27. Minitab output resulting from fitting a simple linear regression model with

Question

27. Minitab output resulting from fitting a simple linear regression model with time as the explanatory variable and BOD as the response follows. 10pts Predictor Constant Time Coef T 0.6578 0.1657 3.97 0.003 0.17806 0.014 12.72 0.000 R-Sq(adj) 94.1% S = 0.287281 R-Sq = 94.7% Analysis of Variance Source Regression Residual Error Total DF SS MS 1 13.344 13.344 161.69 0.000 0.743 0.083 10 14.087 (a) Assuming that a simple linear regression model is appropriate, estimate the regression model relating BOD ) to the time (). (b)What is the estimate of the variance? (c) What is the estimate of expected BOD level when the time is 9 days? (d) What change in mean BOD is expected when the time increases by 3 days? (e) Suppose the time used is 6 days. Calculate the fitted value of y and the corresponding residual. y 1.9,e-y- y(calculated). This exam is given under the Honor System and by signing here submitted is your work alone and that you neither gave nor received help from others on this exam. , you have agreed that the work

Explanation / Answer

a)

BOD=0.6578+0.17806*time

b)

estimate of variance =0.083

c)

expected BOD =0.6578+0.17806*9 =2.26034

d)

chane in BOD =0.17806*3=0.53418

e)

fited value =0.6578+0.17806*6 =1.72616

residual =1.9-1.72616 =0.17384

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