The data in MEAPSINGLE were used to estimate the following equations relating school-level performance on a fourth-grade math test to socioeconomic characteristics of students attending school. The variable free, measured at the school level, is the percentage of students eligible for the federal free lunch program. The variable medinc is median income in the ZIP code, and pctsgle is percent of students not living with two parents (also measured at the ZIP code level). See also Computer Exercise C11 in Chapter 3.

(i) Interpret the coefficient on the variable pctsgle in the first equation. Comment on what happens when free is added as an explanatory variable.

(ii) Does expenditure per pupil, entered in logarithmic form, have a statistically significant effect on performance? How big is the estimated effect?

(iii) If you had to choose among the four equations as your best estimate of the effect of pctsgle and obtain a 95% confidence interval of bpctsgle, which would you choose? Why?

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math4 = 96.77 - 833 pctsgle (1.60) (.071) n = 299, R? = .380 math4 = 93.00 - .275 pctsgle – 402 free (1.63) (.117) (.070) n = 299, R = 459 math4 = 24.49 – .274 pctsgle – 422 free - .752 Imedinc + 9.01 lexppp (59.24) (.161) (.071) (5.358) (4.04) n = 299, R? = .472 math4 = 17.52 - .259 pctsgle - 420 free + 8.80 lexppp (.070) (32.25) (.117) (3.76) = 299, R = .472.