(10 marks) Consider the following regression model

Yi=0+1X1i+2X2i+3X3i+4X4i+5X5i+ui

This model has been estimated by OLS. The Gretl output is below, followed by the estimate of the covariance matrix of the estimated parameters.

Model 1: OLS, using observations 1-64

coefficient std. error t-ratio p-value

Const -2.1251 0.6699 -3.1722 0.0024

X1 1.0808 0.2870 3.7654 0.0004

X2 0.3086 0.6461 0.4777 0.6347

X3 -0.1845 0.1963 -0.9399. 0.3512

X4 -1.1133 0.1819 -6.1205 0.0000

X5. 1.1584 0.1610 7.1974 0.0000

Mean dependent var = 2.4923

S.D. dependent var = 3.5275

Sum squared resid = 242.69

S.E. of regression = 2.0456

R-squared = 0.69042

Adjusted R-squared = 0.66373

F(5, 58) = 25.87

P-value(F) = 0

Log-likelihood = 133.47

Akaike criterion = 278.93

Schwarz criterion = 291.88

Hannan-Quinn = 284.03

Const X1 X2 X3 X4 X5

Const 0.44875 0.06749- 0.23991 -0.04240 -0.04398. -0.04214

X1 0.06749 0.08239. 0.00832. -0.00466 0.00449. -0.00669

X2 -0.23991 0.00832 0.41743 -0.01234 -0.00227. -0.00740

X3 -0.04240. -0.00466 -0.01234. 0.03854 0.00301 -0.00216

X4 -0.04398. 0.00449. -0.00227. 0.00301 0.03309 0.00245

X5 -0.04214 -0.00669 -0.00740 -0.00216 0.00245. 0.02590

Use a t-test with the critical value method and a significance level of 5% to test 0:4=3against1:43