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

Larson 8th Edition

Ch. 9 - Correlation and Regression

Problem 9.T.1

Chapter 9, Problem 9.T.1

"1. Net Sales The equation used to predict the net sales (in millions of dollars) for a fiscal
year for a clothing retailer is y=23,769 + 9.18x_1 - 8.41x_2
where x_1 is the number of stores open at the end of the fiscal year and x_2 is the average
square footage per store. Use the multiple regression equation to predict the y-values for
the values of the independent variables.
a. x_1 = 1057, x_2 = 3698
b. x_1 = 1012, x_2 = 3659
c. x_1 = 952, x_2 = 3601
d. x_1 = 914, x_2 = 3594"

Verified step by step guidance

Identify the multiple regression equation given:

y = 23769 + 9.18 x_1 - 8.41 x_2

, where

x_1

is the number of stores and

x_2

is the average square footage per store.

For each set of values of

x_1

and

x_2

, substitute these values into the regression equation. For example, for part (a), substitute

x_1 = 1057

and

x_2 = 3698

Perform the multiplication for each term involving the independent variables: multiply 9.18 by

x_1

and multiply -8.41 by

x_2

Add the constant term 23769 to the results of the multiplications to calculate the predicted net sales

y

for each case.

Repeat steps 2 to 4 for each set of values given in parts (b), (c), and (d) to find all predicted net sales values.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Multiple Linear Regression

Multiple linear regression models the relationship between one dependent variable and two or more independent variables. It estimates how changes in each independent variable affect the dependent variable, holding others constant. The equation y = b0 + b1x1 + b2x2 represents this, where coefficients quantify the impact of each predictor.

Interpreting Regression Coefficients

Regression coefficients indicate the expected change in the dependent variable for a one-unit increase in an independent variable, assuming other variables remain fixed. For example, a coefficient of 9.18 for x1 means net sales increase by 9.18 million dollars per additional store, all else equal.

Prediction Using Regression Equations

Prediction involves substituting given values of independent variables into the regression equation to calculate the estimated dependent variable. This process helps forecast outcomes, such as net sales, based on specific inputs like number of stores and average store size.

Recommended video:

Guided course

04:57

Using Regression Lines to Predict Values

Related Practice

Textbook Question

Writing Use an appropriate research source to find a real-life data set with the indicated cause-and-effect relationship. Write a paragraph describing each variable and explain why you think the variables have the indicated cause-and-effect relationship.

a. Direct Cause-and-Effect: Changes in one variable cause changes in the other variable.

views

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"

140

views

Textbook Question

"[APPLET] For Exercises 2–9, use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary library science teachers in the United States for 12 years. (Source: U.S. Bureau of Labor Statistics)

7. Find the coefficient of determination r^2 and interpret the result."

views

Textbook Question

8. Find the standard error of estimate Se and interpret the result."

views

Textbook Question

"The U.S. Food and Drug Administration (FDA) requires nutrition labeling for most foods. Un FDA regulations, manufacturers are required to list the amounts of certain nutrients in their foods, such as calories, sugar, fat, and carbohydrates. This nutritional information is displayed in the ""Nutrition Facts"" panel on the food's package.

The table shows the nutritional content below for one cup of each of 21 different breakfast

cereals.

C = calories

S = sugar in grams

F = fat in grams

R = carbohydrates in grams

7. Use the equations from Exercise 6 to predict the calories in 1 cup of cereal that has 7 grams of sugar, 0.5 gram of fat, and 31 grams of carbohydrates."

views

Textbook Question

6. Use the regression equation that you found in Exercise 5 to predict the average annual salary of postsecondary library science teachers when the average annual salary of librarians is \$61,000."

views