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.

• Managerial Report

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.

• Given Data

Income ($1000s)	Household Size	Amount Charged ($)
54	3	4,016
30	2	3,159
32	4	5,100
50	5	4,742
31	2	1,864
55	2	4,070
37	1	2,731
40	2	3,348
66	4	4,764
51	3	4,110
25	3	4,208
48	4	4,219
27	1	2,477
33	2	2,514
65	3	4,214
63	4	4,965
42	6	4,412
21	2	2,448
44	1	2,995
37	5	4,171
62	6	5,678
21	3	3,623
55	7	5,301
42	2	3,020
41	7	4,828
54	6	5,573
30	1	2,583
48	2	3,866
34	5	3,586
67	4	5,037
50	2	3,605
67	5	5,345
55	6	5,370
52	2	3,890
62	3	4,705
64	2	4,157
22	3	3,579
29	4	3,890
39	2	2,972
35	1	3,121
39	4	4,183
54	3	3,730
23	6	4,127
27	2	2,921
26	7	4,603
61	2	4,273
30	2	3,067
22	4	3,074
46	5	4,820
66	4	5,149

Consider the complete data set,Consumer.

• Descriptive Statistics

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

A.

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

B. Develop a scatter diagram using income as the independent variable and amount charged as the dependent variable.

C. Comment on the relationship between income and amount charged.

There appears to be ---Select--- a positive a negative no apparent relationship between income and amount charged.

D. Develop a scatter diagram using household size as the independent variable and amount charged as the dependent variable.

E. Comment on the relationship between household size and amount charged.

There appears to be ---Select--- a positive a negative no apparent relationship between household size and amount charged.

• Linear Regression Equations

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.)

=

ComputeR². (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.)

=

ComputeR². (Round your answer to three decimal places.)

R²=

Which variable is the better predictor of annual credit card charges? Discuss your findings.

The better predictor is evidenced by the ---Select--- larger smaller value ofR². Therefore, the ---Select--- annual income household size is the better predictor of annual credit card charges.

• Multiple Regression Equation Analysis

Develop an estimated regression equation with annual income and household size as the independent variables. (Letx₁represent the annual income ($1,000s),x₂represent the household size, andyrepresent the annual credit card charges. Round your numerical values to the nearest integer.)

=

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 ---Select--- small large , the estimated regression equation ---Select--- provides does not provide a good fit. The plot of the standardized residuals shows ---Select--- 0 1 2 3 more than 3 residuals outside the range of2 and +2. Thus, we ---Select--- have have no 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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