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
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