b please The model yi = beta_1 + beta_2 x_i2 + beta_3 x_i3 + beta_4 x_i4 + u_ is

Question

b please

The model yi = beta_1 + beta_2 x_i2 + beta_3 x_i3 + beta_4 x_i4 + u_ is estimated by the LS method based on 26 observations. The results are as in the following: y_i = 2 + 3.5x_i2 - 07x_i3 + 2x_4 +| u_ t_x2 = 1.9, t_x3 = 2.2, t_x4 = 1.5, and R^2 = 0.982 where T_xx denotes t - ratio of x_n. Now, with restriction beta_2 = beta_2 = beta_4, the estimated results are as in the following y_i = 1.5 + 3(x_i2 + x_i4) - 0.6 x_i3 u_i t_x2 + x4 = 2.7, x_3 = 2.4, and R^2 = 0.876 (a) Test the overall significance of the original model. (b) Test the hypothesis H_0: beta_2 = beta_4. State the assumptions if needed.

Explanation / Answer

Excel formula:

given R-sq= 0.982 no. of obs n= 26 (a) We test the model significance using F-test F-stat = MSR/MSE = =(SSR/(K-1))/(SSE/(N-K)) =SSR*(26-4)/(SSE*3) =(Rsq*SST*22/((1-Rsq)*SST*3) 400.0740741 P-VALUE= 2.46552E-19 <0.05; REJECT H0 & conclude that yes, regression is significant (b) we will check if the model is significantly changed in terms of R-sq. If not changed then we can conclude that beta2=beta4 H0: no change in Rsq Ha: changed F-stat= 1.121004566 p-value= 0.393245694 >0.05; so don’t reject H0 and conclude that both models have almost equal R-sq for beta2=beta4 assumption is reasonable

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