $10\%$significance level, whether the data provide sufficient evidence to conclude that $x$is useful for predicting $y$:

(b) Find a $90\%$confidence interval for the slope of the population regression line.

14.7 The difference between an observed value and a predicted value of the response variable is called a________

14.95 Plant Emissions. Following are the data on plant weight and quantity of volatile emissions from Exercise 14.25.

a. Obtain a point estimate for the mean quantity of volatile emissions of all (Solanum tuberosum) plants that weigh $60\mathrm{g}$.
b. Find a $95\%$confidence interval for the mean quantity of volatile emissions of all plants that weigh $60\mathrm{g}$.
c. Find the predicted quantity of volatile emissions for a plant that weighs $60\mathrm{g}$.
d. Determine a $95\%$prediction interval for the quantity of volatile emissions for a plant that weighs $60\mathrm{g}$.

14.97 Study Time and Score. Following are the data on total hours studied over 2 weeks and test score at the end of the 2 weeks from Exercise 14.27.

a. Determine a point estimate for the mean test score of all beginning calculus students who study for $15$hours.
b. Find a $99\%$ confidence interval for the mean test score of all beginning calculus students who study for $15$ hours.
c. Find the predicted test score of a beginning calculus student who studies for $15$ hours.
d. Determine a $99\%$ prediction interval for the test score of a beginning calculus student who studies for $15$hours.

U.S. Presidents. The data from Exercise $14.35$ for the ages at inauguration and of death for the presidents of the United States are on the Weiss Stats site.