University of California at Berkeley
Economics Department
Economics 140
Homework 4
1. Using matrix notation, demonstrate that given y=X+
1
ˆOLS X T X X T y 2. Using matrix notation, demonstrate that given y=X+
R2 T X T X
Y TY 3. Demonstrate that the OLS error term can be written as e I X XTX 1 X T y My 4. Demonstrate that M is symmetric and idempotent.
5. Let yˆ Xˆ X ( X T X ) X T y Py . Show that P is symmetric and idempotent
6. Use data set uslifeexp.dta to answer the following:
A. What are the regression estimates for the model
Years Life Expec tan cyi 1Yeart 2 Malei 3White i Report your estimated coefficients, standard errors, and t-statistic in a table. Demarcate
statistical significance with *** at α=.01; ** at α=.05, and * at α=.10 next to the
coefficient.
B B. Which variables are significant in explaining Life Expectancy?
C C. Is the model significant in explaining Life Expectancy? D. What is the variation in Life Expectancy that can be explained by variation in the
model?
7. Use data set women.dta to estimate the following equation:
WHRS i 1 Agei 2 Agei2 3 HHRS 4 Fa min ci i where whrsi is the number of hours worked by a women in a year; hhrsi is the number of
hours her husband works during the year, and faminci is family income. Report your
estimated coefficients, standard errors, and t-statistic in a table. Demarcate statistical
significance with *** at α=.01; ** at α=.05, and * at α=.10 next to the coefficient.
A. What is the estimated regression equation for the model?
B. Which variables are significant in explaining women’s work hour?
D C. Is the model significant in explaining women’s work hours?
D. What is the variation in women’s work hours that can be explained by variation in the
model?

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