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HW5 1) The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year's usage and temperatures are in the following table: Month Jan. Feb. Mar. Apr. May June Temp. 21 24 32 47 50 59 Usage/ 1000 185.79 214.47 Month Temp. July. 68 Aug. 74 288.03 Sept. 62 Oct. 50 424.84 454.58 Nov. 41 539.03 Dec. 30 Usage/ 1000 621.55 675.06 562.03 452.93 369.95 273.98 a) Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). What is the estimate of o2? b) What is the estimate of expected stem usage when the average temperature is 55 F? c) What change in mean stem usage is expected when the monthly average temperature changes by 1 F? d) Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual. e) Test for significance of regression using a-0.01 (Use ANOVA). f) Calculate the r' of the model. g) Find a 99% CI for ₁.

HW5 1) The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year's usage and temperatures are in the following table: Month Jan. Feb. Mar. Apr. May June Temp. 21 24 32 47 50 59 Usage/ 1000 185.79 214.47 Month Temp. July. 68 Aug. 74 288.03 Sept. 62 Oct. 50 424.84 454.58 Nov. 41 539.03 Dec. 30 Usage/ 1000 621.55 675.06 562.03 452.93 369.95 273.98 a) Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). What is the estimate of o2? b) What is the estimate of expected stem usage when the average temperature is 55 F? c) What change in mean stem usage is expected when the monthly average temperature changes by 1 F? d) Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual. e) Test for significance of regression using a-0.01 (Use ANOVA). f) Calculate the r' of the model. g) Find a 99% CI for ₁.

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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Can you review the attached statistics homework and advise if there are errors we can discuss. Thank you.

--- ### MSC 600 Quantitative Methods #### Homework Assignment 5 (HW5) #### 1. Steam Usage and Temperature Analysis The task involves analyzing the number of pounds of steam used per month by a chemical plant and its relation to the average ambient temperature (in degrees Fahrenheit) for that month. The data for the past year is tabulated as follows: | Month | Temp (°F) | Usage (x1000 lbs) | Month | Temp (°F) | Usage (x1000 lbs) | |-------|-----------|-------------------|-------|-----------|-------------------| | Jan. | 21 | 185.79 | July | 68 | 621.55 | | Feb. | 24 | 214.47 | Aug. | 74 | 675.06 | | Mar. | 30 | 238.03 | Sept. | 62 | 562.03 | | Apr. | 37 | 284.84 | Oct. | 50 | 452.93 | | May | 50 | 454.58 | Nov. | 41 | 369.95 | | June | 59 | 530.03 | Dec. | 30 | 273.98 | #### Questions: a) Assuming a simple linear regression model is appropriate, fit the regression model relating steam usage (y) to the average temperature (x). What is the estimate of \( \sigma^2 \)? - Answer: \( \sigma^2 \) = 2.79 b) What is the estimate of expected steam usage when the average temperature is 55°F? - Calculation: \( \hat{y} = -6.34 + 9.21(55) \) - Answer: \( \hat{y} = 500.12 \) (thousand pounds) c) What change in mean steam usage is expected when the monthly average temperature changes by 1°F? - Answer: 9.21°F d) Calculate the fitted value of y and the corresponding residual if the monthly average temperature is 47°F. - Given: \( x = 47, \hat{y} = 424.84 \) - Fitted value calculation:
Transcribed Image Text:--- ### MSC 600 Quantitative Methods #### Homework Assignment 5 (HW5) #### 1. Steam Usage and Temperature Analysis The task involves analyzing the number of pounds of steam used per month by a chemical plant and its relation to the average ambient temperature (in degrees Fahrenheit) for that month. The data for the past year is tabulated as follows: | Month | Temp (°F) | Usage (x1000 lbs) | Month | Temp (°F) | Usage (x1000 lbs) | |-------|-----------|-------------------|-------|-----------|-------------------| | Jan. | 21 | 185.79 | July | 68 | 621.55 | | Feb. | 24 | 214.47 | Aug. | 74 | 675.06 | | Mar. | 30 | 238.03 | Sept. | 62 | 562.03 | | Apr. | 37 | 284.84 | Oct. | 50 | 452.93 | | May | 50 | 454.58 | Nov. | 41 | 369.95 | | June | 59 | 530.03 | Dec. | 30 | 273.98 | #### Questions: a) Assuming a simple linear regression model is appropriate, fit the regression model relating steam usage (y) to the average temperature (x). What is the estimate of \( \sigma^2 \)? - Answer: \( \sigma^2 \) = 2.79 b) What is the estimate of expected steam usage when the average temperature is 55°F? - Calculation: \( \hat{y} = -6.34 + 9.21(55) \) - Answer: \( \hat{y} = 500.12 \) (thousand pounds) c) What change in mean steam usage is expected when the monthly average temperature changes by 1°F? - Answer: 9.21°F d) Calculate the fitted value of y and the corresponding residual if the monthly average temperature is 47°F. - Given: \( x = 47, \hat{y} = 424.84 \) - Fitted value calculation:
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