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Water pollution is a serious problem in the tanning industry. Tannery wastes are

ID: 3233941 • Letter: W

Question

Water pollution is a serious problem in the tanning industry. Tannery wastes are characterized high values of chemical demand. In a study, 33 samples of chemically treated waste were taken and readings on x, the percentage reduction in total solids and y, the percent reduction in chemical oxygen demand were recorded. Based on these data, the following summary statistics have been obtained: sigma^33 _i = 1 x_i = 1104, sigma^33 _i = 1 y_i = 1124, sigma^33 _i = 1 x^2 _i = 41, 086, sigma^33 _i = 1 x_i y_i = 41, 355, sigma^33 _i = 1 y^2 _i = 41, 988. Use these values for Problems 5-7 below. Estimate the regression line mu_Y |x = b_0 + b_1 x for these pollution data. Mao give an unbiased estimate s^2 for the model error variance.

Explanation / Answer

here SSx=41086-(1104)2/33=4152.182

SSy=41988-(1124)2/33=3703.879

Sxy=41355-1104*1124/33=3752.091

hence b1=Sxy/SSx =0.9036

and bo=ybar-xbar*bo=1124/33 -0.9036*1024/33=6.0203

hence line equation:Yhat=6.0203+0.9036x

R2 =(Sxy)2/(SSx*SSy)=0.9154

SSE =(1-R2)*SSy=313.33

here estimated s2 =SSE/(n-2)=10.107