The electric power consumed each month by a chemical plant is thought to be related to 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: regression model is y = -102.7132 + 0.6054X1 + 8.9236X2 + 1.4374 X3 + 0.0136X4 a) Estimate sigma^2 b.) Using ANOVA, test for significance of regression using α=0.05. Determine the critical value of the test statistic (2 decimal places only). c.) Using ANOVA, test for significance of regression using α=0.05. Determine the computed value of the test statistic d) Calculate R^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %). e) Calculate R_adj^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %). f) Test the significance of x3 at α=0.05. Determine the value of the test statistic. g) Determine the lower limit of the 95% confidence interval on b(beta)2
The electric power consumed each month by a chemical plant is thought to be related to 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:
regression model is y = -102.7132 + 0.6054X1 + 8.9236X2 + 1.4374 X3 + 0.0136X4
a) Estimate sigma^2
b.) Using ANOVA, test for significance of regression using α=0.05. Determine the critical value of the test statistic (2 decimal places only).
c.) Using ANOVA, test for significance of regression using α=0.05. Determine the computed value of the test statistic
d) Calculate R^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %).
e) Calculate R_adj^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %).
f) Test the significance of x3 at α=0.05. Determine the value of the test statistic.
g) Determine the lower limit of the 95% confidence interval on b(beta)2
h) Determine the upper limit of the 95% confidence interval on b(beta)3 .
![y
240
236
290
274
301
316
300
296
267
276
288
261
x1
25
31
45
60
65
72
80
84
75
60
50
38
x2
24
21
24
25
25
26
25
25
24
25
25
23
x3
91
90
88
87
91
94
87
86
88
91
90
89
x4
100
95
110
88
94
99
97
96
110
105
100
98](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65394695-8c71-48ea-bdef-f5ba29cbfd19%2Fb8e4a5ec-9001-4398-92de-f436303d974e%2Fg5o4phc_processed.png&w=3840&q=75)
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