Question

2. An econometrician estimates the following two equations: = 2.4 + 4.8 X‘ + 42.6 Z. + 4.98 Si + 1.42T, (28.21 (15) (1.10)(6.42) (4.42) (t-statistics in parentheses) and -1.78 + 3.3as, + 7.67; The sample consists of 45 observations. The error sum of squares for the first regression is 400 and the a) At a 5% significance level, which of the independent variables in the first equation have a significant (b) At a 5% significance level, use a Wald test to test for the joint significance of the variables X and error sum of squares for the second regression is 500. effect on the dependent variable? Explain. (10 points) 2. (15 points)

Answer 1

a)

t = Coefficient / Error

p-value = TDIST(t,n-1,2)

VariableCoefficient Error p-value 2.91 0.005664 38.73 0.000000 4.8 42.6 4.98 1.42 1.65 1.1 5.42 24.42 0.920.3632 0.06 0.953893

From the above table, p-value for X and Z is less than 0.05. Hence at 5% significance level, X and Z are significant variables.

b)

Null and Alternate Hypothesis

H₀: β₁ = β₂ = 0

H_a: β₁ <> 0 or β₂ <> 0

Test Statistic

(SSR - SSRurq SSRur(n (k+ 1))

Where,

SSR_r is the sum of the squared residuals of the restricted model = 500

SSR_ur is the sum of the squared residuals for unrestricted model = 400

n = 45

k is the number of independent variables in the unrestricted model = 4

q is the number of restrictions (or the number of coefficients being jointly tested) = 2

Hence, F = {(500-400)/2}/{400/(45-4-1} = 5

Alpha = 0.05

F_Critical (q,n-k-1) = 3.23

Result

Since our F is greater than F_Critical we reject the null hypothesis.

Conclusion

Removing X and Z from the Model affects the residuals.