Suppose you fit the model y = 0 + 1x1 + 2x21 + 3x2 + 4x1x2 to

Suppose you fit the model
y = β0 + β1x1 + β2x21 + β3x2 + β4x1x2
to n = 25 data points and find that
β̂0 = 1.26 β̂1 = -2.43 β̂2 = .05 β̂3 = .62 β̂4 = 1.81
= sβ̂1 = 1.21 sβ̂2 = .16 sβ̂3 = .26 sβ̂4 = 1.49
SSE = .41 R2 = .83
a. Is there sufficient evidence to conclude that at least one of the parameters β1, β2, β3, and β4 is nonzero? Test, using α = .05.
b. Test H0: β1 = 0 against Hα: β1 < 0. Use α = .05.
c. Test H0: β2 = 0 against Hα: β2 > 0. Use α = .05.
d. Test H0: β3 = 0 against Hα: β3 ≠ 0. Use α = .05.