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. The following data are contained in the file Consumer.A. Develop scatter plots of amount charged versus annual income, and amount charged versus household size. Comment on the relationship between amount charged and these two variables. B. Develop an estimated regression equation that can be used to predict the amount charged given the two independent variables (annual income, and household size). C. Interpret the coefficients on the annual income, and household size variables. D. Do a residual plot of standard residuals on the predicted values. Are all four regression assumptions satisfied? Income($1000s)HouseholdSizeAmountCharged ($)5434,0163023,1593245,1005054,7423121,8645524,0703712,7314023,3486644,7645134,1102534,2084844,2192712,4773322,5146534,2146344,9654264,4122122,4484412,9953754,1716265,6782133,6235575,3014223,0204174,8285465,5733012,5834823,8663453,5866745,0375023,6056755,3455565,3705223,8906234,7056424,1572233,5792943,8903922,9723513,1213944,1835433,7302364,1272722,9212674,6036124,2733023,0672243,0744654,8206645,149

Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a time so we are answering the first three as you have not mentioned which of these you are looking for. Please re-submit the question separately for the remaining sub-parts. Given data: Income($1000s) HouseholdSize AmountCharged ($) 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 A. The scatterplot is a graph that is constructed to depict the linear relationship between two quantitative variables. To develop the scatter plots of the amount charged versus annual income we will use Excel. Enter the data into Excel, select data, and click on Insert. Now choose scatterplot. The scatterplot will be depicted as follows: The scatterplot depicts that the relationship between the amount of the variable charged and the annual income is positive. If the income increases, the amount charged will also increase. The relationship between the variables can be considered positive and strong. To develop the scatter plots of the amount charged versus household size, enter the data into Excel, Now, select data, and click on Insert. Now choose scatterplot. The scatterplot will be depicted as follows: The scatterplot depicts that the relationship between the amount of the variable charged and the household size is positive. If the household size increases, the amount charged will also increase. The relationship between the variables can be considered positive and strong.B. In order to develop an estimated regression equation that can be used to predict the amount charged given the two independent variables (annual income, and household size), use Excel. Enter the data into Excel. Select Data> Data analysis> Regression. Click Ok. Now, choose the dependent variable Amount charges for the Y variable and the other two variables together for the X variable along with the labels. Tick mark on Labels as we have included the labels too. Click Okay. The regression output is depicted as follows: The general form of the regression equation for two independent variables is: Y⏞=a+b1X1+b2X2 Here, a = intercept b = Slope coefficient of each of the independent variables Now, the estimated regression equation that can be used to predict the amount charged given the two independent variables (annual income, and household size) can be written as: Y^=1304.9+33.13X1+356.3X2 Here, X1=IncomeX2=Household size C. The coefficient of annual income is 33.13 which is positive and indicates that by increasing each additional income (in $1000), the amount charged will be 33.13 higher. The coefficient of household size is 356.3 which is positive and indicates that by increasing each household size, the amount charged will be 356.3 higher.

Answered: Consumer Research, Inc., is an…

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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. The following data are contained in the file Consumer.

A. Develop scatter plots of amount charged versus annual income, and amount charged versus household size. Comment on the relationship between amount charged and these two variables.


B. Develop an estimated regression equation that can be used to predict the amount charged given the two independent variables (annual income, and household size).


C. Interpret the coefficients on the annual income, and household size variables.


D. Do a residual plot of standard residuals on the predicted values. Are all four regression assumptions satisfied?

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