vinben only

due 11/27

Question

1

10.6

a. y =

4

+ x

a. y = 

5

 –

2

x

b. y = –4 +

3

x

c. y = –2x

d. y = x

e. y = .50 + 1.5x

Give the slope and y-intercept for each of the lines graphed

Question 2 10.19

Rank

ing driving performance of professional golfers. Refer to The Sport Journal(Winter 2007) study of a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour, 

Exercise 2.50

 (p. 

63

). Recall that the method computes a driving performance index based on a golfer’s average driving distance (yards) and driving accuracy (percent of drives that land in the fairway). Data for the top

40

PGA golfers (as ranked by the new method) are saved in the PGADRIVER file. (The first five and last five observations are listed in the table.)

⋮

⋮

⋮

⋮

Rank	Player	Driving Distance (yards)	Driving Accuracy (%)	Driving Performance Index
1	Woods	316.1	54.6	3.58
2	Perry	304.7	63.4	3.48
3	Gutschewski	310.5	57.9	3.27
4	Wetterich	311.7	56.6	3.18
5	Hearn	2 95 .2	68.5	2. 82
				⋮
36	Senden	2 91	66	1.31
37	Mickelson	300	58.7	1.30
38	Watney	298.9	59.4	1.26
39	Trahan	295.8	61.8	1.23
40	Pappas	309.4	50.6	1.17

Source: Wiseman, F., et al. “A new method for ranking total driving performance on the PGA Tour,” The Sport Journal, Vol. 10, No. 1, Winter 2007 (Table 2).

a. Write the equation of a straight-line model relating driving accuracy (y) to driving distance (x).

b. Fit the model, part a, to the data using simple linear regression. Give the least squares prediction equation.

c. Interpret the estimated y-intercept of the line.

d. Interpret the estimated slope of the line.

e. In 

Exercise 2.126

 (p. 

95

), you were informed that a professional golfer, practicing a new swing to increase his average driving distance, is concerned that his driving accuracy will be lower. Which of the two estimates, y-intercept or slope, will help you determine if the golfer’s concern is a valid one? Explain.

Question 3 10.23

Survey of the top business schools. Each year, the Wall Street Journal and Harris Interactive track the opinions and experiences of college recruiters for large corporations and summarize the results in the Business

School

Survey. In 2005, the survey included rankings of 76 business schools. Survey data for the top 10 business schools are given in the table below. All the data are saved in theBSCHOOL file.

92

95

86

School	Enrollment (# full-time students)	Annual Tuition ($)	Mean GMAT	% with Job Offer	Avg. Salary ($)
Dartmouth	503	38,400	704	—	119,800
Michigan	1,873	33,076	690	91	105,9 86
Carnegie Mellon	661	38,800	691	93	95,531
Northwestern	2,650	38,844	700	94	117,060
Yale	468	36,800	696		86	104,018
Pennsylvania	1,840	40,458	716		92	117,471
Cal., Berkeley	1,281	21,512	701	112,699
Columbia	1,796	38,290	709	126,319
North Carolina	855	16,375	652	92,565
Southern Cal.	1,588	37,558	685	82	88,839

Source: “Wall Street Journal’s annual rankings of business schools,” The Wall Street Journal, Sep. 21, 2005. Copyright 2005 by Dow Jones & Company, Inc. in the format Textbook via Copyright Clearance Center.

a. Select one of the variables as the dependent variable, y, and another as the independent variable, x. Use your knowledge of the subject area and common sense to help you select the variables.

b. Fit the simple linear model, E(y) = β0 + β1x, to the data in the BSCHOOLfile. Interpret the estimates of the slope and y-intercept

Question 4 11.3

Suppose you fit the multiple regression model

y = β0 + β1×1 + β2×2 + β3×3 + ε

to n = 30 data points and obtain the following result:

ŷ = 3.4 – 4.6×1 + 2.7×2 + .93×3

The estimated standard errors of  and  are 1.86 and .29, respectively.

a. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha:β2 ≠ 0. Use α = .05.

b. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha:β3 ≠ 0. Use α = .05.

c. The null hypothesis H0: β2 = 0 is not rejected. In contrast, the null hypothesis H0: β3 = 0 is rejected. Explain how this can happen even though.

Question 5 11.12

Trust in e-retailers. Electronic commerce (or “e-commerce”) describes the use of electronic networks to simplify a business operation. With e-commerce, retailers now can advertise and sell their products easily over the Web. In Internet Research: Electronic Networking Applications and Policy (Vol. 11, 2001), Canadian researchers investigated the factors that impact the level of trust in Web e-retailers. Five quantitative independent variables were used to model level of trust (y):

x1	= ease of navigation on the Web site
x2	= consistency of the Web site
x3	= ease of learning the Web interface
x4	= perception of the interface design
x5	= level of support available to the user

a. Write a first-order model for level of trust as a function of the five independent variables.

b. The model, part a, was fit to data collected for n = 66 visitors to e-retailers’ Web sites and yielded a coefficient of determination of R2 = .58. Interpret this result.

c. Compute the F-statistic used to test the global utility of the model.

d. Using α = .10, give the appropriate conclusion for the test, part c.

Question

1

10.

4

0

Do the accompanying data provide sufficient evidence to conclude that a straight line is useful for characterizing the relationship between x and y?

4

2

4

3

2

4

x				4			2		3
y	1	6	5

Question 2 10.58

In business, do nice guys finish first or last? Refer to the Nature (March 20, 2008) study of the use of punishment in cooperation games, 

Exercise 10.14

 (p.

572

). Recall that college students repeatedly played a version of the game “prisoner’s dilemma,” and the researchers recorded the average payoff and the number of times cooperation, defection, and punishment were used for each player.

a. A test of no correlation between cooperation use (x) and average payoff (y) yielded a p-value of .33. Interpret this result.

b. A test of no correlation between defection use (x) and average payoff (y) yielded a p-value of .66. Interpret this result.

c. A test of no correlation between punishment use (x) and average payoff (y) yielded a p-value of .001. Interpret this result.

Question 3 11.26

Predicting runs scored in baseball. Refer to the Chance (Fall 2000) study of runs scored in Major League Baseball games, 

Exercise 11.14

 (p. 

640

). Multiple regression was used to model total number of runs scored (y) of a team during the season as a function of number of walks (x1), number of singles (x2), number of doubles (x3), number of triples (x4), number of home runs (x5), number of stolen bases (x6), number of times caught stealing (x7), number of strikeouts (x8), and total number of outs (x9). Using the β estimates given in 
Exercise 11.14
, predict the number of runs scored by your favorite Major League Baseball team last year. How close is the predicted value to the actual number of runs scored by your team? [Note: You can find data on your favorite team on the Internet at 

www.mlb.com

.]

Exercise 11.14
—>(a sample of n = 234), the results in the next table were obtained.

Independent Variable

β Estimate

Standard Error

Intercept

3.70

15.00

Walks (x1)

.34

.02

Singles (x2)

.49

.03

Doubles (x3)

.72

.05

Triples (x4)

1.14

.19

Home runs (x5)

1.51

.05

Stolen bases (x6)

.26

.05

Caught stealing (x7)

–.14

.14

Strikeouts (x8)

–.10

.01

Outs (x9)

–.10

.01