A chemical firm tests the yield that results from the presence of varying amounts of two catalysts. Yields are measured for five different amounts of catalyst 1 paired with four different amounts of catalyst 2. A second- order model is fit to approximate the anticipated nonlinear relation. The variables are y = yield, x1 = amount of catalyst 1, x2 = amount of catalyst 2, x3 = x21, x4 = x1x2, and x5 = x22. Selected output from the regression analysis is shown here.

a. Write the estimated complete model.
b. Write the estimated reduced model.
c. Locate the R2 values for the complete and reduced models.
d. Is there convincing evidence that the addition of the second- order terms improves the predictive ability of the model?

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Multipie Regression Analysia Dependent variable: Yield Table ot D3timates Standard Error Dstimate Value Value Constant Cati cat2 catisq Gcaticat2 catzsq 50:0195 4.3905 2.01212 2.73977 0.301968 0.319573 0.50529 11.39 3.30 2.67 4.08 -2.42 -2.33 0 0300 0 005 0.018 0:0011 0:0299 0.0355 6.64357 7.3145 -1.23143 0.7724 -1.1355 R-squared 6-24 Adjusted R-squared = Bl .33% Standard error of estimation 2.25973 Analy뮤1s or variance Sum of Source Model Error Squares D.P. ean Sqare F-Ratio Value 448.193 71.489 17 55 0.0000 14 S.10636 Total (corr.) 519.682 19 Conditional Sums of Equares Sum of Source Squares D.F Hean Square F-Ratto value 286.439 19.3688 84 9193 29.8301 27.636 296.439 Cati Cat2 catisq eCaticat2 catzsg Model 19.3698 84.9193 29.8301 27 636 56.09 0.0000 3 790.0719 16.63 0.0011 5 B4 0.0299 5.41 0.0355 448-193 Miltiple Regression Analys18 Dependent vartabie: rield Table of Estimates scandard Error Estimate Value Value Cons tant Cati Cat2 70.31 -2.676 -0 . е 802 2. 57001 0:560922 0.70939 27.36 -4.37 0.0000 0.0002 0,2315 R-squared 5g,85 Adjusted R-squared 54.008 Standard error of estimation3.54695 Analysis of variance Sum of Gource squares D.E. Mean Square -Ratio Value Model rror 2 152.904 17 05 809 12 150.0005 213.874 12.5009 Totai (corr 519.682