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Unformatted text preview: Jeffrey Wan 20232018 Homework 3 STAT 331 Fall 2008 1. DESCRIPTIVE ABSTRACT: The data set was derived from two sources: 1) U.S. News & World Report's 1995 Guide to Americas Best Colleges and 2) AAUP's (American Association of University Professors) 1994 Salary Survey (see http://www.stat.duke.edu). VARIABLE DESCRIPTIONS: tuition College tuition ("out-of-state" rate for those with in-state discount). pcttop25 Percent of new students from the top 25% of high school class. sf_ratio Student to faculty ratio. fac_comp Average faculty compensation. accrate Fraction of applicants accepted for admission. graduat Percent of students who graduate. pct_phd Percent of faculty with Ph.D.'s. fulltime Percent of undergraduates who are full time students. alumni Percent of alumni who donate. num_enrl Number of new students enrolled. public Is the college a public or private institution? (public=0, private=1) Values are aligned and delimited by blanks. Not available observations are denoted as NA. YOUR TASK Based on a linear regression model to be developed, answer the following questions: 1 1) What variables are related to tuition? Why? Justify your answer. > l <- lm(data$tuition ~ data$pcttop25 + data$sf_ratio + data$fac_comp + data$accrate + data$graduat + data$pct_phd + data$fulltime + data$alumni + data$num_enrl + data$public) > summary(l) Call: lm(formula = data$tuition ~ data$pcttop25 + data$sf_ratio + data$fac_comp + data$accrate + data$graduat + data$pct_phd + data$fulltime + data$alumni + data$num_enrl + data$public) Residuals: Min 1Q Median 3Q Max -9085.95 -1257.75 -18.33 1256.65 11017.37 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -2.542e+03 9.887e+02 -2.571 0.010328 * data$pcttop25 -3.048e-01 5.426e+00 -0.056 0.955208 data$sf_ratio -1.749e+02 2.319e+01 -7.544 1.25e-13 *** data$fac_comp 1.288e-01 1.043e-02 12.340 < 2e-16 *** data$accrate 6.292e+00 6.357e+02 0.010 0.992105 data$graduat 2.700e+01 5.651e+00 4.778 2.11e-06 *** data$pct_phd 3.136e+01 6.861e+00 4.572 5.61e-06 *** data$fulltime 1.259e+01 5.201e+00 2.420 0.015730 * data$alumni 4.483e+01 7.663e+00 5.850 7.17e-09 *** data$num_enrl -3.907e-01 1.120e-01 -3.490 0.000509 *** data$public 3.952e+03 2.487e+02 15.892 < 2e-16 ***--- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2118 on 793 degrees of freedom Multiple R-squared: 0.7403, Adjusted R-squared: 0.737 F-statistic: 226 on 10 and 793 DF, p-value: < 2.2e-16 Forward Stepwise Refinement step(lm(data$tuition~data$sf_ratio),~data$pcttop25 + data$sf_ratio + data$fac_comp + data$accrate + data$graduat + data$pct_phd + data$fulltime +data$alumni + data$num_enrl + data$public, direction="forward") Start: AIC=13053.57 data$tuition ~ data$sf_ratio Df Sum of Sq RSS AIC + data$graduat 1 2323028162 6676272814 12816 + data$alumni 1 1726654068 7272646908 12884 + data$public 1 1636502242 7362798734 12894 + data$fac_comp 1 1587989107 7411311869 12899 + data$pcttop25 1 1420556109 7578744867...
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This note was uploaded on 06/10/2010 for the course STAT 331 taught by Professor Yuliagel during the Spring '08 term at Waterloo.
- Spring '08