Question

Mini-Case Study 3: Debt Spending

A study found that American consumers are making average monthly debt payments of $983 (Experian.com- November 11th, 2010). However, the study of 26 metropolitan areas reveals quite a bit of variation in debt payments, depending on where consumers live. For example, the Washington, DC, residents pay the most ($1,285 per month), while Pittsburghers pay the least ($763 per month). Madelyn Davis, an economist at a large bank, believes that income differences between cities are the primary reason for the disparate debt payments. For example, the Washington, DC, area’s high incomes have likely contributed to its placement at the top of the list. Madelyn also wonders about the likely effect of unemployment on consumer debt payments. She wonders areas with higher unemployment rates will leave consumers struggling to pay their bills and thus lower debt payments. On the other hand, higher unemployment rates may reduce consumer debt payments, as consumers forgo making major purchases such as homes and cars. In order to analyze the relationship between income, the unemployment rate, and consumer debt payments, Madelyn gathers data from the same 26 metropolitan areas used in the debt payment study. Specifically, she collects each area’s 2010-2011 median household income as well as the monthly unemployment rate and average consumer debt for August 2010.

Metropolitan area	Debt	Inc	Unemp
Washington, D.C.	1,285	103.5	6.3
Seattle	1,135	81.7	8.5
Baltimore	1,133	82.2	8.1
Boston	1,133	89.5	7.6
Denver	1,104	75.9	8.1
San Francisco	1,098	93.4	9.3
San Diego	1,076	75.5	10.6
Sacramento	1,045	73.1	12.4
Los Angeles	1,024	68.2	12.9
Chicago	1,017	75.1	9.7
Philadelphia	1,011	78.3	9.2
Minneapolis	1,011	84	7
New York	989	78.3	9.3
Atlanta	986	71.8	10.3
Dallas	970	68.3	8.4
Phoenix	957	66.6	9.1
Portland	948	71.2	10.2
Cincinnati	920	69.5	9.3
Houston	889	65.1	8.7
Columbus	888	68.6	8.3
St. Louis	886	68.3	9.9
Miami	867	60.2	14.5
Detroit	832	69.8	15.7
Cleveland	812	64.8	9.6
Tampa	791	59.4	12.6
Pittsburgh	763	63	8.3

Madelyn asks for your group’s help to:

1. Use the ‘Data Analysis Toolpack’ to fit a regression. Be sure to include all steps including interpreting the model. Be thorough in describing your process. (20 points)

2. Use your final equation to predict the average debt payment of a metropolitan area whose median income is $41,203 and whose unemployment rate is 8.04%. (3 points)

3. Does the intercept have meaning? (3 points)

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.867561816
R Square	0.752663505
Adjusted R Square	0.731155983
Standard Error	64.60976155
Observations	26
ANOVA
	df	SS	MS	F	Significance F
Regression	2	292170.7719	146085.386	34.99536244	1.05394E-07
Residual	23	96011.68963	4174.421288
Total	25	388182.4615
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	198.9955611	156.3619079	1.272660099	0.215853972	-124.4636895
Inc	10.51215911	1.47652528	7.119525312	2.98439E-07	7.457733849
Unemp	0.618572208	6.867902274	0.090067124	0.929013632	-13.5887661

data-> data analysis -> regression

debt^ =198.9956 + 10.5122 * Income +0.6186 * Unemployment

this model is significant as p-value < 0.01

R^2 = 0.7527 which is good too.

when median income increases by 1 unit, on average debt increases by 10.5122

when unemployment increases by 1 % , on average debt increases by 0.6186