Suppose that, from a sample of 63 observations, the least squares estimates and the corresponding estimated covariance matrix are given by

Using a 5\% significance level, and an alternative hypothesis that the equality does not hold, test each of the following null hypotheses:

a. \(\beta_{2}=0\)

b. \(\beta_{1}+2 \beta_{2}=5\)

c. \(\beta_{1}-\beta_{2}+\beta_{3}=4\)

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b b b3 2 3-21 = 3 cov (b, b,b) = = -2 4 0 1 03