Question

> ml < lm(grad.rate-Average.loans+SAT.reading.25p+SAT.math.25p+SFR +sector,data-ouryearipeda) summary (ml) Call: Im(formulagrad.rateAverage.loansSAT.reading.25p SAT.math.25p SFR +sector, data-fouryearipeda.) Residuals: -54.768 -6.150 0.596 6.601 38.514 Coefficients: Min 1Q Median 3Q Max Estimate Std. Error t value Pr>ltl) -4.331e+01 3.046e+00 -14.221 <2e-16 (Intercept) Average.loans SAT.reading.25p SAT.math.25p SFR sectorPublic, 4-year or above -2.602e+00 7.907e-01 -3.291 0.00103* .573e-03 1.963e-04 8.011 2.77e-15 8.455e-02 1.178e-02 7.177 1.27e-12* 1.086e-01 1.072e-02 10.138 <2e-16 -1.812e-01 9.119e-02 -1.988 0.04710 Residual standard error: 9.855 on 1149 degrees of freedom (1219 observations deleted due toniAnǐngnes Multiple R-squared: 0.6859, Adjusted R-squared: 0.6845 P-statistic: 501.7 on 5 and 1149 DF, p-value 2.2e-16 > anova (m1) Analysis of Variance Table Response: grad.rate Df Sum Sq Mean Sq F value Pr>F) Average.loans SAT.reading.25p SAT.math.25p SFR sector Residuals 1 11715 11715 120.6182.2e-16 1 220038 220038 2265.507 2.2e-16 1 8646 8646 89.014< 2.2e-16 1 2198 2198 22.628 2.215-06* 1149 111597 Sigpif. codes: 0* 0.0010.01*0.050.1'' 1 grad.rate: the percent of students who graduate within four years. Values are integers that represent percents. For example, 23 means the graduation rate is 23%. sector: Indicates whether public or private school. Average.loan: in dollars, the average student debt at graduation SAT.read.25p: the 25th percentile of the SAT reading score for enrolled students SAT.math.25p: the 25th percentile of the SAT math score for enrolled students. SFR: student-faculty ratio. (Number of students per full-time faculty member) 1. (3) According to the output, do public schools and private schools differ in mean graduation rates, controlling for the other variables? Give an answer ("yes" or "no") and explain how you reached this conclusion. Use a 5% significance level

Answer 1

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