BUS204: Business Statistics

Solution to Exercise 12.1

• a. Independent: Age; Dependent: Fatalities
• d. Independent: Power Consumption; Dependent: Utility

Solution to Exercise 12.3

• b. $\hat y= 88.7206 - 0.0432x$
• c. -0.8533, Yes
  
• g. No
• h. No.
• i. 2.97, Yes
• j. slope = -0.0432. As the year increases by one, the welfare family size decreases by 0.0432 people.

Solution to Exercise 12.5

• b. Yes
• c. $\hat y= 102.4287 + 11.7585x$
• d. 0.9436; yes
• e. 478.70 feet; 1207.73 feet
  
• g. Yes
• h. Yes; (57, 1050)
• i. 172.98; No
• j. 11.7585 feet
• k. slope = 11.7585. As the number of stories increases by one, the height of the building increases by 11.7585 feet.

Solution to Exercise 12.7

• b. Yes
• c. $\hat y= -266.8863 + 0.1656x$
• d. 0.9448; Yes
• e. 62.9206; 62.4237
  
• h. No
• i. 72.639; No
• j. slope = 0.1656. As the year increases by one, the percent of workers paid hourly rates increases by 0.1565.

Solution to Exercise 12.9

• b. Yes
• c. $\hat y= 3.5984 + 0.0371x$
• d. 0.9986; Yes
• e. $5.08
• f. $6.93
  
• i. No
• j. Not valid
• k. slope = 0.0371. As the number of ounces increases by one, the cost of the liquid detergent increases by $0.0371 (or about 4 cents).

Solution to Exercise 12.11

• c.Yes
• d. $\hat y= -337,424.6478 + 0.5463x$
• e. 0.9964; Yes
• f. $208,872.49; $1,028,318.20
  
• h. Yes
• i. No
• k. slope = 0.5463. As the net taxable estate increases by one dollar, the approximate probate fees and taxes increases by 0.5463 dollars (about 55 cents).

Solution to Exercise 12.13

• c. Yes
• d. $\hat y= 65.0876 + 7.0948x$
• e. 0.9761; yes
• f. 72.2 cm; 143.13 cm
  
• h. Yes
• i. No
• j. 505.0 cm; No
• k. slope = 7.0948. As the age of an American boy increases by one year, the average height increases by 7.0948 cm

Solution to Exercise 12.15

• c. No
• d. $\hat y= 47.03 - 0.216x$
• e. -0.4280
• f. 6; 5

Solution to Exercise 12.21

• C

Solution to Exercise 12.26

• b. r = -0.8, significant
• c. yhat = 48.4-0.00725x
• d. For every one pound increase in weight, the fuel efficiency decreases by 0.00725 miles per gallon. (For every one thousand pound increase in weight, the fuel efficiency decreases by 7.25 miles per gallon).
• e. 64% of the variation in fuel efficiency is explained by the variation in weight using the regression line.
  
• g. yhat=48.4-0.00725(3000)=26.65 mpg. y-yhat=25-26.65=-1.65. Because yhat=26.5 is greater than y=25, the line overestimates the observed fuel efficiency.
  
• h. (2750,38) is the outlier. Be sure you know how to justify it using the requested graphical or numerical methods, not just by guessing.
  
• i. yhat = 42.4-0.00578x
  
• j. Without outlier, r=-0.885, rsquare=0.76; with outlier, r=-0.8, rsquare=0.64. The new linear model is a better fit, after the outlier is removed from the data, because the new correlation coefficient is farther from and the new coefficient of determination is larger.