The general manager of the Cleveland Indians baseball team is inthe process of determining which minor-league players to bring intothe team so that later they would play as major-league players inhis team. He is aware that his team needs players with high numbersof home-run (HR) hits and would like to find a way to predict thenumber of home runs a player will hit in major leagues. He gathersa random sample of players and records the number of home runs eachplayer hit in his first two full years as a major-leagueplayer, the number of home runs he hits in his last full year inthe minor leagues, his age, and the number of years ofprofessional baseball.

Major HR	Minor HR	Age	Years Pro
19	13	19	3
23	15	21	3
6	4	22	5
6	12	21	3
7	21	19	2
18	19	21	3
3	0	19	2
7	8	20	1
20	20	21	3
9	12	22	4
11	16	23	6
7	10	21	5
25	19	22	3
4	11	19	3
35	19	20	3
13	12	18	1
18	11	21	3
6	14	21	2
8	10	19	2
12	1	19	2
20	18	24	5
4	22	18	1
11	13	18	2
32	20	23	5
2	4	19	2
22	16	20	4
2	2	19	2
2	2	21	2
9	9	20	2
32	19	19	2
3	6	19	1
10	9	23	6
5	6	21	4
24	18	20	2
10	12	21	3
10	11	22	3
19	12	21	3
2	1	23	4
16	10	21	3
11	26	19	4
28	15	23	3
20	13	24	7
18	12	24	4
9	14	21	3
0	5	18	0
10	12	22	2
20	29	19	2
11	10	20	2
12	10	22	3
8	19	20	4
12	9	23	5
21	13	21	4
11	11	21	2
28	24	21	3
4	7	20	2
38	22	19	2
8	7	23	5
7	8	21	4
4	6	18	1
15	11	23	6
12	12	18	1
3	3	19	3
8	12	18	1
3	0	21	2
24	22	22	4
23	14	23	5
17	12	18	1
22	17	23	4
23	12	24	6
12	11	23	5
6	8	19	2
34	23	20	2
5	15	20	4
21	13	22	3
13	24	21	2
4	5	24	3
8	17	23	4
20	11	21	4
17	10	20	4
11	19	23	4
23	25	23	3
7	28	23	3
5	2	23	3
25	12	24	4
12	25	20	2
6	7	20	1
21	17	22	5
28	26	23	2
7	5	23	5
21	11	19	3
5	13	20	3
22	21	20	2
7	6	21	3
3	6	21	3
7	8	22	4
13	14	18	2
15	12	24	7
26	20	20	2
18	10	24	4
4	7	19	1
19	14	22	4
16	33	22	3
12	21	21	2
10	14	18	1
23	12	20	4
6	9	23	3
16	15	19	2
10	24	22	3
3	0	22	4
2	7	19	2
17	12	24	6
6	11	19	2
19	12	19	3
6	5	24	4
10	9	20	2
6	18	21	3
3	2	20	2
11	11	20	2
18	10	19	1
4	6	21	2
6	12	21	3
29	31	21	2
12	16	18	2
7	22	20	2
8	35	20	1
30	23	23	3

PART 1: Use the data in sheet “data for part 1”

Question 1

Looking at the range of values the variable number of home runhits in minor leagues can take,this variable is a ?

Select one:

a. Quantitative variable

b. Categorical variable

Question 2

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2-In this problem,number of hits in minor leagues is a …?

Select one:

a. predictor variable

b. response variable

c. none of the above

Question 3

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3-Which of the following equations properly explains thedependence of major home run hits on minor home run hits,age,andexperience?

Select one:

a. Major HR = Minor HR + age + experience

b. Major HR = -0.206 + 7.640 Minor HR + 0.259 age + 1.754experience

c. Major HR = -1.970 Minor HR + 0.666 age + 0.136 experience

d. Major HR = -1.970 + 0.666 Minor HR + 0.136 age + 1.176experience

e. Major HR = 3.306 + 0.486 Minor HR + 0.320 age -1.073experience

Question 4

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4-If the multiplier of age were 6.1 in the above model,it wouldbest mean?

Select one:

a. If a player is one year older,he can hit 6.1 more major homeruns on average.

b. For any given player,if one year passes with no baseballactivity,he can hit 6.1 more major home runs.

c. If one year passes for a typical player with no baseballactivity,he can hit 6.1 more major home runs on average.

d. If one year passes for a typical player who has been involvedin professional baseball within the year,he can hit 6.1 more majorhome runs on average.

