MINITAB was used to fit the complete second-order model
E(y) = β0 + β1x1 + β2x2 + β3x1x2 + β4x12 + β5x22
To n = 39 data points. (See the MINITAB printout on page 652.)
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 Y -24.56 + 1.12 x1 + 27.99 X2-0.54 X1X2-0.004 X1SQ + 0.002 X2SQ Predictor Constant X1 X2 X1X2 x1S0 X2so Coef -24.563 1.19848 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 -0.52 0.605 0.0004-10.74 .000 0.0033 0.60 0.550 S-2.762 R-Sq 79.7s R-Sq (adj ) 76.6 # # nalysis of variance Source Regression Residual Erro 33 251.81 Total DF S 989.30 197.86 25.93 0.000 7.63 38 1241.11