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.

Required:

1. Use methods of descriptive statistics to summarize the data. Comment on the findings.
2. 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.
3. Develop an estimated regression equation with annual income and household size as the independent variables. Discuss your findings.
4. What is the predicted annual credit card charge for a three-person household with an annual income of $40,000?
5. Discuss the need for other independent variables that could be added to the model. What additional variables might be helpful?

Answer 1

Required:

1. . 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.

2. 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.

4. The predicted annual credit card charge will be

1305.0.34+ 356.34*3 + 40*33.121 = 3698.894

5. 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.