Repeat problem 1 for the regression of problem 3.
Problem 1
Produce residual plots for the regression of problem 2. Is there any apparent model inadequacy?
Problem 2
An article in the Journal of Monetary Economics assesses the relationship between percentage growth in wealth over a decade and a half of savings for baby boomers of age 40 to 55 with these people's income quartiles. The article presents a table showing five income quartiles, and for each quartile there is a reported percentage growth in wealth. The data are as follows.
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Income quartile:
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1
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2
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3
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4
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5
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Wealth growth (%):
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17.3
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23.6
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40.2
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45.8
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56.8
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Run a simple linear regression of these five pairs of numbers and estimate a linear relationship between income and percentage growth in wealth.
Problem 3
Recently, research efforts have focused on the problem of predicting a manufacturer's market share by using information on the quality of its product. Suppose that the following data are available on market share, in percentage (Y ), and product quality, on a scale of 0 to 100, determined by an objective evaluation procedure (X ):
X: 27 39 73 66 33 43 47 55 60 68 70 75 82
Y: 2 3 10 9 4 6 5 8 7 9 10 13 12
Estimate the simple linear regression relationship between market share and product quality rating.