13 The data in MEAPSINGLE were used to estimate the following equations relating school-level perfor mance on a fourth-grade math test to socioeconomic characteristics of students attending school. The vari- able free, measured at the school level, is the percentage of students eligible for the federal free lunclh program. The variable medinc is median income in the ZIP code, and pctsgle is percent of students not liv- ing with two parents (also measured at the ZIP code level). See also Computer Exercise C11 in Chapter 3 math4 -96.77-833 pctsgle n 299, R2380 math4 93.00 275 pctsgle - 402 free 1.60) (.071) 070) n 299,R 459 math4 24.49 274 pctsgle- 422 free- .752 Imedinc +9.01 lexppp 59.24) (.161) n 299, R 472 (071) (358) (4.04) ath4 1752- .259 pctsgle - 420 free +8.80 lexppp 070) (3.76) (32.25) (.117) n 299, R472. ssion Analysis with Cross-Sectional Data (i) Interpret the coefficient on the variable pctsgle in the first equation. Comment on what happens (ii Does expenditure per pupil, entered in logarithmic form, have a statistically significant effect on (iii) If you had to choose among the four equations as your best estimate of the effect ofpotsgle and when free is added as an explanatory variable. performance? How big is the estimated effect? obtain a 95% confidence interval of Botsee, which would you choose? why