Let mathl0 denote the percentage of students at a Michigan high school receiving a passing score on

Question:

Let mathl0 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 - (0 + (1 log(expend) + (2 log(enroll) + (3 poverty + u,
Where poverty is the percentage of students living in poverty.
(i) The variable Inchprg 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 Inchprg as an explanatory variable.

Explain why the effect of expenditures on mathl0 is lower in column (2) than in column (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 Inchprg in column (2).
(v) What do you make substantial increase in R2 from column (1) to column (2)?