Question

Data from the U.S. Federal Reserve board ( Household Debt Service burder,2002) on consumer debt ( as a percentage of personal income) and mortgage debt ( also a percentage of personal income) for selected years are shown in the following tableConsumer Debt 7.8 5.3 6.2 Household Debt 8.4 5.0 7.3 9.4 4.8 3.6What is the value of correlation coefficient (r) for this data set? Based on the value of r, what can you say about their linear relationship?

If Consumer debt is independent (predictor) variable and household debt is dependent (response) variable. Find the linear regression equation and predict the value of y for x=9?

Find the value of coefficient of determination (r2 ) and interpret based on percentage of variation explained.

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Answer #1

a & c.

Correlation Y) XAz 60.84 28.09 38.44 64 12.96 0 204.33 X-Y 65.52 26.5 45.26 75.2 17.28 Count- 7.8 5.3 6.2 70.56 25 53.29 88.3

b.

Line ofRegressionYonXie Y = bo + bl X (Xi Mean) 2 (Yi Mean)2 (Xi-Mean) (Yi-Mean) 7.8 5.3 6.2 2.624 0.774 0 3.312 6.656 8.4 7.

value of y for x=9 => Y'=0.4764+1.0524*(9) = 9.948

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