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4. (35 points) The data in the table below was taken from the article Applying Stepwise Multiple Regression Analysis to the Reaction of Formaldehyde with Cotton Cellulose by E. J. Gonzales and S. P. Rowland (Textile Research J., 1984: 157-165). The response variable y is durable press rating, a quantitative measure of wrinkle resistance. The four independent variables (predictors) used in the model building process are c1 = HCHO (formaldehyde) concentration, 12, catalyst ratio, 3, curing temperature and ra, curing time.100 1.4 2 1.80 2.2 1.80 4.6 120 4.9 1.80 1.6 1.80 4.7 7 13 140 4.6 5 7 4.5 9 140 10 5 100 1.4 11 140 4.7 12 2 100 1.6 13 180 4.5 14 120 4.7 15 10 13 180 16 160 4.6 17 13 100 4.3 10 10 120 7 4.9 19 100 1.7 201 13 140 4.6 21 10 1 180 2.6 22 2 13 140 3.1 23 13 140 4.7 24 7 120 2.5 25 5 13 140 4.5 160 7 2.1 27 180 1.F 28 160 1.5 100 1.3 30 100 7 4.6Consider the full model consisting of predictors: 21, .... IA, Is = Ti, ..., I; = Pj, Ig = Ijl2, ..., $14 = rar (all first- and second-order predictors). Is the inclusion of the second-order predictors justified? That is, should the reduced model consisting of just the predictors r1, 12, ra and ra, be used? The output resulting from fitting the two models follows: Parameter Estimate for Reduced Model Estimate for Full Model Bo -.9122 -8.807 B1 16073 1768 82 .21978 .7580 Ba .011226 10400 BA .10197 -5052 -.04393 Be -.035887 - -.00003271 -.01646 .00588 B10 .002702 811 I -01178 812 I -.0006547 Bia .00242 B14 .002526 12 .692 921 SSE 17.4951 4.4782 a. What is the mull hypothesis? b. What is the test statistic? What is its value? c. Should we reject the null hypothesis at an a = 0.01