This analysis randomly samples from UCM’s Fall 2011 admitted first-time freshmen. The goal of this analysis is to explain factors explain Enrollment in the Fall 2011 term.
library(tidyverse)
admits <- read_csv("C:/Users/pattiz/Desktop/MidAir Workshop/admits_data.csv")
admits_DF <-
admits %>%
rename(HS_GPA = `HS GPA`, ACT_COMP = `ACT COMP`) %>%
mutate(INSTITUTION_RANK = as.factor(INSTITUTION_RANK))summary(admits_DF)## COUNTY_IND FIRST_GEN ACT_COMP LEGACY
## Min. :0.0000 Min. :0.0000 Min. :13.00 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:19.00 1st Qu.:0.0000
## Median :0.0000 Median :1.0000 Median :22.00 Median :0.0000
## Mean :0.0704 Mean :0.5188 Mean :21.98 Mean :0.1164
## 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:24.00 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :34.00 Max. :1.0000
## NA's :41
## HS_GPA SCHOLARSHIP_IND PELL_IND INSTITUTION_RANK
## Min. :1.300 Min. :0.0000 Min. :0.0000 1 :1988
## 1st Qu.:2.930 1st Qu.:0.0000 1st Qu.:0.0000 2 : 48
## Median :3.360 Median :1.0000 Median :0.0000 3 : 12
## Mean :3.305 Mean :0.5124 Mean :0.3356 4 : 402
## 3rd Qu.:3.730 3rd Qu.:1.0000 3rd Qu.:1.0000 NA's: 50
## Max. :4.930 Max. :1.0000 Max. :1.0000
## NA's :23
## ENROLLED
## Min. :0.000
## 1st Qu.:0.000
## Median :0.000
## Mean :0.462
## 3rd Qu.:1.000
## Max. :1.000
## admit_model <- glm(ENROLLED ~ COUNTY_IND + FIRST_GEN + LEGACY + HS_GPA + ACT_COMP + SCHOLARSHIP_IND +
PELL_IND + INSTITUTION_RANK, data = admits_DF, family = "binomial")
attributes(admit_model)## $names
## [1] "coefficients" "residuals" "fitted.values"
## [4] "effects" "R" "rank"
## [7] "qr" "family" "linear.predictors"
## [10] "deviance" "aic" "null.deviance"
## [13] "iter" "weights" "prior.weights"
## [16] "df.residual" "df.null" "y"
## [19] "converged" "boundary" "model"
## [22] "na.action" "call" "formula"
## [25] "terms" "data" "offset"
## [28] "control" "method" "contrasts"
## [31] "xlevels"
##
## $class
## [1] "glm" "lm"summary(admit_model)##
## Call:
## glm(formula = ENROLLED ~ COUNTY_IND + FIRST_GEN + LEGACY + HS_GPA +
## ACT_COMP + SCHOLARSHIP_IND + PELL_IND + INSTITUTION_RANK,
## family = "binomial", data = admits_DF)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1029 -1.1450 -0.1823 1.0455 2.8382
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.02635 0.45072 -0.058 0.9534
## COUNTY_IND 0.96993 0.21135 4.589 4.45e-06 ***
## FIRST_GEN 0.10161 0.10323 0.984 0.3250
## LEGACY 0.42962 0.15985 2.688 0.0072 **
## HS_GPA -0.17678 0.11114 -1.591 0.1117
## ACT_COMP 0.02935 0.01660 1.768 0.0771 .
## SCHOLARSHIP_IND -0.22993 0.12894 -1.783 0.0746 .
## PELL_IND 0.48084 0.10207 4.711 2.47e-06 ***
## INSTITUTION_RANK2 -1.95674 0.41688 -4.694 2.68e-06 ***
## INSTITUTION_RANK3 -1.78805 0.78183 -2.287 0.0222 *
## INSTITUTION_RANK4 -3.94452 0.34152 -11.550 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3317.9 on 2403 degrees of freedom
## Residual deviance: 2724.7 on 2393 degrees of freedom
## (96 observations deleted due to missingness)
## AIC: 2746.7
##
## Number of Fisher Scoring iterations: 6To evaluate the overall performance of the saturated model compared to the null model, look at the null deviance and residual deviance. The difference between the deviances of the two models follows a \(\chi^2_{10}\) distribution.
1 - pchisq(593, df= 10)## [1] 0This the null hypothesis is rejected.
Any odds ratio larger than will shows an association between Enrollment and the explainatory varable.
exp(cbind(ODDS_RATIO = coef(admit_model), confint(admit_model)))## ODDS_RATIO 2.5 % 97.5 %
## (Intercept) 0.97399199 0.401996523 2.35463244
## COUNTY_IND 2.63776627 1.762376850 4.04482355
## FIRST_GEN 1.10695625 0.904061796 1.35515180
## LEGACY 1.53667282 1.125082747 2.10650378
## HS_GPA 0.83796682 0.673565750 1.04155020
## ACT_COMP 1.02978818 0.996875869 1.06394546
## SCHOLARSHIP_IND 0.79459210 0.616818496 1.02275296
## PELL_IND 1.61743283 1.324877028 1.97695121
## INSTITUTION_RANK2 0.14131871 0.057218524 0.30054636
## INSTITUTION_RANK3 0.16728597 0.025473022 0.64573613
## INSTITUTION_RANK4 0.01936053 0.009183549 0.03558603