During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x1), Test 2 score (x2), and Test3 score (x3). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y) = B1 + B1x1 + B2x2 + B3x3 The first-order model was fit to the data for each of 12 units sampled from the production line. The results are summarized in the printout. SOURCE DF F VALUE PROB>F SS MS MODEL ERROR TOTAL 3 151417 50472 18.16 .0075 22231 2779 12 173648 ROOT MSE 52.72 R-SQUARE 0.872 DEP MEAN 645.8 ADJ R-SQ 0.824 PARAMETER STANDARD T FOR 0 VARIABLE ESTIMATE ERROR PARAMETER =0 PROB> ITI 0. S85 0.039 0.005 0.004 0. 15 11.98 0.2745 INTERCEPT S0.50 x1(TESTI) 0.1111 2.47 X2(TEST2) X3(TEST3) Suppose the 95% confidence interval for B 3 is (.15, .47). Which of the following statements is incorrect? O We are 95% confident that the increase in Test4 score for every 1-point increase in Test3 score falls between .15 and 47, holding Test1 and Test2 fixed. O We are 95% confident that the Test3 is a useful linear predictor of Test4 score, holding Test1 and Test2 fixed. O We are 95% confident that the estimated slope for the Test4-Test3 line falls between .15 and .47 holding Test1 and Test2 fixed. O At a = .05, there is insufficient evidence to reject Ho: 83 = 0 in favor of Ha: B3 # 0. 0.0986 0.08os 0.3762 3.82 0.3265 4.04
During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x1), Test 2 score (x2), and Test3 score (x3). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y) = B1 + B1x1 + B2x2 + B3x3 The first-order model was fit to the data for each of 12 units sampled from the production line. The results are summarized in the printout. SOURCE DF F VALUE PROB>F SS MS MODEL ERROR TOTAL 3 151417 50472 18.16 .0075 22231 2779 12 173648 ROOT MSE 52.72 R-SQUARE 0.872 DEP MEAN 645.8 ADJ R-SQ 0.824 PARAMETER STANDARD T FOR 0 VARIABLE ESTIMATE ERROR PARAMETER =0 PROB> ITI 0. S85 0.039 0.005 0.004 0. 15 11.98 0.2745 INTERCEPT S0.50 x1(TESTI) 0.1111 2.47 X2(TEST2) X3(TEST3) Suppose the 95% confidence interval for B 3 is (.15, .47). Which of the following statements is incorrect? O We are 95% confident that the increase in Test4 score for every 1-point increase in Test3 score falls between .15 and 47, holding Test1 and Test2 fixed. O We are 95% confident that the Test3 is a useful linear predictor of Test4 score, holding Test1 and Test2 fixed. O We are 95% confident that the estimated slope for the Test4-Test3 line falls between .15 and .47 holding Test1 and Test2 fixed. O At a = .05, there is insufficient evidence to reject Ho: 83 = 0 in favor of Ha: B3 # 0. 0.0986 0.08os 0.3762 3.82 0.3265 4.04
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Question
![During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first
three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x1), Test 2 score (x2), and Test3 score (x3). [Note: All test scores range from 200 to 800, with
higher scores indicative of a higher quality product.] Consider the model:
E(y) = B1 + B1x1 + B2x2 + B3x3
The first-order model was fit to the data for each of 12 units sampled from the production line. The results are summarized in the printout.
SOURCE
DF
MS
F VALUE
PROB>F
MODEL
3
151417
50472
18.16
.0075
ERROR
22231
2779
TOTAL
12
173648
ROOT MSE 52.72
R-SQUARE
0.872
DEP MEAN
645.8
ADJ R-SQ
0.824
PARAMETER STANDARD
T FOR 0:
VARIABLE
ESTIMATE
ERROR
PARAMETER = 0
PROB> ITI
INTERCEPT
11.98
80.50
0.15
0.885
0.039
0.005
0.004
X1(TESTI)
X2(TEST2)
X3(TEST3)
Suppose the 95% confidence interval for B 3 is (.15, .47). Which of the following statements is incorrect?
O We are 95% confident that the increase in Test4 score for every 1-point increase in Test3 score falls between .15 and .47, holding Test1 and Test2 fixed.
O We are 95% confident that the Test3 is a useful linear predictor of Test4 score, holding Test1 and Test2 fixed.
O We are 95% confident that the estimated slope for the Test4-Test3 line falls between .15 and 47 holding Test1 and Test2 fixed.
O At a = .05, there is insufficient evidence to reject Ho: B3 = 0 in favor of Ha: B3 # 0.
0.2745
0.1111
2.47
0.3762
0.3265
0.0986
3.82
0.0808
4.04](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2e25a82-bcfd-447c-8081-9d5a308dcd35%2Fcea1971c-240a-487a-b59f-0216f37ede8e%2Fe90pd2_processed.png&w=3840&q=75)
Transcribed Image Text:During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first
three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x1), Test 2 score (x2), and Test3 score (x3). [Note: All test scores range from 200 to 800, with
higher scores indicative of a higher quality product.] Consider the model:
E(y) = B1 + B1x1 + B2x2 + B3x3
The first-order model was fit to the data for each of 12 units sampled from the production line. The results are summarized in the printout.
SOURCE
DF
MS
F VALUE
PROB>F
MODEL
3
151417
50472
18.16
.0075
ERROR
22231
2779
TOTAL
12
173648
ROOT MSE 52.72
R-SQUARE
0.872
DEP MEAN
645.8
ADJ R-SQ
0.824
PARAMETER STANDARD
T FOR 0:
VARIABLE
ESTIMATE
ERROR
PARAMETER = 0
PROB> ITI
INTERCEPT
11.98
80.50
0.15
0.885
0.039
0.005
0.004
X1(TESTI)
X2(TEST2)
X3(TEST3)
Suppose the 95% confidence interval for B 3 is (.15, .47). Which of the following statements is incorrect?
O We are 95% confident that the increase in Test4 score for every 1-point increase in Test3 score falls between .15 and .47, holding Test1 and Test2 fixed.
O We are 95% confident that the Test3 is a useful linear predictor of Test4 score, holding Test1 and Test2 fixed.
O We are 95% confident that the estimated slope for the Test4-Test3 line falls between .15 and 47 holding Test1 and Test2 fixed.
O At a = .05, there is insufficient evidence to reject Ho: B3 = 0 in favor of Ha: B3 # 0.
0.2745
0.1111
2.47
0.3762
0.3265
0.0986
3.82
0.0808
4.04
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