Question

A plant distills liquid air to produce oxygen, nitrogen, and argon. The percentage of impurity in the oxygen is thought to be linearly related to the amount of impurities in the air as measured by the "pollution count" in parts per million (ppm). A sample of plant operating data is shown below: x:Purity (%) 93.3 92.0 92.4 91.7 94.0 94.6 93.6 1.2 1.5 1.6 0.8 Pollution count (ppm) Summary statistics: x-93.09, sx-1.08, у-1.24, sy-0.28, pXY-_0.97 (linear correlation coefficient) (a) Fit a linear regression model on the data using least square. y + βιχ + €,e-N(0,02) (b) Predict the pollution count when the purity in the oxygen is 90% (c) Find the estimate of σ 2 (variance of error terms) (d) Find the goodness-of-fit of the model (R2), (e) Find the 95% confidence interval on the slope. Is the effect of percentage of impurity in the oxygen significant?

Answer 1

Ba Sy ty bd -,0.97 -0,2933 ニー0,276 Sx 124-(-0,271c) C93,og)

C To find So 11 27-C8 7)2 2 '3774 K1-2) : 0 075 das explained by ac 82.-t,ー

β'--0,2716. , L-O ルイ097 ) (-σ.gri, con fielamcem