Reference no: EM13116106

We want to understand the determinant factors that explain students' performance in fifth-grade tests. We observe a sample of 420 districts in California and the following variables:

- TESTSCR: average score of the district in math & reading test
- STR: average Students-Teacher Ratio in the district
- AVGINC: average income in the district (measured in thousand of $)
- EL_PCT: % of students for which English is second language
- MEAL_PCT: % of students in the district eligible for reduced price lunch
- COMP_STU: average number of computers per student

We estimate by OLS the following regression model in Rviews:

Dependent Variable: LOG(TESTSCR)
Included observations: 420
Variable	Coefficient	Std. Error
C	6.47807	0.012361
STR	-0.000764	0.000365
LOG(AVGINC)	0.018158	0.002708
EL_PCT	-0.000431	0.000117
EL PCT^2	0.000002	0.000001
MEAL PCT	-0.000588	4.76E-05
COMP_STU	0.024809	0.010622
R-squared	0.802032
Sum squared resid	0.070317

1. Interpret the coefficient of LOG(AVGINC). Are its sign consistent with your expectations? Justify your answer.

2. Test the significance of the coefficient of MEAL_PCT at the 5% significance level) against the alternative hypothesis that it is negative.

3. Based on the regression results in table 1, is there evidence of a quadratic relationship between the dependent variable and EL_PCT? Justify your answer.

4. Test the overall significance of the regression

5. Discuss the goodness of fit of the model in table 1.

You are provided the following regression output:

Dependent Variable: LOG(TESTSCR)
Included observations: 420
Variable	Coefficient	Std. Error
C	6.387050	0.010417
STR	-0.000306	0.000410
LOG(AVGINC)	0.043558	0.002089
EL PCT	-0.001161	0.000119
EL_PCTA2	8.55E-06	1.91 E-06
R-squared		0.725978
Sum squared resid		0.097331