Suppose that a scientist takes experimental data on the radius of a propellant grain Y as a function of powder temperature x₁, extrusion rate X2, and die temperature x3. The accompanying data set is available below. Complete parts (a) and (b) below. Click here to view the coded data. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. (a) A case can be made for eliminating x₁, powder temperature, from the model since the P-value based on the F-test is 0.3488 while P-values for X₂ and x3 are near zero. Reduce the model by eliminating x₁, thereby producing a full and a restricted (or reduced) model, and compare them on the basis of R2 adj The full model is y = 127.50 + (1.25)x₁+ (18.25¹) x₂ + (26.25") (Round to two decimal places as needed.) The restricted model is y = 127.50 +(18.25) x₂ + (26.25) X3. (Round to two decimal places as needed.) X3. For the full model, R² = 0.991, for the restricted model, R² = 0.990, so there appears to be adj adj model. a small advantage when using the full (Round to three decimal places as needed.) (b) Compare the full and restricted models using the width of the 95% prediction intervals on a new observation. The better of the two models would be that with the tightened prediction intervals. Use the average of the width of the prediction intervals. For the full model, the average width is 22.68. For the restricted model, the average width is 20.35¹. So, the model without x, appears to be the better model. (Round to two decimal places as needed.)
Suppose that a scientist takes experimental data on the radius of a propellant grain Y as a function of powder temperature x₁, extrusion rate X2, and die temperature x3. The accompanying data set is available below. Complete parts (a) and (b) below. Click here to view the coded data. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. (a) A case can be made for eliminating x₁, powder temperature, from the model since the P-value based on the F-test is 0.3488 while P-values for X₂ and x3 are near zero. Reduce the model by eliminating x₁, thereby producing a full and a restricted (or reduced) model, and compare them on the basis of R2 adj The full model is y = 127.50 + (1.25)x₁+ (18.25¹) x₂ + (26.25") (Round to two decimal places as needed.) The restricted model is y = 127.50 +(18.25) x₂ + (26.25) X3. (Round to two decimal places as needed.) X3. For the full model, R² = 0.991, for the restricted model, R² = 0.990, so there appears to be adj adj model. a small advantage when using the full (Round to three decimal places as needed.) (b) Compare the full and restricted models using the width of the 95% prediction intervals on a new observation. The better of the two models would be that with the tightened prediction intervals. Use the average of the width of the prediction intervals. For the full model, the average width is 22.68. For the restricted model, the average width is 20.35¹. So, the model without x, appears to be the better model. (Round to two decimal places as needed.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Grain Radius Data
Grain
Radius
y
158
162
122
67
110
112
109
72
Powder
Temperature
X₁
1
- 1
1
Print
Extrusion
Rate
X2
1
1
1
Done
Die
Temperature
X3
1
1
1
- 1
X
Transcribed Image Text:Suppose that a scientist takes experimental data on the radius of a propellant grain Y as a function of powder temperature x₁, extrusion rate
X₂, and die temperature x3. The accompanying data set is available below. Complete parts (a) and (b) below.
Click here to view the coded data.
Click here to view page 1 of the table of critical values of the t-distribution.
Click here to view page 2 of the table of critical values of the t-distribution.
(a) A case can be made for eliminating x₁, powder temperature, from the model since the P-value based on the F-test is 0.3488 while
P-values for X₂ and x3 are near zero. Reduce the model by eliminating x₁, thereby producing a full and a restricted (or reduced) model, and
compare them on the basis of R²
adj
The full model is ŷ = 127.50 + (1.25) x₁ + (18.25) x₂ + (26.25¹) x3.
(Round to two decimal places as needed.)
The restricted model is ŷ= 127.50 + (18.25¹) x₂ + (26.25) X3.
(Round to two decimal places as needed.)
For the full model, R² = 0.991, for the restricted model, R²
adj
adj
model.
a small advantage when using the full
(Round to three decimal places as needed.)
=
0.990, so there appears to be
(b) Compare the full and restricted models using the width of the 95% prediction intervals on a new observation. The better of the two models
would be that with the tightened prediction intervals. Use the average of the width of the prediction intervals.
For the full model, the average width is 22.68. For the restricted model, the average width is 20.35. So, the model without x, appears to
be the better model.
(Round to two decimal places as needed.)
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