# Provide detailed steps and solution to the questions.

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Question description

Provide detailed steps and solution to the questions.

1. Consider multiple regression model,
݊ , … ,௞௜ ൅ ݁, ݅ ൌ 1, 2ݔߚ ൅ ⋯ ൅ ௜ଶݔߚ ൅ ௜ଵݔߚ ൅ ߚ ൌݕ
i) (15 points) Express above regression equation in the matrix form ࢟ൌ ࢋ ൅ ࢼࢄwhere ࢼൌ ሺߚ ߚߚሻ′. Denote
dimensions of each matrix and vector.
ii) (15 points) What are the assumptions for the model in matrix form?
iii) (15 points) OLS estimator for vector ෡ ࢼis ሺࢄࢄሻିଵ .࢟′ࢄCheck unbiasedness of .෡ ࢼ
iv) (15 points) Derive variance covariance matrix of .෡ ࢼ
2. Hypothesis test
You want to know the effect of education and experience on hourly wage. So, you ran eViews two times to see their
marginal effects. One is mean model which has only one parameter as a regressor. The other is multiple regression
model which has two independent variables and intercept term. Results are as follows.
Case 1) Mean model: ݁݃ܽݓൌ ݑ ൅ ߚ
Note that ܽ݃݁ݓis hourly wage in cents.
Dependent Variable: WAGE
Method: Least Squares
observations: 935
Variable Coefficient Std. Error
C 957.9455 13.22401
R‐squared 0 Mean dependent var 957.9455
Adjusted R‐squared 0 S.D. dependent var 404.3608
S.E. of regression 404.3608 Akaike info criterion 14.84356
Sum squared resid 153000000 Schwarz criterion 14.84874
Log likelihood ‐6938.365 Hannan‐Quinn criter. 14.84554
Durbin‐Watson stat 1.729921

Case 2) Multiple regression: ܽ݃݁ݓൌ ߚ ൅ ߚ݁݀ߚ ൅ ܿݑ݁݁ ൅ ݎ݁݌ݔ
Dependent Variable: WAGE
Method: Least Squares
observations: 935
Variable Coefficient Std. Error
C ‐272.5279 107.2627
EDUC 76.21639 6.296604
EXPER 17.63777 3.161775
R‐squared 0.135853 Mean dependent var 957.9455
Adjusted R‐squared 0.133999 S.D. dependent var 404.3608
S.E. of regression 376.2948 Akaike info criterion 14.70183
Sum squared resid 132000000 Schwarz criterion 14.71736
Log likelihood ‐6870.104 Hannan‐Quinn criter. 14.70775
Note that
݁݀ ܿݑis years of education and ݁ ݎ݁݌ݔis years of labor market experience.
i) (20 points) Test the hypothesis at the 10% significant level that education is useless to explain the wage. (You must
show how did you calculate test statistic and why you made your decision.)
ߚ :ܪൌ 0 vs ܪ: ߚ് 0
ii) (20 points) Test the hypothesis at the 5% significant level that education and experience do not explain the wage.
(You must show how did you calculate test statistic and why you made your decision.)
ߚ :ܪൌ 0 ൌ ߚvs ܪ: ߚ് 0, and ߚ് 0

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