In a study to predict temperature from air pressure in a piston-cylinder device, 19 measurements were made of temperature in °F (y) and air pressure in psi (x). Three models were fit: the linear model y = Bo + B,x + ɛ, the quadratic model y = Bo + Bix + B2x² + ɛ, and the cubic model y = Bo + B,x + B2x? + Bx3 + E. The residuals and fitted values for each model are presented in the following table. Plot the residuals versus the fitted values for each model. For each model, state whether the model is appropriate, and explain. %3D Quadratic Model Fit Linear Model Cubic Model Residual Fit Residual Residual Fit -56.2 125.6 11.2 58.2 3.3 66.1 -34.0 153.1 -7.4 126.5 -6.7 125.7 8.4 179.8 4.9 183.4 9.2 179.0 21.4 207.2 -3.6 232.2 0.9 227.8 28.6 234.7 -8.2 271.5 -5.9 269.2 46.9 260.9 8.1 299.7 7.3 300.5 47.2 288.1 15.7 319.6 12.1 323.2 8.5 314.4 -7.0 329.8 -11.7 334.6 -7.1 342.0 4.0 330.9 1.0 333.9 -47.1 139.3 -1.3 93.6 -4.1 96.4 -1.6 166.2 9.1 155.5 12.1 152.5 38.0 220.9 5.9 253.0 9.5 249.4 247.8 286.7 286.0 313.7 35.7 -3.2 -2.4 34.1 275.1 -2.1 311.3 -4.5 34.6 301.1 9.9 325.8 5.5 330.2 1.0 328.2 -2.4 331.6 -6.7 335.9 -23.2 355.3 4.1 327.9 3.5 328.5 -50.7 368.4 -5.0 322.7 -2.1 319.9 -72.9 382.1 -5.7 314.9 2.1 307.1

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter8: Polynomials
Section8.1: Adding And Subtracting Polynomials
Problem 58PPS
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Question
In a study to predict temperature from air pressure in a piston-cylinder device, 19
measurements were made of temperature in °F (y) and air pressure in psi (x). Three models
were fit: the linear model y = Bo + B,x + ɛ, the quadratic model y = Bo + Bix + B2x² + ɛ, and
the cubic model y = Bo + B,x + B2x? + Bx3 + E. The residuals and fitted values for each
model are presented in the following table. Plot the residuals versus the fitted values for
each model. For each model, state whether the model is appropriate, and explain.
%3D
Quadratic Model
Fit
Linear Model
Cubic Model
Residual
Fit
Residual
Residual
Fit
-56.2
125.6
11.2
58.2
3.3
66.1
-34.0
153.1
-7.4
126.5
-6.7
125.7
8.4
179.8
4.9
183.4
9.2
179.0
21.4
207.2
-3.6
232.2
0.9
227.8
28.6
234.7
-8.2
271.5
-5.9
269.2
46.9
260.9
8.1
299.7
7.3
300.5
47.2
288.1
15.7
319.6
12.1
323.2
8.5
314.4
-7.0
329.8
-11.7
334.6
-7.1
342.0
4.0
330.9
1.0
333.9
-47.1
139.3
-1.3
93.6
-4.1
96.4
-1.6
166.2
9.1
155.5
12.1
152.5
38.0
220.9
5.9
253.0
9.5
249.4
247.8
286.7
286.0
313.7
35.7
-3.2
-2.4
34.1
275.1
-2.1
311.3
-4.5
34.6
301.1
9.9
325.8
5.5
330.2
1.0
328.2
-2.4
331.6
-6.7
335.9
-23.2
355.3
4.1
327.9
3.5
328.5
-50.7
368.4
-5.0
322.7
-2.1
319.9
-72.9
382.1
-5.7
314.9
2.1
307.1
Transcribed Image Text:In a study to predict temperature from air pressure in a piston-cylinder device, 19 measurements were made of temperature in °F (y) and air pressure in psi (x). Three models were fit: the linear model y = Bo + B,x + ɛ, the quadratic model y = Bo + Bix + B2x² + ɛ, and the cubic model y = Bo + B,x + B2x? + Bx3 + E. The residuals and fitted values for each model are presented in the following table. Plot the residuals versus the fitted values for each model. For each model, state whether the model is appropriate, and explain. %3D Quadratic Model Fit Linear Model Cubic Model Residual Fit Residual Residual Fit -56.2 125.6 11.2 58.2 3.3 66.1 -34.0 153.1 -7.4 126.5 -6.7 125.7 8.4 179.8 4.9 183.4 9.2 179.0 21.4 207.2 -3.6 232.2 0.9 227.8 28.6 234.7 -8.2 271.5 -5.9 269.2 46.9 260.9 8.1 299.7 7.3 300.5 47.2 288.1 15.7 319.6 12.1 323.2 8.5 314.4 -7.0 329.8 -11.7 334.6 -7.1 342.0 4.0 330.9 1.0 333.9 -47.1 139.3 -1.3 93.6 -4.1 96.4 -1.6 166.2 9.1 155.5 12.1 152.5 38.0 220.9 5.9 253.0 9.5 249.4 247.8 286.7 286.0 313.7 35.7 -3.2 -2.4 34.1 275.1 -2.1 311.3 -4.5 34.6 301.1 9.9 325.8 5.5 330.2 1.0 328.2 -2.4 331.6 -6.7 335.9 -23.2 355.3 4.1 327.9 3.5 328.5 -50.7 368.4 -5.0 322.7 -2.1 319.9 -72.9 382.1 -5.7 314.9 2.1 307.1
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