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Ch. 9 - Correlation and Regression
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 9 - Correlation and RegressionProblem 9.R.28
Chapter 9, Problem 9.R.28

"In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.
28. Use the regression equation found in Exercise 25.
a. x_1 = 9.0, x_2 = 0.70
b. x_1 = 3.0, x_2 = 0.25
c. x_1 = 8.0, x_2 = 0.60
d. x_1 = 5.2, x_2 = 0.46"

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1
Recall the multiple regression equation from Exercise 25, which has the general form: y = b0 + b1 x1 + b2 x2, where b0 is the intercept, and b1 and b2 are the coefficients for the independent variables x1 and x2 respectively.
For each set of values of x1 and x2 given (a through d), substitute these values into the regression equation in place of x1 and x2.
Perform the multiplication of each coefficient by its corresponding x value: calculate b1 × x1 and b2 × x2 for each case.
Add the intercept b0 to the sum of the products from the previous step to find the predicted value of y for each set of independent variables.
Repeat this process for all four sets of values to obtain the predicted y-values corresponding to each pair of x1 and x2.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Multiple Regression Equation

A multiple regression equation models the relationship between one dependent variable and two or more independent variables. It takes the form y = b0 + b1*x1 + b2*x2 + ... + bn*xn, where b0 is the intercept and b1, b2, ..., bn are coefficients representing the effect of each independent variable on y.
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Prediction Using Regression

Prediction involves substituting given values of independent variables into the regression equation to calculate the estimated value of the dependent variable. This process helps in forecasting outcomes based on the model derived from observed data.
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Interpretation of Coefficients

Each coefficient in a multiple regression represents the expected change in the dependent variable for a one-unit increase in the corresponding independent variable, holding other variables constant. Understanding these helps in assessing the influence of each predictor on the outcome.
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Related Practice
Textbook Question

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?

13. r =- 0.450"

Textbook Question

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?

15. r = 0.642"

Textbook Question

"In Exercises 17 and 18, use the data to (a) find the coefficient of determination r^2 and interpret

the result, and (b) find the standard error of estimate s_e and interpret the result.

17. The table shows the times (in seconds) to accelerate from 0 to 60 miles per hour and the top speeds (in miles per hour) for eight electric cars. The regression equation is y =- 14.399x + 196.996. (Source: Car and Driver)

Textbook Question

"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."

Textbook Question

"In Exercises 13-16, use the value of the correlation coefficient r to calculate the coefficient of determination r^2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation?

14.r =- 0.937"

Textbook Question

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

21. Construct a 95% prediction interval for the number of hours of sleep for an adult in Exercise 11 who is 45 years old."