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2. (6 marks) Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1, MLR.2, MLR.3, MLR.4, MLR.5 and MLR.6: y = ?0 + ?1 x1 + ?2 x2 + ?3 x3 + u You would like to test the null hypothesis: ?1 - 5?2 = 3. i. Let ??1 and ??2 denote the OLS estimators of ?1 and ?2. Find var(??1 - 5??2) in terms of the variances of ??1 and ??2 and the covariance between them. What is the standard error of ??1 - 5??2 in terms of the standard errors of ??1 and ??2 and the covariance between them? ii. Write the t statistic for testing ?1 - 5?2 = 3. iii. Define ?1 = ?1 - 5?2 and ??1 = ??1 - 5??2. Write a regression equation involving ?0, ?1, ?2, and ?3 that allows you to directly obtain ??1 and its standard error.

          2. (6 marks) Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1, MLR.2, MLR.3, MLR.4, MLR.5 and MLR.6:

y = ?0 + ?1 x1 + ?2 x2 + ?3 x3 + u

You would like to test the null hypothesis: ?1 - 5?2 = 3.

i. Let ??1 and ??2 denote the OLS estimators of ?1 and ?2. Find var(??1 - 5??2) in terms of the variances of ??1 and ??2 and the covariance between them. What is the standard error of ??1 - 5??2 in terms of the standard errors of ??1 and ??2 and the covariance between them?

ii. Write the t statistic for testing ?1 - 5?2 = 3.

iii. Define ?1 = ?1 - 5?2 and ??1 = ??1 - 5??2. Write a regression equation involving ?0, ?1, ?2, and ?3 that allows you to directly obtain ??1 and its standard error.

2. (6 marks) Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1, MLR.2, MLR.3, MLR.4, MLR.5 and MLR.6:

y = ?0 + ?1 x1 + ?2 x2 + ?3 x3 + u

You would like to test the null hypothesis: ?1 - 5?2 = 3.

i. Let ??1 and ??2 denote the OLS estimators of ?1 and ?2. Find var(??1 - 5??2) in terms of the variances of ??1 and ??2 and the covariance between them. What is the standard error of ??1 - 5??2 in terms of the standard errors of ??1 and ??2 and the covariance between them?

ii. Write the t statistic for testing ?1 - 5?2 = 3.

iii. Define ?1 = ?1 - 5?2 and ??1 = ??1 - 5??2. Write a regression equation involving ?0, ?1, ?2, and ?3 that allows you to directly obtain ??1 and its standard error.

Added by Sophia L.

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