Use technology to find (a) the multiple regression equation for the data shown in the accompanying table, (b) the standard error estimate and interpret the result, and (c) the coefficient of determination and interpret the result. The accompanying table shows the total square footages (in billions) of retailing space at shopping centers, the numbers (in thousands) of shopping centers, and the sales (in billions of dollars) for shopping centers for eight years. Click the icon to view the data table on shopping center sales. (a) What is the regression equation? ŷ = 1 + ( )×₁ + (1)×2 (Round to two decimal places as needed.) (b) The standard error is ☐ (Round to two decimal places as needed.) Interpret the standard error. Choose the correct answer below. Shopping center sales Sales, y Total square footage, X₁ Shopping centers, X2 123.4 211.5 385.6 475.5 641.3 716.5 768.2 806.8 851.7 893.9 933.7 1.3 2.8 3.3 3.7 4.1 4.6 4.7 4.8 4.9 5.0 5.1 13.6 17.3 22.2 25.5 32.8 38.0 39.1 39.2 40.5 41.2 42.1 Print Done A. The standard error is the expected error of the predicted sales given a specific total square footage and number of shopping centers. B. The standard error is the average predicted sales for the multiple regression model. C. The standard error is the percent of variation explained by the multiple regression model. D. The standard error is the sum of unexplained error in the multiple regression model. (c) The coefficient of determination is ☐ . (Round to three decimal places as needed.) Interpret the coefficient of determination. Choose the correct answer below. ○ A. The coefficient of determination measures the average predicted sales for the multiple regression model. B. The coefficient of determination measures the expected error of the predicted sales given a specific total square footage and number of shopping centers. C. The coefficient of determination measures the percent of variation not explained by the multiple regression model. ○ D. The coefficient of determination measures the percent of variation explained by the multiple regression model.
Use technology to find (a) the multiple regression equation for the data shown in the accompanying table, (b) the standard error estimate and interpret the result, and (c) the coefficient of determination and interpret the result. The accompanying table shows the total square footages (in billions) of retailing space at shopping centers, the numbers (in thousands) of shopping centers, and the sales (in billions of dollars) for shopping centers for eight years. Click the icon to view the data table on shopping center sales. (a) What is the regression equation? ŷ = 1 + ( )×₁ + (1)×2 (Round to two decimal places as needed.) (b) The standard error is ☐ (Round to two decimal places as needed.) Interpret the standard error. Choose the correct answer below. Shopping center sales Sales, y Total square footage, X₁ Shopping centers, X2 123.4 211.5 385.6 475.5 641.3 716.5 768.2 806.8 851.7 893.9 933.7 1.3 2.8 3.3 3.7 4.1 4.6 4.7 4.8 4.9 5.0 5.1 13.6 17.3 22.2 25.5 32.8 38.0 39.1 39.2 40.5 41.2 42.1 Print Done A. The standard error is the expected error of the predicted sales given a specific total square footage and number of shopping centers. B. The standard error is the average predicted sales for the multiple regression model. C. The standard error is the percent of variation explained by the multiple regression model. D. The standard error is the sum of unexplained error in the multiple regression model. (c) The coefficient of determination is ☐ . (Round to three decimal places as needed.) Interpret the coefficient of determination. Choose the correct answer below. ○ A. The coefficient of determination measures the average predicted sales for the multiple regression model. B. The coefficient of determination measures the expected error of the predicted sales given a specific total square footage and number of shopping centers. C. The coefficient of determination measures the percent of variation not explained by the multiple regression model. ○ D. The coefficient of determination measures the percent of variation explained by the multiple regression model.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 4SGR
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Question
Transcribed Image Text:Use technology to find (a) the multiple regression equation for the data shown in the accompanying table, (b) the standard error estimate and interpret the result, and (c) the coefficient of
determination and interpret the result.
The accompanying table shows the total square footages (in billions) of retailing space at shopping centers, the numbers (in thousands) of shopping centers, and the sales (in billions of dollars) for
shopping centers for eight years.
Click the icon to view the data table on shopping center sales.
(a) What is the regression equation?
ŷ = 1 + ( )×₁ + (1)×2
(Round to two decimal places as needed.)
(b) The standard error is ☐
(Round to two decimal places as needed.)
Interpret the standard error. Choose the correct answer below.
Shopping center sales
Sales, y
Total square footage, X₁
Shopping centers, X2
123.4 211.5 385.6 475.5 641.3 716.5 768.2 806.8 851.7 893.9 933.7
1.3 2.8 3.3 3.7 4.1 4.6 4.7 4.8 4.9 5.0 5.1
13.6 17.3 22.2 25.5 32.8 38.0 39.1 39.2 40.5 41.2 42.1
Print
Done
A. The standard error is the expected error of the predicted sales given a specific total square footage and number of shopping centers.
B. The standard error is the average predicted sales for the multiple regression model.
C. The standard error is the percent of variation explained by the multiple regression model.
D. The standard error is the sum of unexplained error in the multiple regression model.
(c) The coefficient of determination is ☐ .
(Round to three decimal places as needed.)
Interpret the coefficient of determination. Choose the correct answer below.
○ A. The coefficient of determination measures the average predicted sales for the multiple regression model.
B. The coefficient of determination measures the expected error of the predicted sales given a specific total square footage and number of shopping centers.
C. The coefficient of determination measures the percent of variation not explained by the multiple regression model.
○ D. The coefficient of determination measures the percent of variation explained by the multiple regression model.
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