ii. Estimate the regression model

educ = ₀ + ₁motheduc + ₂fatheduc + u

by OLS and report the results in equation form.

A:

iii. How much sample variation in educ is explained by parents' education? Interpret the coefficient motheduc.

A:

iv. Estimate the regression model

educ = ₀ + ₁motheduc + ₂fatheduc + ₃abil + u

by OLS and report the results in equation form.

A:

v. Does the variable abil (a measure of cognitive ability) help explain variations in education even after controlling for parents' education? Explain.

A:

vi. Using the equation in part (iv), test H₀: ₁ = ₂ against the two-sided alternative. What is the p-value of the test? What do the results of this test indicate in common language?

A:

regress educ motheduc fatheduc Source SS d f MS Number of obs = 1, 230 F (2, 1227) - 203. 68 Model 1697 . 9676 2 848 . 9838 Prob > F 0 . 0000 Residual 5114. 31207 1, 227 4. 1681435 R-squared 0 . 2493 Adj R-squared 0 . 2480 Total 6812. 27967 1, 229 5. 54294522 Root MSE 2 . 0416 educ Coefficient Std. err. t P> [ t | [95% conf. interval] motheduc . 3041971 . 0319266 9.53 0 . 000 . 2415603 . 366834 fatheduc . 1902858 . 0222839 8 .54 0 . 000 . 1465669 . 2340046 cons 6. 964355 3198205 21. 78 0 . 000 6 . 336899 7 . 59181regress educ motheduc fatheduc abil Source SS df MS Number of obs 1, 230 F (3, 1226) 305. 17 Model 2912 . 30705 3 970 . 769018 Prob > F 0 . 0000 Residual 3899. 97262 1, 226 3. 18105434 R-squared 0 . 4275 Adj R-squared 0 . 4261 Total 6812 . 27967 1, 229 5.54294522 Root MSE = 1 . 7836 educ Coefficient Std. err. t P> | t | [95% conf. interval] motheduc 1891314 0285062 6. 63 0 . 000 . 1332051 2450578 fatheduc . 1110854 . 0198849 5 . 59 0 . 000 0720733 1500976 abil . 5024829 . 025718 19.54 0 . 000 . 4520268 552939 _cons 8 . 44869 . 2895407 29 . 18 0 . 000 7 . 88064 9 . 01674