Customer Research on Consumer Attitudes and Behaviors .
Task 1
Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and behaviours 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 recorded for Consumer information.
Income ($1000s) | Household Size | Amount Charged ($) | Income ($1000s) | Household Size | Amount Charged ($) |
54 | 3 | 4016 | 54 | 6 | 5573 |
30 | 2 | 3159 | 30 | 1 | 2583 |
32 | 4 | 5100 | 48 | 2 | 3866 |
50 | 5 | 4742 | 34 | 5 | 3586 |
31 | 2 | 1864 | 67 | 4 | 5037 |
55 | 2 | 4070 | 50 | 2 | 3605 |
37 | 1 | 2731 | 67 | 5 | 5345 |
40 | 2 | 3348 | 55 | 6 | 5370 |
66 | 4 | 4764 | 52 | 2 | 3890 |
51 | 3 | 4110 | 62 | 3 | 4705 |
25 | 3 | 4208 | 64 | 2 | 4157 |
48 | 4 | 4219 | 22 | 3 | 3579 |
27 | 1 | 2477 | 29 | 4 | 3890 |
33 | 2 | 2514 | 39 | 2 | 2972 |
65 | 3 | 4214 | 35 | 1 | 3121 |
63 | 4 | 4965 | 39 | 4 | 4183 |
42 | 6 | 4412 | 54 | 3 | 3720 |
21 | 2 | 2448 | 23 | 6 | 4127 |
44 | 1 | 2995 | 27 | 2 | 2921 |
37 | 5 | 4171 | 26 | 7 | 4603 |
62 | 6 | 5678 | 61 | 2 | 4273 |
21 | 3 | 3623 | 30 | 2 | 3067 |
55 | 7 | 5301 | 22 | 4 | 3074 |
42 | 2 | 3020 | 46 | 5 | 4820 |
41 | 7 | 4828 | 66 | 4 | 5149 |
Required:
- Use methods of descriptive statistics to summarize the data. Comment on the findings.
- Develop estimated regression equations, first using annual income as the in- dependent variable and then using household size as the independent variable. Which variable is the better predictor of annual credit card charges? Discuss your findings.
- Develop an estimated regression equation with annual income and household size as the independent variables. Discuss your findings.
- What is the predicted annual credit card charge for a three-person household with an annual income of $40,000?
- Discuss the need for other independent variables that could be added to the model. What additional variables might be helpful?
Answer 1
Income ($1000s) | Household Size | Amount Charged ($) | Income ($1000s) | Household Size | Amount Charged ($) |
54 | 3 | 4016 | 54 | 6 | 5573 |
30 | 2 | 3159 | 30 | 1 | 2583 |
32 | 4 | 5100 | 48 | 2 | 3866 |
50 | 5 | 4742 | 34 | 5 | 3586 |
31 | 2 | 1864 | 67 | 4 | 5037 |
55 | 2 | 4070 | 50 | 2 | 3605 |
37 | 1 | 2731 | 67 | 5 | 5345 |
40 | 2 | 3348 | 55 | 6 | 5370 |
66 | 4 | 4764 | 52 | 2 | 3890 |
51 | 3 | 4110 | 62 | 3 | 4705 |
25 | 3 | 4208 | 64 | 2 | 4157 |
48 | 4 | 4219 | 22 | 3 | 3579 |
27 | 1 | 2477 | 29 | 4 | 3890 |
33 | 2 | 2514 | 39 | 2 | 2972 |
65 | 3 | 4214 | 35 | 1 | 3121 |
63 | 4 | 4965 | 39 | 4 | 4183 |
42 | 6 | 4412 | 54 | 3 | 3720 |
21 | 2 | 2448 | 23 | 6 | 4127 |
44 | 1 | 2995 | 27 | 2 | 2921 |
37 | 5 | 4171 | 26 | 7 | 4603 |
62 | 6 | 5678 | 61 | 2 | 4273 |
21 | 3 | 3623 | 30 | 2 | 3067 |
55 | 7 | 5301 | 22 | 4 | 3074 |
42 | 2 | 3020 | 46 | 5 | 4820 |
41 | 7 | 4828 | 66 | 4 | 5149 |
Required:
- . summarize income1000s householdsize amountcharged
Variable | Obs Mean Std. Dev. Min Max
————-+——————————————————–
income1000s | 50 43.48 14.55074 21 67
households~e | 50 3.42 1.738989 1 7
amountchar~d | 50 3963.86 933.5463 1864 5678
the mean household size is over 3 but less than 4 , but generally in studies we consider the average household size as 4 , the income is 43500 approx for the household so average per house person income is 12700 . The amount charged mean is 3963.86 which is within reach of the annual income.
- regress income1000s amountcharged
. regress amountcharged income1000s
Source | SS df MS Number of obs = 50
————-+—————————— F( 1, 48) = 31.72
Model | 16991228.9 1 16991228.9 Prob > F = 0.0000
Residual | 25712699.1 48 535681.231 R-squared = 0.3979
————-+—————————— Adj R-squared = 0.3853
Total | 42703928 49 871508.735 Root MSE = 731.9
——————————————————————————
amountchar~d | Coef. Std. Err. t P>|t| [95% Conf. Interval]
————-+—————————————————————-
income1000s | 40.46963 7.185716 5.63 0.000 26.02178 54.91748
_cons | 2204.241 329.134 6.70 0.000 1542.472 2866.009
——————————————————————————
The equation becomes –
Amount charged = 2204+40.46 * income in 1000
When we use the household size as independent var –
. regress amountcharged householdsize
Source | SS df MS Number of obs = 50
————-+—————————— F( 1, 48) = 62.80
Model | 24204112.3 1 24204112.3 Prob > F = 0.0000
Residual | 18499815.7 48 385412.828 R-squared = 0.5668
————-+—————————— Adj R-squared = 0.5578
Total | 42703928 49 871508.735 Root MSE = 620.82
——————————————————————————-
amountcharged | Coef. Std. Err. t P>|t| [95% Conf. Interval]
————–+—————————————————————-
householdsize | 404.1567 50.99978 7.92 0.000 301.6148 506.6986
_cons | 2581.644 195.2699 13.22 0.000 2189.028 2974.261
Amount charged = 2581.644 +404.15 * household size
Now when we compare the two cases r square value is better in the second case , thus household size displays better variation in the amount charged.
. regress amountcharged householdsize income1000s
Source | SS df MS Number of obs = 50
————-+—————————— F( 2, 47) = 111.07
Model | 35246778.7 2 17623389.4 Prob > F = 0.0000
Residual | 7457149.3 47 158662.751 R-squared = 0.8254
————-+—————————— Adj R-squared = 0.8179
Total | 42703928 49 871508.735 Root MSE = 398.32
——————————————————————————-
amountcharged | Coef. Std. Err. t P>|t| [95% Conf. Interval]
————–+—————————————————————-
householdsize | 356.3402 33.2204 10.73 0.000 289.5094 423.171
income1000s | 33.12196 3.970237 8.34 0.000 25.13487 41.10904
_cons | 1305.034 197.771 6.60 0.000 907.17 1702.898
The equation will be –
Amount charged =1305.034+356.34* household size + 33.121 * income in 1000
R square value is quite high which shows that together the two independent variable shows good variation in credit card amount charged. Both the variables are significant too.
- The predicted annual credit card charge will be
1305.0.34+ 356.34*3 + 40*33.121 = 3698.894
- The other independent variables that could be used to better explain the variation in dependent variable can be per capita income of the household , income of the credit card holders instead of income from all, whether they have multiple accounts in banks etc. This will impose ore restrictions on the individuals.
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