chapter 1

Chapter 12: Simple Linear Regression and Correlationb. Using linear regression to predict HW from BOD POD seems reasonable after looking atthe scatterplot, below.2015HW102712BOD17The least squares linear regression equation, as well as the test statistic and p value for amodel utility test, can be found in the Minitab output below. We see that we do havesignificance, and the coefficient of determination shows that about 75% of the variationin HW can be explained by the variation in BOD.The regression equation isHW = 4.79 + 0.743 BODPredictor Coef StDev T PConstant 4.788 1.215 3.94 0.001BOD 0.7432 0.1003 7.41 0.000S = 2.146 R-Sq = 75.3% R-Sq(adj) = 73.9%Analysis of VarianceSource DF SS MS F PRegression 1 252.98 252.98 54.94 0.000Residual Error 18 82.89 4.60Total 19 335.8785. For the second boiler, n = 19 , x = 125 , y = 472. 0 , 2 = 3625Σ iy i iΣ iΣy 2 i= 37,140.82 , and Σ x = 9749. 5 , giving =ˆ1Σ ix ,γ estimated slope− 503= = −.0821224, γ ˆ0= 80. 377551 , SSE2= 3. 26827 , SSx2= 1020. 833 .6125For boiler #1, n = 8, βˆ1= −. 1333 , SSE1= 8. 733 , and SSx1=1442. 875 . Thus8.733 + 3.286− .1333 + .0821σ ˆ 2 == 1.2, σ ˆ = 1. 095 , and t =101.095 +11442.87511020.833− .0512= = −1.14. t. 025,10= 2. 228 and –1.14 is neither ≥ 2. 228 nor ≤ −2. 228.0448β = .H o is not rejected. It is plausible that11γ, so392