MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
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:
(a) Find a regression relating steam usage to temperature.
(b) Test for significance of regression using a=0.05.
(c) Find a 99% confidence interval for B1
Usage/
1000
Usage/
1000
Month Temp.
Month
Temp.
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.o
50
452.93
47
424.84
Oct.
May
50
454.58
Nov.
41
369.95
June
59
539.03
Dec.
30 a 273.98
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Transcribed Image Text: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: (a) Find a regression relating steam usage to temperature. (b) Test for significance of regression using a=0.05. (c) Find a 99% confidence interval for B1 Usage/ 1000 Usage/ 1000 Month Temp. Month Temp. 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.o 50 452.93 47 424.84 Oct. May 50 454.58 Nov. 41 369.95 June 59 539.03 Dec. 30 a 273.98
Expert Solution
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Step 1

Answer: Regression analysis is concerned with the study of the dependence of one variable, the dependent variable, on one or more other variables, the explanatory variables.

The two - variable linear model, or simple regression analysis, is used for testing hypothesis about the relationship between a dependent variable Y and an independent or explanatory variable X and for prediction. Simple linear regression analysis usually begins by plotting the set of XY values on a scatter diagram and determining by inspection if there exists an approximate linear relationship. It's model is,

Y= α+βX+e         Where α= intercept or constant and β = Slope or coefficient of regressor, e = Error term

In above example Y = The number of pounds of steam usage 

                             X = The average monthly temperature

Fit the regression model Y to X is Yi ^ =α ^ +β^ Xi  where Ee = 0by α ^ = Yi ^ -β^ Xiβ ^ = Cov(X,Y)δx2

                                                     β^ = nXiYi- XiYinXi2 -Xi2 

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