Lab 10
Charlie Phelan
2024-06-11
Read in the data
library(ggplot2)
enroll = read.csv("enrollmentForecast.csv")look at data structure
str(enroll)## 'data.frame': 29 obs. of 5 variables:
## $ YEAR : int 1 2 3 4 5 6 7 8 9 10 ...
## $ ROLL : int 5501 5945 6629 7556 8716 9369 9920 10167 11084 12504 ...
## $ UNEM : num 8.1 7 7.3 7.5 7 6.4 6.5 6.4 6.3 7.7 ...
## $ HGRAD: int 9552 9680 9731 11666 14675 15265 15484 15723 16501 16890 ...
## $ INC : int 1923 1961 1979 2030 2112 2192 2235 2351 2411 2475 ...summary(enroll)## YEAR ROLL UNEM HGRAD INC
## Min. : 1 Min. : 5501 Min. : 5.700 Min. : 9552 Min. :1923
## 1st Qu.: 8 1st Qu.:10167 1st Qu.: 7.000 1st Qu.:15723 1st Qu.:2351
## Median :15 Median :14395 Median : 7.500 Median :17203 Median :2863
## Mean :15 Mean :12707 Mean : 7.717 Mean :16528 Mean :2729
## 3rd Qu.:22 3rd Qu.:14969 3rd Qu.: 8.200 3rd Qu.:18266 3rd Qu.:3127
## Max. :29 Max. :16081 Max. :10.100 Max. :19800 Max. :3345make scatterplots of ROLL against the other variables
ggplot(enroll, aes(x = ROLL, y = YEAR)) + geom_point() + ggtitle("Enrollment per Year")
ggplot(enroll, aes(x = ROLL, y = UNEM)) + geom_point() + ggtitle("Enrollment per Unemployment Rate")
ggplot(enroll, aes(x = ROLL, y = HGRAD)) + geom_point() + ggtitle("Enrollment per High School Graduates")
ggplot(enroll, aes(x = ROLL, y = INC)) + geom_point() + ggtitle("Enrollment per Monthly per Capita Income")
Build a linear model using the unemployment rate UNEM and
number of spring high school graduates HGRAD to predict the
fall enrollment ROLL, i.e.
enroll$UNEM.cen = enroll$UNEM - mean(enroll$UNEM)
enroll.fit = lm(ROLL ~ UNEM.cen + HGRAD, data = enroll)Use the summary() and anova() functions to investigate the model
summary(enroll.fit)##
## Call:
## lm(formula = ROLL ~ UNEM.cen + HGRAD, data = enroll)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2102.2 -861.6 -349.4 374.5 3603.5
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.867e+03 1.444e+03 -1.985 0.05777 .
## UNEM.cen 6.983e+02 2.244e+02 3.111 0.00449 **
## HGRAD 9.423e-01 8.613e-02 10.941 3.16e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1313 on 26 degrees of freedom
## Multiple R-squared: 0.8489, Adjusted R-squared: 0.8373
## F-statistic: 73.03 on 2 and 26 DF, p-value: 2.144e-11anova(enroll.fit)## Analysis of Variance Table
##
## Response: ROLL
## Df Sum Sq Mean Sq F value Pr(>F)
## UNEM.cen 1 45407767 45407767 26.349 2.366e-05 ***
## HGRAD 1 206279143 206279143 119.701 3.157e-11 ***
## Residuals 26 44805568 1723291
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Which variable is the most closely related to enrollment?
## High school graduates are the most closely related to enrollmentMake a residual plot and check for any bias in the model
plot(enroll.fit, which = 1)
Use the predict() function to estimate the expected fall
enrollment, if the current year’s unemployment rate is 9% and the size
of the spring high school graduating class is 25,000 students
enrollpredict = data.frame(UNEM.cen = 0.09, HGRAD = 25000)
predict(enroll.fit, enrollpredict)## 1
## 20752.72Build a second model which includes per capita income INC.
enroll.inc = lm(ROLL~ UNEM.cen + HGRAD + INC, data = enroll)Compare the two models with anova(). Does including this variable improve the model?
anova(enroll.fit)## Analysis of Variance Table
##
## Response: ROLL
## Df Sum Sq Mean Sq F value Pr(>F)
## UNEM.cen 1 45407767 45407767 26.349 2.366e-05 ***
## HGRAD 1 206279143 206279143 119.701 3.157e-11 ***
## Residuals 26 44805568 1723291
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(enroll.inc)## Analysis of Variance Table
##
## Response: ROLL
## Df Sum Sq Mean Sq F value Pr(>F)
## UNEM.cen 1 45407767 45407767 101.02 2.894e-10 ***
## HGRAD 1 206279143 206279143 458.92 < 2.2e-16 ***
## INC 1 33568255 33568255 74.68 5.594e-09 ***
## Residuals 25 11237313 449493
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1