11.7.7 WP VS SS An article in the Journal of the American Statistical Association ["Markov Chain Monte Carlo Methods for Computing Bayes Factors: A Comparative Review" (2001, Vol. 96, pp. 1122-1132)] analyzed the tabulated data on compres- sive strength parallel to the grain versus resin-adjusted density for specimens of radiata pine. The data are shown below. Compressive Strength 3040 2470 3610 3480 3810 2330 1800 3110 3160 2310 4360 1880 3670 1740 2250 2650 4970 2620 2900 1670 2540 Density 29.2 24.7 32.3 31.3 31.5 24.5 19.9 27.3 27.1 24.0 33.8 21.5 32.2 22.5 27.5 25.6 34.5 26.2 26.7 21.1 24.1 Compressive Strength 3840 3800 4600 1900 2530 2920 4990 1670 3310 3450 3600 2850 1590 3770 3850 2480 3570 2620 1890 3030 3030 Density 30.7 32.7 32.6 22.1 25.3 30.8 38.9 22.1 29.2 30.1 31.4 26.7 22.1 30.3 32.0 23.2 30.3 29.9 20.8 33.2 28.2 a. Fit a regression model relating compressive strength to density. b. Test for significance of regression with a = 0.05. c. Estimate o² for this model. d. Calculate R2 for this model. Provide an interpretation of this quantity. e. Prepare a normal probability plot of the residuals and interpret this display. f. Plot the residuals versus ŷ and versus .x. Does the assump- tion of constant variance seem to be satisfied?
11.7.7 WP VS SS An article in the Journal of the American Statistical Association ["Markov Chain Monte Carlo Methods for Computing Bayes Factors: A Comparative Review" (2001, Vol. 96, pp. 1122-1132)] analyzed the tabulated data on compres- sive strength parallel to the grain versus resin-adjusted density for specimens of radiata pine. The data are shown below. Compressive Strength 3040 2470 3610 3480 3810 2330 1800 3110 3160 2310 4360 1880 3670 1740 2250 2650 4970 2620 2900 1670 2540 Density 29.2 24.7 32.3 31.3 31.5 24.5 19.9 27.3 27.1 24.0 33.8 21.5 32.2 22.5 27.5 25.6 34.5 26.2 26.7 21.1 24.1 Compressive Strength 3840 3800 4600 1900 2530 2920 4990 1670 3310 3450 3600 2850 1590 3770 3850 2480 3570 2620 1890 3030 3030 Density 30.7 32.7 32.6 22.1 25.3 30.8 38.9 22.1 29.2 30.1 31.4 26.7 22.1 30.3 32.0 23.2 30.3 29.9 20.8 33.2 28.2 a. Fit a regression model relating compressive strength to density. b. Test for significance of regression with a = 0.05. c. Estimate o² for this model. d. Calculate R2 for this model. Provide an interpretation of this quantity. e. Prepare a normal probability plot of the residuals and interpret this display. f. Plot the residuals versus ŷ and versus .x. Does the assump- tion of constant variance seem to be satisfied?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Question
Solve by hand or r code
![11.7.7 WP VS SS An article in the Journal of the American
Statistical Association ["Markov Chain Monte Carlo Methods
for Computing Bayes Factors: A Comparative Review" (2001,
Vol. 96, pp. 1122-1132)] analyzed the tabulated data on compres-
sive strength parallel to the grain versus resin-adjusted density for
specimens of radiata pine. The data are shown below.
Compressive
Strength
3040
2470
3610
3480
3810
2330
1800
3110
3160
2310
4360
1880
3670
1740
2250
2650
4970
2620
2900
1670
2540
Density
29.2
24.7
32.3
31.3
31.5
24.5
19.9
27.3
27.1
24.0
33.8
21.5
32.2
22.5
27.5
25.6
34.5
26.2
26.7
21.1
24.1
Compressive
Strength
3840
3800
4600
1900
2530
2920
4990
1670
3310
3450
3600
2850
1590
3770
3850
2480
3570
2620
1890
3030
3030
Density
30.7
32.7
32.6
22.1
25.3
30.8
38.9
22.1
29.2
30.1
31.4
26.7
22.1
30.3
32.0
23.2
30.3
29.9
20.8
33.2
28.2
a. Fit a regression model relating compressive strength to
density.
b. Test for significance of regression with a = 0.05.
c. Estimate o2 for this model.
d. Calculate R2 for this model. Provide an interpretation of
this quantity.
e. Prepare a normal probability plot of the residuals and
interpret this display.
f. Plot the residuals versus ŷ and versus x. Does the assump-
tion of constant variance seem to be satisfied?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1da296ee-2468-43bb-ac80-be0eb8484519%2Fecc711fc-1a39-4b3f-bda9-eb31443f2d9b%2F4pqz7gh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11.7.7 WP VS SS An article in the Journal of the American
Statistical Association ["Markov Chain Monte Carlo Methods
for Computing Bayes Factors: A Comparative Review" (2001,
Vol. 96, pp. 1122-1132)] analyzed the tabulated data on compres-
sive strength parallel to the grain versus resin-adjusted density for
specimens of radiata pine. The data are shown below.
Compressive
Strength
3040
2470
3610
3480
3810
2330
1800
3110
3160
2310
4360
1880
3670
1740
2250
2650
4970
2620
2900
1670
2540
Density
29.2
24.7
32.3
31.3
31.5
24.5
19.9
27.3
27.1
24.0
33.8
21.5
32.2
22.5
27.5
25.6
34.5
26.2
26.7
21.1
24.1
Compressive
Strength
3840
3800
4600
1900
2530
2920
4990
1670
3310
3450
3600
2850
1590
3770
3850
2480
3570
2620
1890
3030
3030
Density
30.7
32.7
32.6
22.1
25.3
30.8
38.9
22.1
29.2
30.1
31.4
26.7
22.1
30.3
32.0
23.2
30.3
29.9
20.8
33.2
28.2
a. Fit a regression model relating compressive strength to
density.
b. Test for significance of regression with a = 0.05.
c. Estimate o2 for this model.
d. Calculate R2 for this model. Provide an interpretation of
this quantity.
e. Prepare a normal probability plot of the residuals and
interpret this display.
f. Plot the residuals versus ŷ and versus x. Does the assump-
tion of constant variance seem to be satisfied?
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Step 1: Given Information
VIEWStep 2: Determining the regression model
VIEWStep 3: Testing the significance of model
VIEWStep 4: Obtaining the estimate of error variance
VIEWStep 5: Computing the coefficient of determination value
VIEWStep 6: Constructing the normal probability curve for the residuals
VIEWStep 7: Checking whether the assumption of constant variance is satisfied or not
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