Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and behaviors for a variety of firms. In one study, a client asked for an investigation of consumer characteristics that can be used to predict the amount charged by credit card users. Data were collected on annual income, household size, and annual credit card charges for a sample of 50 consumers. Prepare a managerial report that summarizes findings of an investigation of consumer characteristics that can be used to predict the amount charged by credit card users including annual income, household size, and annual credit card. Consider the complete data set. Income ($1,000s) Household Size Amount Charged ($) 54 3 4,006 30 2 3,169 32 4 5,090 50 5 4,732 31 2 1,854 55 2 4,080 37 1 2,721 40 2 3,358 66 4 4,754 51 3 4,120 25 3 4,198 48 4 4,209 27 1 2,487 33 2 2,524 65 3 4,224 63 4 4,975 42 6 4,422 21 2 2,438 44 1 2,985 37 5 4,161 62 6 5,688 21 3 3,613 55 7 5,291 42 2 3,010 41 7 4,838 54 6 5,563 30 1 2,573 48 2 3,856 34 5 3,596 67 4 5,027 50 2 3,595 67 5 5,335 55 6 5,360 52 2 3,880 62 3 4,715 64 2 4,147 22 3 3,569 29 4 3,900 39 2 2,962 35 1 3,131 39 4 4,193 54 3 3,740 23 6 4,137 27 2 2,911 26 7 4,593 61 2 4,263 30 2 3,077 22 4 3,084 46 5 4,830 66 4 5,159 Compute the mean and standard deviation for the income ($1000s), household size, and amount charged ($). (Round your answers to two decimal places.) Mean Standard Deviation Income ($1000s) Household Size Amount Charged ($) Develop an estimated regression equation using annual income ($1000s) as the independent variable and annual credit card charges as the dependent variable. (Round your numerical values to the nearest integer.) ŷ = Compute R2. (Round your answer to three decimal places.) R2 = Develop an estimated regression equation using household size as the independent variable and annual credit card charges as the dependent variable. (Round your numerical values to the nearest integer.) ŷ = Compute R2. (Round your answer to three decimal places.) R2 = Develop an estimated regression equation with annual income and household size as the independent variables. (Let x1 represent the annual income ($1,000s), x2 represent the household size, and y represent the annual credit card charges. Round your numerical values to the nearest integer.) ŷ = Compute Ra2. (Round your answer to three decimal places.) Ra2 =

Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and behaviors for a variety of firms. In one study, a client asked for an investigation of consumer characteristics that can be used to predict the amount charged by credit card users. Data were collected on annual income, household size, and annual credit card charges for a sample of 50 consumers. Prepare a managerial report that summarizes findings of an investigation of consumer characteristics that can be used to predict the amount charged by credit card users including annual income, household size, and annual credit card. Consider the complete data set. Income ($1,000s) Household Size Amount Charged ($) 54 3 4,006 30 2 3,169 32 4 5,090 50 5 4,732 31 2 1,854 55 2 4,080 37 1 2,721 40 2 3,358 66 4 4,754 51 3 4,120 25 3 4,198 48 4 4,209 27 1 2,487 33 2 2,524 65 3 4,224 63 4 4,975 42 6 4,422 21 2 2,438 44 1 2,985 37 5 4,161 62 6 5,688 21 3 3,613 55 7 5,291 42 2 3,010 41 7 4,838 54 6 5,563 30 1 2,573 48 2 3,856 34 5 3,596 67 4 5,027 50 2 3,595 67 5 5,335 55 6 5,360 52 2 3,880 62 3 4,715 64 2 4,147 22 3 3,569 29 4 3,900 39 2 2,962 35 1 3,131 39 4 4,193 54 3 3,740 23 6 4,137 27 2 2,911 26 7 4,593 61 2 4,263 30 2 3,077 22 4 3,084 46 5 4,830 66 4 5,159 Compute the mean and standard deviation for the income ($1000s), household size, and amount charged ($). (Round your answers to two decimal places.) Mean Standard Deviation Income ($1000s) Household Size Amount Charged ($) Develop an estimated regression equation using annual income ($1000s) as the independent variable and annual credit card charges as the dependent variable. (Round your numerical values to the nearest integer.) ŷ = Compute R2. (Round your answer to three decimal places.) R2 = Develop an estimated regression equation using household size as the independent variable and annual credit card charges as the dependent variable. (Round your numerical values to the nearest integer.) ŷ = Compute R2. (Round your answer to three decimal places.) R2 = Develop an estimated regression equation with annual income and household size as the independent variables. (Let x1 represent the annual income ($1,000s), x2 represent the household size, and y represent the annual credit card charges. Round your numerical values to the nearest integer.) ŷ = Compute Ra2. (Round your answer to three decimal places.) Ra2 =

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 8SGR

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Question

15)

Prepare a managerial report that summarizes findings of an investigation of consumer characteristics that can be used to predict the amount charged by credit card users including annual income, household size, and annual credit card.

Consider the complete data set.

Income ($1,000s)	Household Size	Amount Charged ($)
54	3	4,006
30	2	3,169
32	4	5,090
50	5	4,732
31	2	1,854
55	2	4,080
37	1	2,721
40	2	3,358
66	4	4,754
51	3	4,120
25	3	4,198
48	4	4,209
27	1	2,487
33	2	2,524
65	3	4,224
63	4	4,975
42	6	4,422
21	2	2,438
44	1	2,985
37	5	4,161
62	6	5,688
21	3	3,613
55	7	5,291
42	2	3,010
41	7	4,838
54	6	5,563
30	1	2,573
48	2	3,856
34	5	3,596
67	4	5,027
50	2	3,595
67	5	5,335
55	6	5,360
52	2	3,880
62	3	4,715
64	2	4,147
22	3	3,569
29	4	3,900
39	2	2,962
35	1	3,131
39	4	4,193
54	3	3,740
23	6	4,137
27	2	2,911
26	7	4,593
61	2	4,263
30	2	3,077
22	4	3,084
46	5	4,830
66	4	5,159

Compute the mean and standard deviation for the income ($1000s), household size, and amount charged ($). (Round your answers to two decimal places.)

	Mean	Standard Deviation
Income ($1000s)
Household Size
Amount Charged ($)

Develop an estimated regression equation using annual income ($1000s) as the independent variable and annual credit card charges as the dependent variable. (Round your numerical values to the nearest integer.)

ŷ =

Compute R². (Round your answer to three decimal places.)

R² =

Develop an estimated regression equation using household size as the independent variable and annual credit card charges as the dependent variable. (Round your numerical values to the nearest integer.)

ŷ =

Compute R². (Round your answer to three decimal places.)

R² =

Develop an estimated regression equation with annual income and household size as the independent variables. (Let x₁ represent the annual income ($1,000s), x₂ represent the household size, and y represent the annual credit card charges. Round your numerical values to the nearest integer.)

ŷ =

Compute

R_a².

(Round your answer to three decimal places.)

R_a² =

Plot the standardized residuals against the predicted annual credit charges. Discuss your findings from this analysis. (Consider a proportion large if it is at least 0.55.)

Since

R_a²

is , the estimated regression equation a good fit. The plot of the standardized residuals shows residuals outside the range of −2 and +2. Thus, we reason to conclude that the error term is normally distributed.

Use the estimated regression equation to predict the annual credit card charges (in $) for a three-person household with an annual income of $40,000. (Round your answer to the nearest dollar.)

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