3. The electric power consumed each month by a chemical plant is thought to be related to 1 the average ambient temperature (x1), the number of days in the month (x2), the average product purity (x3), and the tons of product produced (x4). The past year's historical data are available and are presented in the following table. x2 x3 X4 240 25 24 91 100 236 31 21 90 95 290 45 24 88 110 274 60 25 87 88 301 65 25 91 94 316 72 26 94 99 300 80 25 87 97 296 84 25 86 96 267 75 24 88 110 276 60 25 91 105 288 50 25 90 100 261 38 23 89 98 a) Fit a multiple linear regression model to the data. b) Predict power consumption for a month in which x1 = 75, х2 — 24, хз — 90, х4 — 98. c) Test for significance of regression using a = 0.05. What is the P-value of this test? d) Estimate o². e) Use the t-test to assess the contribution of each regressor to the model. Using a = 0.05, what conclusions can you draw? f) Find 95% confidence intervals on B1, B2, B3, B4. g) Find a 95% confidence interval on the mean of Y for the values of regressors from b). h) Find a 95% prediction interval on the power consumption for the values of regressors from b). i) Calculate R² and adjusted R² for this model. Interpret these quantities. j) Plot the residuals versus ĝ. Interpret this plot. k) Construct a normal probability plot of the residuals and comment on the normality assump- tion.
3. The electric power consumed each month by a chemical plant is thought to be related to 1 the average ambient temperature (x1), the number of days in the month (x2), the average product purity (x3), and the tons of product produced (x4). The past year's historical data are available and are presented in the following table. x2 x3 X4 240 25 24 91 100 236 31 21 90 95 290 45 24 88 110 274 60 25 87 88 301 65 25 91 94 316 72 26 94 99 300 80 25 87 97 296 84 25 86 96 267 75 24 88 110 276 60 25 91 105 288 50 25 90 100 261 38 23 89 98 a) Fit a multiple linear regression model to the data. b) Predict power consumption for a month in which x1 = 75, х2 — 24, хз — 90, х4 — 98. c) Test for significance of regression using a = 0.05. What is the P-value of this test? d) Estimate o². e) Use the t-test to assess the contribution of each regressor to the model. Using a = 0.05, what conclusions can you draw? f) Find 95% confidence intervals on B1, B2, B3, B4. g) Find a 95% confidence interval on the mean of Y for the values of regressors from b). h) Find a 95% prediction interval on the power consumption for the values of regressors from b). i) Calculate R² and adjusted R² for this model. Interpret these quantities. j) Plot the residuals versus ĝ. Interpret this plot. k) Construct a normal probability plot of the residuals and comment on the normality assump- tion.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...
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Question
Transcribed Image Text:3. The electric power consumed each month by a chemical plant is thought to be related to
1
the average ambient temperature (x1), the number of days in the month (x2), the average product
purity (x3), and the tons of product produced (x4). The past year's historical data are available
and are presented in the following table.
x2
x3
X4
240
25
24
91
100
236
31
21
90
95
290
45
24
88
110
274
60
25
87
88
301
65
25
91
94
316
72
26
94
99
300
80
25 87
97
296
84
25
86
96
267
75
24
88
110
276
60
25
91
105
288
50
25
90
100
261
38
23
89
98
a) Fit a multiple linear regression model to the data.
b) Predict power consumption for a month in which x1 =
75, х2 — 24, хз — 90, х4 — 98.
c) Test for significance of regression using a = 0.05. What is the P-value of this test?
d) Estimate o².
e) Use the t-test to assess the contribution of each regressor to the model. Using a = 0.05,
what conclusions can you draw?
f) Find 95% confidence intervals on B1, B2, B3, B4.
g) Find a 95% confidence interval on the mean of Y for the values of regressors from b).
h) Find a 95% prediction interval on the power consumption for the values of regressors from
b).
i) Calculate R² and adjusted R² for this model. Interpret these quantities.
j) Plot the residuals versus ĝ. Interpret this plot.
k) Construct a normal probability plot of the residuals and comment on the normality assump-
tion.
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