Minitab was used to fit the complete second-order model
E(y) = β0 + β1x1 + β2x2 + β3x1x2 + β4x21 + β5x22
to n = 39 data points. The printout is shown below.

a. Is there sufficient evidence to indicate that at least one of the parameters-β1, β2, β3, β4, and β5 -is nonzero? Test using α = .05.
b. Test H0: β4 = 0 against Ha: β4 ‰  0. Use α = .01.
c. Test H0: β5 = 0 against Ha: β5 ‰  0. Use α = .01.
d. Use graphs to explain the consequences of the tests in parts b and c.

The regression equation is 1 24.56 +1.12 XI 27.99 2-0.54 X1X20.004 X1S0 + 0.002 x2sQ Predictor Constant Coef -24.563 1.1984e 27.988 -0.5397 -0.0043 0.0020 SE Coef 6.531 -3-76 0.001 0.1103 10.86 0.000 79.489 0.35 0.727 1.0338-D.52 0.605 0.0004-10.74 0.000 0.0033 0.60 0.550 x1so X2sQ 2 , 762 R-Sq 79.7s R-Sq (adj) 76.6% - Analysis of Variance DF Regzession Residual Error 33 251.81 7.63 Total 5 989.30 197.8625.93 0.000 38 1241.11