Question 5

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5-How much of the variation in data is explained by the abovemodel?

Select one:

a. 35%

b. 59%

c. 5964

d. 6.99

Question 6

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6-How many major home runs a 25 year old novice with absolutelyno professional experience in baseball or leagues is expected tohave?

Select one:

a. -1.79

b. 1.42

c. 3.39

d. 0.14

Question 7

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7-Which of the following residual plots significantly violatesthe regression assumption that residuals should show no significantpattern?

Select one:

a. Plot of residuals versus minor home-runs

b. Plot of residuals versus experience

c. Both

d. None

Question 8

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8-Now create another regression model that would explain thedependence of major home run hits on only minor home run hits andexperience (this is a model similar to question 3,with thedifference that variable age is now excluded).What would be theequation of the regression line?

Select one:

a. Major HR = Minor HR + experience

b. Major HR = 4.485 + 0.658 Minor HR

c. Major HR = 3.306 + 0.486 Minor HR + 0.320 age -1.073experience

d. Major HR = -1.970 + 0.666 Minor HR + 1.176 experience

e. Major HR = 0.453 + 0.668 Minor HR + 1.305 experience

Question 9

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9-Why is the adjusted R-squared in question 8 (with twopredictors) more than that in question 3 (with threepredictors)?

Select one:

a. Because the model with two predictors has a higher R-squaredcompared to the model with three predictors

b. Because the variable age was not explaining enoughvariability in the model with three predictors

c. This is the result of miscalculation by Excel regression

d. Because the variable age in the model with three predictorsis much more influential than the other variables in explaining theresponse variable

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Going back to the model you developed in Question 3, we wouldlike to investigate whether the developed model represents agood-fitting linear model. Assume a 5% significance levelwhenever needed.

Question 10

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10- Which of the following can represent the ALTERNATEhypothesis (H1H1) for testing the overall linear fit ofthe model you developed in mini-project 1 (as described above)?

Select one:

a. ?1??2??3?1??2??3

b. ?1=?2=?3=0?1=?2=?3=0

c. ?1?0?1?0

d. At least two of the ?-values are different

e. At least one ?-value is not zero

Question 11

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11- What is the test statistic for testing the overall linear(the test outlined in question 10)?

Select one:

a. 1.86×10?111.86×10?11

b. 22

c. 0.35

d. 7.64

e. -0.21

Question 12

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12- Which of the following conclusions can be made when testingfor the overall linear fit (the test of question 10)?

Select one:

a. All predictor variables have a significant impact on thenumber of major home runs

b. Number of major home runs has a significant impact on atleast one of the predictor variables

c. At least one of the predictor variables have a significantimpact on the number of major home runs

d. None of the predictor variables have a significant impact onthe number of major home runs

Question 13

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13- Which of the following predictor variables does NOT have asignificant impact on the number of major home runs?

Select one:

a. Number of minor home runs

b. Years of professional experience

c. Both

d. None

Question 14

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14- Which of the following pairs of predictor variables arehighly correlated?

Select one:

a. Number of minor home runs & age

b. Number of minor home runs & years of experience

c. Age & years of experience

d. None

Question 15

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15- Which of the following variables cannot be removed withoutsignificantly hurting the model?

Select one:

a. Number of minor home runs

b. Age

c. Years of professional experience

d. Each one of the above can be removed

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PART 2: Use the data in sheet “data for part 2”

