Are the following statements about the normal linear model y = X + , N (0, 2In)

Question

Are the following statements about the normal linear model y = X + , N (0, 2In) true or false? Please explain why they are true or false.

(i) The hypothesis that the OLS estimator is equal to zero can be tested by means of a t-test.

(ii) If the t-value of a coefficient is smaller than 1.96 (when 2 is known), we accept the null hypothesis that the coefficient is zero with 95% confidence.

(i) If an explanatory variable has a significant impact on the dependent variable at the 10% level, then its impact is also significant at the 5% level.

Explanation / Answer

(i)

True

(t-test allows to check the significance as well as hypothesis testing for a variable)

(ii)

True

(iii)

False

(It is not necessary that the variable will be significant at lower significance level also)

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