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. math4 = 96.77 – .833 pctsgle (1.60) (.071) n = 299, R² = .380 math4 = 93.00 – .275 pctsgle – 402 free (.070) (1.63) (.117) n = 299, R2 = .459 math4 = 24.49 .274 pctsgle – 422 free – .752 Imedinc + 9.01 lexppp (59.24) (.161) n = 299, R2 = .472 (.071) (5.358) (4.04) math4 = 17.52 – .259 pctsgle – 420 free + 8.80 lexppp (32.25) (.117) n = 299, R² = .472. (.070) (3.76) (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 Bpetsgles which would you choose? Why?
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. math4 = 96.77 – .833 pctsgle (1.60) (.071) n = 299, R² = .380 math4 = 93.00 – .275 pctsgle – 402 free (.070) (1.63) (.117) n = 299, R2 = .459 math4 = 24.49 .274 pctsgle – 422 free – .752 Imedinc + 9.01 lexppp (59.24) (.161) n = 299, R2 = .472 (.071) (5.358) (4.04) math4 = 17.52 – .259 pctsgle – 420 free + 8.80 lexppp (32.25) (.117) n = 299, R² = .472. (.070) (3.76) (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 Bpetsgles which would you choose? Why?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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,
Transcribed Image Text: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.
math4 = 96.77 – .833 pctsgle
(1.60) (.071)
n = 299, R² = .380
math4 = 93.00 – .275 pctsgle – 402 free
(.070)
(1.63) (.117)
n = 299, R2 = .459
math4 = 24.49
.274 pctsgle – 422 free – .752 Imedinc + 9.01 lexppp
(59.24) (.161)
n = 299, R2 = .472
(.071)
(5.358)
(4.04)
math4 = 17.52 – .259 pctsgle – 420 free + 8.80 lexppp
(32.25) (.117)
n = 299, R² = .472.
(.070)
(3.76)
(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 Bpetsgles which would you choose? Why?
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