The number of pounds of steam used per month by a chemical plant is thought to b

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 temperature are shown in the following table.

(b) Which of the following is the correct form of the fitted regression line for this example?

(c) Compute the residuals using the fitted regression equation from part (b).

(d) Compute SSE and estimate the variance.

(e) Find the standard error of the slope and intercept coefficients.

(f) Compute the coefficient of determination, R2.

(g) Calculate the t-test statistic for testing H0: 0 = 0 and H0: 1 = 0

(h) calculate the F statistic

(i) Construct 95% CIs on the intercept and slope.

(j) Compute the sample correlation coefficient.

(k) Test for significance of regression by using the F test statistic and bounding the resulting P-value. Select the appropriate conclusion.

(L) Test for significance of the sample correlation coefficient at = 0.05. Find bounds for the corresponding P-value. Based on the P-value, do you reject or fail to reject H: = 0. Select the appropriate conclusion.

Month Temp.
x Usage/1000
y Month Temp.
x Usage/1000
y Jan. 22 186.23 July 68 621.55 Feb. 24 215.20 Aug. 74 674.71 Mar. 32 288.03 Sept. 62 562.03 Apr. 47 424.84 Oct. 49 452.93 May 49 454.33 Nov. 41 369.92 June 59 539.03 Dec. 30 273.98

Explanation / Answer

sol)

The regression equation is

y=a+bx

From Excel

b) The fitted Regression equation is

y= -8.8765 +9.2806(X)

c) Residuals

d) ANOVA

SSE=264.88

e) From Excel

f) Coefficient of determination is 0.99

Coefficients Standard Error Intercept -8.876519519 4.447879129 x 9.280607243 0.090321188

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