nthly expenditure (AME, measured in euros) on average monthly income (AMI, measured in euros) using a random sample of college-educated full-time workers earnings €100 to €1.5 million yields the following: AME = 710.7 + 8.8 × AMI, R2 = 0.030, SER = 540.30 a. Explain what the coefficient values 710.7 and 8.8 mean. b. The standard error of the regression (SER) is 540.
1.
A regression of average monthly expenditure (AME, measured in euros) on average monthly income (AMI, measured in euros) using a random sample of college-educated full-time workers earnings €100 to €1.5 million yields the following:
AME = 710.7 + 8.8 × AMI, R2 = 0.030, SER = 540.30
a. Explain what the coefficient values 710.7 and 8.8 mean.
b. The standard error of the regression (SER) is 540.30. What are the units of measurement for the SER (Euros? Or is it unit-free?)
c.The regression R^2 is 0.030. What are the units of measurement for the R2 (Euros? Or is R^2 unit-free?)
d. What does the regression predict will be the expenditure of a person with an income of €100? With an income of €200?
e. Will the regression give reliable predictions for a person with an income of €2 million? Why or why not? (
f. Given what you know about the distribution of earnings, do you think it is plausible that the distribution of errors in the regression is normal? (Hint: Do you think that the distribution is symmetric or skewed? What is the smallest value of earnings, and is it consistent with a normal distribution?).
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