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:
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Dependent Variable: LOG(TESTSCR)
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Included observations: 420
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Variable
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Coefficient
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Std. Error
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C
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6.47807
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0.012361
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STR
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-0.000764
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0.000365
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LOG(AVGINC)
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0.018158
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0.002708
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EL_PCT
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-0.000431
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0.000117
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EL PCT^2
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0.000002
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0.000001
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MEAL PCT
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-0.000588
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4.76E-05
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COMP_STU
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0.024809
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0.010622
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R-squared
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0.802032
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Sum squared resid
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0.070317
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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:
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Dependent Variable: LOG(TESTSCR)
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Included observations: 420
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Variable
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Coefficient
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Std. Error
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C
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6.387050
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0.010417
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STR
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-0.000306
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0.000410
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LOG(AVGINC)
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0.043558
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0.002089
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EL PCT
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-0.001161
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0.000119
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EL_PCTA2
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8.55E-06
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1.91 E-06
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R-squared
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0.725978
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Sum squared resid
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0.097331
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