#1. Write the meaning of each of the following terms without referring to the book (or your notes), and compare your definition with the version in the text for each:

1. degrees of freedom (p. 53)
2. Estimate (p. 37)
3. Estimator (p. 37)
4. multivariate regression coefficient (p. 41)
5. Ordinary Least Squares (OLS) (p. 36)
6. \({{R}^{2}}\) (p. 50)
7. \({{\bar{R}}^{2}}\) (p. 54)
8. total, explained, and residual sums of squares (pp. 47, 48)

#3. Consider the following two least-squares estimates of the relationship between interest rates and the federal budget deficit in the United States:

Model A: \({{\hat{Y}}_{1}}=0.103-0.079{{X}_{1}},\,\,\,\,\,\,{{R}^{2}}=0.00\)

where:

\({{Y}_{1}}=\) the interest rate on Aaa corporate bonds

\({{X}_{1}}\) = the federal budget deficit as a percentage of GNP

(quarterly model: N = 56)

Model T: \({{\hat{Y}}_{2}}=0.089+0.369{{X}_{2}}+0.88{{X}_{3}},\,\,\,\,\,\,{{R}^{2}}=0.40\)

where: \({{Y}_{2}}\) = the interest rate on 3-month Treasury bills

\({{X}_{2}}\) = the federal budget deficit in billions of dollars

\({{X}_{3}}\) = the rate of inflation (in percent)

(quarterly model: N = 38)

1. What does "least-squares estimates" mean? What is being estimated? What is being squared? In what sense are the squares "least"?
2. What does it mean to have an R ² of .00? Is it possible for an R ² to be negative?

C. Based on economic theory, what signs would you have expected for the estimated slope coefficients of the two models?

d. Compare the two equations. Which model has estimated signs that correspond to your prior expectations? Is Model T automatically better because it has a higher R2? If not, which model do you prefer and why?

#5: Suppose that you have been asked to estimate a regression model to explain the number of people jogging a mile or more on the school track to help decide whether to build a second track to handle all the joggers. You collect data by living in a press box for the spring semester, and you run two possible explanatory equations:

A: \(\hat{Y}=125.0-15.0{{X}_{1}}-1.0{{X}_{2}}+1.5{{X}_{3}}\,\,\,\,\,\,\,\,\,\,\,{{\bar{R}}^{2}}=0.75\)

B: \(\hat{Y}=123.0-14.0{{X}_{1}}+5.5{{X}_{2}}-3.7{{X}_{4}}\,\,\,\,\,\,\,\,\,\,\,{{\bar{R}}^{2}}=0.73\)

where: Y = the number of joggers on a given day

\({{X}_{1}}\) = inches of rain that day

\({{X}_{2}}\) = hours of sunshine that day

\({{X}_{3}}\) = the high temperature for that day (in degrees F)

\({{X}_{4}}\) = the number of classes with term papers due the next day

1. Which of the two (admittedly hypothetical) equations do you prefer? Why?
2. How is it possible to get different estimated signs for the coefficient of the same variable using the same data?

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Solution: The downloadable solution consists of 3 pages, 1039 words.
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