Consumer Research, Inc. - Descriptive Statistics and Regression Analysis

This report presents the findings of a study conducted by Consumer Research, Inc. using descriptive statistics and regression analysis to analyze the relationship between annual income, household size, and annual credit card charges. The report includes a summary of the data using methods of descriptive statistics, estimated regression equations using annual income and household size as independent variables, and a combined regression equation. The report also discusses the need for other independent variables that could be added to the model.

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Consumer Research, Inc.
Student’s name: Obaid Alshaali
Student’s ID:
Institution:

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1. Use methods of descriptive statistics to summarize the data. Comment on the
findings.
Figure 1: Descriptive analysis
The income of the 50 consumers in the sample had a mean of 43.48 thousand dollars and a
standard deviation of 14.55 thousand dollars.
The average household size of the sample was 3.42 with a standard deviation of 1.74.
The amount charged on the sample had a mean of 3,946.06 dollars with a standard deviation of
933.49 dollars.

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2. Develop estimated regression equations, first using annual income as the
independent variable and then using household size as the independent variable.
Which variable is better predictor of annual credit card charges? Discuss your
findings.
Figure 2: Annual income as the independent variable

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Figure 3: Household as the independent variable
The equation for the regression equation between amounts charged and annual income as the
independent variable is:
Amount_Charge = 2,204 + 40.48Annual_income
On the other hand, the equation for the regression equation between amounts charged and the
household size as the independent variable is:
Amount_Charge = 2,581.94 + 404.13Household_Size

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The better predictor of annual credit charge between Annual Income and the Household Size is
Household Size. The rationale behind this decision is based on the adjusted R squared (Bates et
al., 2014). The regression model between household size and the annual income is 0.56.
Therefore, the variables in the model result in 56% of the variability in the regression model.
44% is explained by variables that are not in the model.
On the other hand, the model between annual income and annual credit charge has an adjusted
R-squared of 0.39. Thus, the variables in the model explain for 39% of the variability in the
model. 61% of the variability is explained by variables that are not in the model.
3. Develop an estimated regression equation with annual income and household size as
the independent variables. Discuss your findings.
Figure 4: Combined regression equation

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The combined regression equation where income and household size are the independent
variables is:
Annual_Charge = 1,304.90 + 33.13Income + 356.3Household_Size
Therefore, a unit increase in Income increases the annual charge but 33.13 units all other factors
held constant. Conversely, all other factors kept constant, a unit increase in household size
increases the annual charge by 356.3 units.
4. What is the predicted annual credit charge for three-person household with an
annual income of $40,000?

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The predicted annual credit charge for three-person household with an annual income of $40,000
is:
Annual_Charge = 1,304.90 + 33.13 * 40 + 356.3 * 3
Annual_Charge = 3,699 dollars
Thus, the predicted annual credit charge is 3,699 dollars.
5. Discuss the need for other independent variables that could be added to the model.
What additional variables might be helpful?
From the combined regression model, it is evident that the two variables account for 82% of the
variability in the model. Therefore, 18% of the variability is explained by factors which are not
in the model. Thus, there are other independent variables that should be added to the model to
account for 100% of the variability.
Other factors that affect annual credit charge include the type of credit, payment history, and
legal rate ceiling. Thus, the three can be factored into the regression model to account for a 100%
of the variability.

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Reference:
Bates, D., Maechler, M., Bolker, B., and Walker, S., 2014. lme4: Linear mixed-effects models
using Eigen and S4. R package version, 1(7), pp.1-23.