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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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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## Analyzing the Electric Power Consumption of a Chemical Plant ### Problem Statement The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (\(x_1\)), the number of days in the month (\(x_2\)), the average product purity (\(x_3\)), and the tons of product produced (\(x_4\)). The past year's historical data are available and presented in the following table. #### Data: | \(y\) | \(x_1\) | \(x_2\) | \(x_3\) | \(x_4\) | | ----- | ------ | ------ | ------ | ------ | | 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 | 24 | 94 | 99 | | 300 | 60 | 25 | 87 | 97 | | 296 | 84 | 25 | 86 | 98 | | 267 | 75 | 24 | 92 | 110 | | 276 | 60 | 25 | 91 | 105 | | 288 | 58 | 25 | 90 | 100 | | 261 | 38 | 23 | 89 | 98 | ### Analysis Tasks: a) Fit a multiple linear regression model to the data. b) Predict power consumption for a month in which \(x_1 = 75\), \(x_2 = 24\), \(x_3 = 90\), \(x_4 = 98\). c) Test for significance of regression using \(\alpha = 0.05\). What is the P-value of this test? d) Estimate \(\sigma^2\). e) Use the
Transcribed Image Text:## Analyzing the Electric Power Consumption of a Chemical Plant ### Problem Statement The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (\(x_1\)), the number of days in the month (\(x_2\)), the average product purity (\(x_3\)), and the tons of product produced (\(x_4\)). The past year's historical data are available and presented in the following table. #### Data: | \(y\) | \(x_1\) | \(x_2\) | \(x_3\) | \(x_4\) | | ----- | ------ | ------ | ------ | ------ | | 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 | 24 | 94 | 99 | | 300 | 60 | 25 | 87 | 97 | | 296 | 84 | 25 | 86 | 98 | | 267 | 75 | 24 | 92 | 110 | | 276 | 60 | 25 | 91 | 105 | | 288 | 58 | 25 | 90 | 100 | | 261 | 38 | 23 | 89 | 98 | ### Analysis Tasks: a) Fit a multiple linear regression model to the data. b) Predict power consumption for a month in which \(x_1 = 75\), \(x_2 = 24\), \(x_3 = 90\), \(x_4 = 98\). c) Test for significance of regression using \(\alpha = 0.05\). What is the P-value of this test? d) Estimate \(\sigma^2\). e) Use the
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