The general manager of the Cleveland Indians baseball team is in the process of
ID: 3050669 • Letter: T
Question
The general manager of the Cleveland Indians baseball team is in the process of determining which minor-league players to bring into the team so that later they would play as major-league players in his team. He is aware that his team needs players with high numbers of home-run (HR) hits and would like to find a way to predict the number of home runs a player will hit in major leagues. He gathers a random sample of players and records the number of home runs each player hit in his first two full years as a major-league player, the number of home runs he hits in his last full year in the minor leagues, his age, and the number of years of professional 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 run hits 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 the dependence of major home run hits on minor home run hits,age,and experience?
Select one:
a. Major HR = Minor HR + age + experience
b. Major HR = -0.206 + 7.640 Minor HR + 0.259 age + 1.754 experience
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 + 1.176 experience
e. Major HR = 3.306 + 0.486 Minor HR + 0.320 age -1.073 experience
Question 4
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4-If the multiplier of age were 6.1 in the above model,it would best mean?
Select one:
a. If a player is one year older,he can hit 6.1 more major home runs on average.
b. For any given player,if one year passes with no baseball activity,he can hit 6.1 more major home runs.
c. If one year passes for a typical player with no baseball activity,he can hit 6.1 more major home runs on average.
d. If one year passes for a typical player who has been involved in professional baseball within the year,he can hit 6.1 more major home runs on average.
Question 5
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5-How much of the variation in data is explained by the above model?
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 absolutely no professional experience in baseball or leagues is expected to have?
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 violates the regression assumption that residuals should show no significant pattern?
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 the dependence of major home run hits on only minor home run hits and experience (this is a model similar to question 3,with the difference that variable age is now excluded).What would be the equation 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 -1.073 experience
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 two predictors) more than that in question 3 (with three predictors)?
Select one:
a. Because the model with two predictors has a higher R-squared compared to the model with three predictors
b. Because the variable age was not explaining enough variability 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 predictors is much more influential than the other variables in explaining the response variable
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Going back to the model you developed in Question 3, we would like to investigate whether the developed model represents a good-fitting linear model. Assume a 5% significance level whenever needed.
Question 10
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10- Which of the following can represent the ALTERNATE hypothesis (H1H1) for testing the overall linear fit of the model you developed in mini-project 1 (as described above)?
Select one:
a. 123123
b. 1=2=3=01=2=3=0
c. 1010
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. 1.86×10111.86×1011
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 testing for the overall linear fit (the test of question 10)?
Select one:
a. All predictor variables have a significant impact on the number of major home runs
b. Number of major home runs has a significant impact on at least one of the predictor variables
c. At least one of the predictor variables have a significant impact on the number of major home runs
d. None of the predictor variables have a significant impact on the number of major home runs
Question 13
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13- Which of the following predictor variables does NOT have a significant 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 are highly 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 without significantly 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, the general manager has now acquired more information on the type of the baseball player when hitting the ball. Each player is classified to be either a “power hitter” or a “contact hitter”. Power hitters tend to exert more power when hitting the ball and therefore tend to strike out more often than contact hitters. The full data set is available in the second spreadsheet of the data file.
Question 16
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16 - Create a pivot table to display how does the type of hitter and years of experience influence the number of major home runs. What is the average number of major home runs for power hitters that have 2 or less years of experience (0, 1 or 2 years of experience)? (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 the regression model, which of the following is true when comparing power hitters with contact hitters,when other predictor variables are held constant?
Select one:
a. The difference in major home run hits between the two types of hitters is not significant
b. Power hitters have 3.58 MORE major home run hits than contact hitters on average
c. Power hitters have 3.58 LESS major home run hits than contact hitters on average
d. Power hitters have 4.5 MORE major home run hits than contact hitters on average
e. Power hitters have 4.5 LESS major home run hits than contact hitters on average
Explanation / Answer
1. Home runs is a quantitative variable
2.It is a predictor variable
3.Major HR = -1.970 + 0.666 Minor HR + 0.136 age + 1.176 experience
4.If a player is one year older,he can hit 6.1 more major home runs on average
5.. 59%
6.d. 0.14
7.Both the. Plot of residuals versus minor home-runs and Plot of residuals versus experience
8.Major HR = 0.453 + 0.668 Minor HR + 1.305 experience
9.Because the variable age was not explaining enough variability in the model with three predictors
10.e. At least one -value is not zero
12.c. At least one of the predictor variables have a significant impact on the number of major home runs
13.d. None
14.c. Age & years of experience
15.a. Number of minor home runs
16.c. 13.89
17.b. Power hitters have 3.58 MORE major home run hits than contact hitters on average
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