Question

Linear regression		Number of obs = 714
		F( 10, 703) = 18.63
		Prob > F = 0.0000
		R-squared = 0.2102
		Root MSE = 7.748
Robust
finprof Coef.	Std. Err.	t	P>t	[99% Conf. Interval]
treatment 4.907879	.5935881	8.27	0.000	3.374736 6.441023
numstudents -.0030472	.0009961	-3.06	0.002	-.00562 -.0004745
numteachers .0252369	.0203227	1.24	0.215	-.0272533 .0777272
perc_fem .0570269	.0189111	3.02	0.003	.0081826 .1058712
perc_momsec .0414125	.0224185	1.85	0.065	-.0164909 .099316
perc_dadsec .0113967	.0244705	0.47	0.642	-.0518067 .0746001
perc_transfer -.0719767	.021672	-3.32	0.001	-.127952 -.0160015
perc_comp .0259924	.0187199	1.39	0.165	-.0223581 .074343
perc_failonce -.0945593	.016901	-5.59	0.000	-.1382119 -.0509067
perc_nowork -.0266942	.0173134	-1.54	0.124	-.071412 .0180237
_cons 55.85265	2.146482	26.02	0.000	50.30863 61.39667

As a way to test whether E[ui∨treatmenti]=0, researchers sometimes estimate a regression of treatment on other independent variables and check if they are jointly statistically significant. Perform this exercise by first regressing treatment on the following control variables (in a single regression): number of students in school, number of teachers in school, % female, % mother has secondary schooling, % father has secondary schooling, % receiving cash transfer, % with computer with internet, % students failed at least one year, % students not working.

Then perform a test of model significance, and comment on whether the result does or does not support the assumption E[ui∨treatmenti]=0

Answer 1

First Checking for Individual significance of independent variables

From the given result table we can see there is a column for t-stat and p-value. By considering alpha as 0.05, we can conclude whether the variable is significant or not.

the general rule for testing the significance is "if the p-value is less than alpha result is significant and vice versa"

From the p-value column of regression coefficients we can see that p-values for variables numteachers .0252369 ' , perc_momsec .0414125 " , perc_dadsec .0113967 , perc_comp .0259924 , perc_nowork -.0266942   has p-valus more than alpha hence these variables are not significant and the rest others are significant.

For testing the overall significance we use F-test, it is given that the Prob > F = 0.0000 which says that p-value is zero and we conclude that the overall regression is significant.