Consider the construction project situation and the model y = beta_0 + beta_1 x_

Question

Consider the construction project situation and the model y = beta_0 + beta_1 x_1 + beta_2 x_2 + beta_3 x^2 _1 + beta_4 x_1 x_2 + epsilon a. Using the fact that SSE = 59.9565 for the model y = beta_0 + beta_1 x_1 + beta_2 x_2 + epsilon and using the SAS output of Figure 9.14, calculate the partial F statistic for testing H_0: beta_3 = beta_4 = 0 versus H_1: At least one of beta_3 and beta_4 does not equal zero. b. Using an appropriate rejection point, decide whether or not we can reject H_0 in favor of H_1 by setting alpha equal to 05.

Explanation / Answer

a) F = ((SSE_r -SSE_ur)/q )/(SSE_ur/(n-k-1)

here q = 2 ,k = 4 ,n = 18 , SSR_ur = 12.24795

SSR_r =59.9565

SST is constant

hence required F -statistics

= ((59.9565 - 12.24795)/2)/ ( 12.24795 / (18 - 4-1))

= 25.318977

c) df1 = q = 2 , df2 = n-k-1 = 13

F-critical = 3.81

sinceTS> critical value

we reject the null

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