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 Temperature Usage/1000 Jan 21 185.79 Feb 24 214.47 Mar 32 288.03 Apr 47 424.84 May 50 454.58 Jun 59 593.03 Jul 68 621.55 Aug 74 675.06 Sep 62 562.03 Oct 50 452.93 Nov 41 369.95 Dec 30 273.98 Suppose that the monthly average temperature is 47°F: 1- What will be the corresponding residual for the fitted value of y, suppose that the monthly average temperature is 47°F? 2- What is the expected change in mean steam usage when the monthly average temperature changes by 1°F? 3- What is the estimate of the error standard deviation σ? 4- What is the estimate of expected steam usage when the average temperature is 55°F?
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Step 1: Calculate the residual for the fitted value of y when the monthly average temperature is 47°F. Show more…
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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 Temp. Usage/1000 Jan. 21 185.79 Feb. 24 214.47 Mar. 32 288.03 Apr. 47 424.84 May 50 454.58 June 59 539.03 July 68 621.55 Aug. 74 675.06 Sept. 62 562.03 Oct. 50 452.93 Nov. 41 369.95 Dec. 30 273.98 (a) Assuming that 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 σ²? (b) What is the estimate of expected steam usage when the average temperature is 55°F? (c) What change in mean steam 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.
Lucas F.
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 | Temp. | Usage/1000 | Month | Temp. | Usage/1000 ---|---|---|---|---|--- Jan. | 21 | 185.79 | July | 68 | 621.55 Feb. | 24 | 214.47 | Aug. | 74 | 675.06 Mar. | 32 | 288.03 | Sept. | 62 | 562.03 Apr. | 47 | 424.84 | Oct. | 50 | 452.93 May | 50 | 454.58 | Nov. | 41 | 369.95 June | 59 | 539.03 | Dec. | 30 | 273.98 (a) Assuming that a simple linear regression model is appropriate, fit the regression model relating steam usage (y) to the average temperature (x). Linear regression model: ŷ = _ * x + _ R squared value for above model: R^2 = _ (b) What is the estimate of expected steam usage when the average temperature is 55°F? (c) What change in mean steam usage is expected when the monthly average temperature changes by 1°F?
Adi S.
The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 50 Buffalo residents the mean is 22.5 miles a day and the standard deviation is 8.4 miles a day, and for an independent simple random sample of 40 Boston residents the mean is 18.6 miles a day and the standard deviation is 7.4 miles a day. a. What is the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day? b. What is the 95$\%$ confidence interval for the difference between the two population means?
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