Let math10 denote the percentage of students at a Michigan high school receiving a passing score on a standardized math test (see also Example 4.2). We are interested in estimating the effect of per student spending on math performance. A simple model is
math10 5 b0 1 b1log(expend) 1 b2log(enroll) 1 b3 poverty 1 u,
where poverty is the percentage of students living in poverty.
(i) The variable lnchprg is the percentage of students eligible for the federally funded school lunch program. Why is this a sensible proxy variable for poverty?
(ii) The table that follows contains OLS estimates, with and without lnchprg as an explanatory variable.
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Dependent Variable: math10
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Independent Variables
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(1)
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(2)
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log(expend)
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11.13
(3.30)
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7.75
(3.04)
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log(enroll)
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.022
(.615)
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-1.26
(.58)
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lnchprg
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-
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-.324
(.036)
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intercept
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269.24
(26.72)
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223.14
(24.99)
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Observations
R-squared
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428
.0297
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428
.1893
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Explain why the effect of expenditures on math10 is lower in column (2) than in col- umn (1). Is the effect in column (2) still statistically greater than zero?
(iii) Does it appear that pass rates are lower at larger schools, other factors being equal? Explain.
(iv) Interpret the coefficient on lnchprg in column (2).
(v) What do you make of the substantial increase in R2 from column (1) to column (2)?