Use Regression for the following data. Then answer the questions below Question

Question

Use Regression for the following data. Then answer the questions below

Question 1- Which of the following conclusions can be made when testing for the overall linear fit (At least one -value is not zero)?

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 2- Which of the following predictor variables does NOT have a significant impact on the number of major home runs?

a. Number of minor home runs

b. Years of professional experience

c. Both

d. None

Question 3- Which of the following pairs of predictor variables are highly correlated?

a. Number of minor home runs & age

b. Number of minor home runs & years of experience

c. Age & years of experience

d. None

Question 4- Which of the following variables cannot be removed without significantly hurting the model?

a. Number of minor home runs

b. Age

c. Years of professional experience

d. Each one of the above can be removed

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

Explanation / Answer

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Regression Analysis: Major HR versus Minor HR, Age, Years Pro

The regression equation is
Major HR = - 1.97 + 0.666 Minor HR + 0.136 Age + 1.18 Years Pro

Predictor Coef SE Coef T P
Constant -1.970 9.547 -0.21 0.837
Minor HR 0.66584 0.08715 7.64 0.000
Age 0.1357 0.5241 0.26 0.796
Years Pro 1.1764 0.6706 1.75 0.082

S = 6.99210 R-Sq = 35.1% R-Sq(adj) = 33.5%

Analysis of Variance

Source DF SS MS F P
Regression 3 3227.6 1075.9 22.01 0.000
Residual Error 122 5964.5 48.9
Total 125 9192.1

Source DF Seq SS
Minor HR 1 2818.2
Age 1 258.9
Years Pro 1 150.4

Unusual Observations

Obs Minor HR Major HR Fit SE Fit Residual St Resid
15 19.0 35.000 16.925 0.953 18.075 2.61R
30 19.0 32.000 15.613 1.060 16.387 2.37R
56 22.0 38.000 17.610 1.213 20.390 2.96R
72 23.0 34.000 18.412 1.136 15.588 2.26R
82 28.0 7.000 23.324 1.736 -16.324 -2.41R
125 35.0 8.000 25.225 2.185 -17.225 -2.59RX

R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.

Question 1:

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

Because , p value < alpha.

Question 2:

a. Number of minor home runs  does NOT have a significant impact on the number of major home runs.

Its p value is zero.

Queation 4:

b. Age cannot be removed without significantly hurting the model

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