hw_T - 16 4290.53971 268.15873 C Total 19 19514.06800 Root...

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An experiment carried out to study the effect of the mole contents of cobalt (x1) and the calcination temperature (x2) on the surface area of an ironÂcobalt hydroxide catalyst (y) resulted in the following data ("Structural Changes and Surface Properties of CoxFe3ÂxO4 Spinels," J. of Chemical Tech. and Biotech., 1994: 161Â170): x1: .6 .6 .6 .6 .6 1.0 1.0 1.0 1.0 1.0 2.6 2.6 2.6 2.6 x2: 200 250 400 500 600 200 250 400 500 600 200 250 400 500 y: 90.6 82.7 58.7 43.2 25.0 127.1 112.3 19.6 17.8 9.1 53.1 52.0 43.4 42.4 x1: 2.6 2.8 2.8 2.8 2.8 2.8 x2: 600 200 250 400 500 600 y: 31.6 40.9 37.9 27.5 27.3 19.0 A request to the SAS package to fit a+b1*x1+b2*x2+b3*x3, where x3 = x1*x2 (an interaction predictor), yielded the following output: Dependent Variable: SURFAREA Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 3 15223.52829 5074.50943 18.924 0.0001 Error
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Unformatted text preview: 16 4290.53971 268.15873 C Total 19 19514.06800 Root MSE 16.37555 R-square 0.7801 Dep Mean 48.06000 Adj R-sq 0.7389 C.V. 34.07314 Parameter Estimates Parameter Standard T for H0: Prob Variable DF Estimate Error Parameter=0 > |T| INTERCEP 1 185.485740 21.19747682 8.750 0.0001 COBCON 1 -45.969466 10.61201173 -4.332 0.0005 TEMP 1 -0.301503 0.05074421 -5.942 0.0001 CONTEMP 1 0.088801 0.02540388 3.496 0.0030 a) Interpret the value of the coefficient of multiple determination. b) Predict the value of surface area when cobalt content is 2.6 and temperature is 250, and calculate the value of the corresponding residual. c) Since b1 is about -46.0, is it legitimate to conclude that if cobalt content increases by 1 unit while the values of the other predictors remain fixed, surface area can be expected to decrease by roughly 46 units? Explain your reasoning....
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hw_T - 16 4290.53971 268.15873 C Total 19 19514.06800 Root...

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