Exercises -
8.1- For each of the following pairs, explain why you believe that they are positively related, negatively related, or essentially unrelated. If they are related, identify the dependent variable.
a. The cost of constructing a house and its market price.
b. The winter price of corn and the number of acres of corn planted by Iowa farmers the following spring.
c. The price of steak and the amount purchased by a college dining hall.
d. The price of gasoline and sales of large cars.
e. The number of wins by the New York Yankees and the price of tea in China.
8.2- Figure 8.13 is a scatter diagram of the annual rates of return on Apple and Microsoft stock during the years 1998-2008:
a. What was the highest annual return for Apple?
b. What was the lowest annual return for Microsoft?
c. Was the average annual return higher for Apple or for Microsoft?
d. Was there a greater dispersion in Apple or Microsoft returns?
e. Were Apple and Microsoft stock returns positively related, negatively related, or unrelated?
8.3- Use the data in Table 1.2 to calculate least squares estimates of the relationship between income and spending. What is the estimated slope?
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Table 1.2 Family Income and Spending, 1935-1936 [12]
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Income Range ($)
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Average Income ($)
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Average Spending ($)
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< 500
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292
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493
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500-999
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730
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802
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1000-1499
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1176
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1196
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1500-1999
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1636
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1598
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2000-2999
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2292
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2124
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3000-3999
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3243
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2814
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4000-4999
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4207
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3467
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5000-10,000
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6598
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4950
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8.4- Use the data in Table 1.6 to estimate a simple linear regression model where the dependent variable is 2003 prices and the explanatory variable is the hard drive size.
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Table 1.6 Prices of Hard Drives of Various Sizes [16]
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Size (Gigabytes)
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2003
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2004
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2005
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2006
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2007
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80
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$155
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$115
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$85
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$80
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$70
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120
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$245
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$150
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$115
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$115
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$80
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160
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$500
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$200
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$145
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$120
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$85
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200
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$749
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$260
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$159
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$140
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$100
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8.5- Use the data in Table 1.6 to estimate a simple linear regression model where the dependent variable is 2007 prices and the explanatory variable is the hard drive size.
8.6- Use the data in Table 1.6 to estimate a simple linear regression model where:
a. The dependent variable is the price of an 80-GB hard drive and the explanatory variable is the year.
b. The dependent variable is the natural logarithm of the price of an 80-GB hard drive and the explanatory variable is the year.
Which of these equations seems to describe the data better? Explain your reasoning.
8.9- A least squares regression was used to estimate the relationship between the dollar price P of 45 used 2001 Audi A4 2.8L sedans with manual transmission and the number of miles M the car had been driven:
P^ = 19,958 - 0.0677M, R2 = 0.70
(2,553) (0.0233)
The standard errors are in parentheses.
a. Does the value 16,958 seem reasonable?
b. Does the value -0.0677 seem reasonable?
c. Does the value 0.70 seem reasonable?
d. Is the estimated relationship between M and P statistically significant at the 5 percent level?
e. Should the variables be reversed, with M on the left-hand side and P on the right-hand side? Why or why not?
Textbook - Essential Statistics Regression, and Econometrics Second Edition by Gray Smith.