12. Regression

"Using the sample data from Problem 8 in Section 12.3,

c. Predict the value of y if x=1.8."

Using the sample data from Problem 7 in Section 12.3

b. Construct a 95% confidence interval for the mean value of y if x=1.4.

Credit Scores Use the results of Problem 12 from Section 12.3 to answer the following questions:

b. Construct a 90% confidence interval for the mean interest rate of all individuals whose credit score is 730.

"An Unhealthy Commute Use the results of Problem 11 from Section 12.3 to answer the following questions:

a. Predict the mean well-being index composite score of all individuals whose commute time is 20 minutes."

"Confidence Intervals for y-Intercept and Slope

You can construct confidence intervals for the y-intercept B and slope M of the regression line y = Mx + B for the population by using the inequalities below.

y-intercept B :

b - E < B < b + E

where

E = t_c s_e \(\sqrt{\frac{1}{n}\) + \(\frac{\overline{x}\)^2}{\(\sum\) x^2 - \(\frac{(\Sigma x)^2}{n}\)}}

slope M :

m - E < M < m + E

where

E = \(\frac{t_c s_e}{\sqrt{\sum x^2 - \frac{(\Sigma x)^2}{n}\)}}

The values of m and b are obtained from the sample data, and the critical value t_c is found using Table 5 in Appendix B with n - 2 degrees of freedom.

In Exercises 37 and 38, construct the indicated confidence intervals for B and M using the gross domestic products and carbon dioxide emissions data found in Example 2.

38. 99% confidence interval"

"[APPLET] For Exercises 1–8, use the data in the table, which shows the average annual salaries (both in thousands of dollars) for secondary and elementary school teachers, excluding special and vocational education teachers, in the United States for 11 years. (Source: U.S. Bureau of Labor Statistics)

8. Construct a 95% prediction interval for the average annual salary of elementary school teachers when the average annual salary of secondary school teachers is \$63,500. Interpret the results."

Tar and Nicotine Use the results of Problem 16 in Section 12.3 to answer the following questions:

b. Construct a 95% confidence interval for the tar content found in part (a).

Using the sample data from Problem 6 in Section 12.3,

d. Construct a 95% prediction interval for the value of y if x=8.

A linear regression model predicts weekly revenue from ad spending. You find the prediction interval for exactly \$200 in ad spending is (\$520, \$610). Choose the answer that best describes what this interval means.

"Using the sample data from Problem 8 in Section 12.3,

a. Predict the mean value of y if x=1.8."

"Concrete Use the results of Problem 15 from Section 12.3 to answer the following questions:

a. Predict the mean 28-day strength of concrete whose 7-day strength is 2550 psi."

Variation and Prediction Intervals

In Exercises 17–20, find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. In each case, there is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions.

Weighing Seals with a Camera The table below lists overhead widths (cm) of seals measured from photographs and the weights (kg) of the seals (based on “Mass Estimation of Weddell Seals Using Techniques of Photogrammetry,” by R. Garrott of Montana State University). For the prediction interval, use a 99% confidence level with an overhead width of 9.0 cm.

Hurricanes Use the results of Problem 14 in Section 12.3 to answer the following questions:

d. Construct a 95% prediction interval for the wind speed found in part (c).

[DATA] Seat Choice and GPA A biology professor wants to investigate the relation between the seat location chosen by a student on the first day of class and their cumulative grade point average (GPA). He randomly selected an introductory biology class and obtained the following information for the 38 students in the class.

i. Construct a 95% prediction interval for the GPA found in part (h).

"In Exercises 19-24, construct the indicated prediction interval and interpret the results.

22. Construct a 95% prediction interval for the fuel efficiency of an automobile in Exercise 12 that has an engine displacement of 265 cubic inches."