Major HR	Minor HR	Age	Years Pro	Type of hitter
19	13	19	3	power hitter
23	15	21	3	contact hitter
6	4	22	5	contact hitter
6	12	21	3	contact hitter
7	21	19	2	contact hitter
18	19	21	3	contact hitter
3	0	19	2	contact hitter
7	8	20	1	contact hitter
20	20	21	3	power hitter
9	12	22	4	contact hitter
11	16	23	6	power hitter
7	10	21	5	power hitter
25	19	22	3	power hitter
4	11	19	3	contact hitter
35	19	20	3	power hitter
13	12	18	1	power hitter
18	11	21	3	power hitter
6	14	21	2	contact hitter
8	10	19	2	power hitter
12	1	19	2	power hitter
20	18	24	5	power hitter
4	22	18	1	contact hitter
11	13	18	2	power hitter
32	20	23	5	power hitter
2	4	19	2	contact hitter
22	16	20	4	power hitter
2	2	19	2	contact hitter
2	2	21	2	contact hitter
9	9	20	2	power hitter
32	19	19	2	power hitter
3	6	19	1	contact hitter
10	9	23	6	contact hitter
5	6	21	4	contact hitter
24	18	20	2	power hitter
10	12	21	3	contact hitter
10	11	22	3	contact hitter
19	12	21	3	contact hitter
2	1	23	4	contact hitter
16	10	21	3	contact hitter
11	26	19	4	contact hitter
28	15	23	3	power hitter
20	13	24	7	contact hitter
18	12	24	4	power hitter
9	14	21	3	contact hitter
0	5	18	0	contact hitter
10	12	22	2	contact hitter
20	29	19	2	contact hitter
11	10	20	2	power hitter
12	10	22	3	contact hitter
8	19	20	4	power hitter
12	9	23	5	contact hitter
21	13	21	4	power hitter
11	11	21	2	power hitter
28	24	21	3	power hitter
4	7	20	2	power hitter
38	22	19	2	power hitter
8	7	23	5	power hitter
7	8	21	4	contact hitter
4	6	18	1	power hitter
15	11	23	6	contact hitter
12	12	18	1	power hitter
3	3	19	3	contact hitter
8	12	18	1	contact hitter
3	0	21	2	contact hitter
24	22	22	4	power hitter
23	14	23	5	power hitter
17	12	18	1	power hitter
22	17	23	4	power hitter
23	12	24	6	contact hitter
12	11	23	5	contact hitter
6	8	19	2	contact hitter
34	23	20	2	power hitter
5	15	20	4	power hitter
21	13	22	3	power hitter
13	24	21	2	power hitter
4	5	24	3	power hitter
8	17	23	4	contact hitter
20	11	21	4	contact hitter
17	10	20	4	contact hitter
11	19	23	4	contact hitter
23	25	23	3	power hitter
7	28	23	3	power hitter
5	2	23	3	contact hitter
25	12	24	4	contact hitter
12	25	20	2	contact hitter
6	7	20	1	power hitter
21	17	22	5	contact hitter
28	26	23	2	power hitter
7	5	23	5	contact hitter
21	11	19	3	contact hitter
5	13	20	3	power hitter
22	21	20	2	contact hitter
7	6	21	3	contact hitter
3	6	21	3	contact hitter
7	8	22	4	contact hitter
13	14	18	2	power hitter
15	12	24	7	contact hitter
26	20	20	2	power hitter
18	10	24	4	contact hitter
4	7	19	1	contact hitter
19	14	22	4	power hitter
16	33	22	3	power hitter
12	21	21	2	contact hitter
10	14	18	1	power hitter
23	12	20	4	power hitter
6	9	23	3	contact hitter
16	15	19	2	contact hitter
10	24	22	3	contact hitter
3	0	22	4	power hitter
2	7	19	2	contact hitter
17	12	24	6	power hitter
6	11	19	2	power hitter
19	12	19	3	power hitter
6	5	24	4	contact hitter
10	9	20	2	contact hitter
6	18	21	3	power hitter
3	2	20	2	contact hitter
11	11	20	2	power hitter
18	10	19	1	contact hitter
4	6	21	2	contact hitter
6	12	21	3	contact hitter
29	31	21	2	power hitter
12	16	18	2	contact hitter
7	22	20	2	contact hitter
8	35	20	1	power hitter
30	23	23	3	power hitter

In addition to the data set that was available before, thegeneral manager has now acquired more information on the type ofthe baseball player when hitting the ball. Each player isclassified to be either a “power hitter” or a “contact hitter”.Power hitters tend to exert more power when hitting the ball andtherefore tend to strike out more often than contact hitters. Thefull data set is available in the second spreadsheet of the datafile.

Question 16

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16 - Create a pivot table to display how does the type of hitterand years of experience influence the number of major home runs.What is the average number of major home runs for power hittersthat have 2 or less years of experience (0, 1 or 2 years ofexperience)? (hint: “grouping” would be helpful)

Select one:

a. 10

b. 17.78

c. 13.89

d. 15.6

e. 13.15

Question 17

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17- Including the new variable for type of the hitter inside theregression model, which of the following is true when comparingpower hitters with contact hitters,when other predictor variablesare held constant?

Select one:

a. The difference in major home run hits between the two typesof hitters is not significant

b. Power hitters have 3.58 MORE major home run hits than contacthitters on average

c. Power hitters have 3.58 LESS major home run hits than contacthitters on average

d. Power hitters have 4.5 MORE major home run hits than contacthitters on average

e. Power hitters have 4.5 LESS major home run hits than contacthitters on average