Consumer Research, Inc. is an independent agency that conducts research on consu

Question

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 customers.

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 independent variable, and then using the 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?

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

Explanation / Answer

1) Use the "Descriptive statistics option of Excel "Data Analysis" add-on to get the following result -

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2)

Again use Regression option of Data analysis add-on.

a) Amount Charged vs Annual Income -

b) Amount Charged vs household size -

So, we can see that the R-square value of second model is higher than the first one. So, the variable 'Household Size' is a better predictor of the annual credit card charges. R-square value is the amount of variation in dependent variable explained by the independent variable. So, "household Size" explains more variation. Hence a good predictor.

Incom0e ($1000s) Household Size Amount Charged ($) Mean 43.48 Mean 3.42 Mean 3964.06 Standard Error 2.057785614 Standard Error 0.245930138 Standard Error 132.0159991 Median 42 Median 3 Median 4090 Mode 54 Mode 2 Mode 3890 Standard Deviation 14.55074162 Standard Deviation 1.738988681 Standard Deviation 933.4940816 Sample Variance 211.7240816 Sample Variance 3.024081633 Sample Variance 871411.2004 Kurtosis -1.247719422 Kurtosis -0.722808552 Kurtosis -0.741830067 Skewness 0.095855639 Skewness 0.527895977 Skewness -0.129506489 Range 46 Range 6 Range 3814 Minimum 21 Minimum 1 Minimum 1864 Maximum 67 Maximum 7 Maximum 5678 Sum 2174 Sum 171 Sum 198203 Count 50 Count 50 Count 50 Largest(1) 67 Largest(1) 7 Largest(1) 5678 Smallest(1) 21 Smallest(1) 1 Smallest(1) 1864 Confidence Level(95.0%) 4.135275013 Confidence Level(95.0%) 0.494215115 Confidence Level(95.0%) 265.2960826

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