# Set working directory and load data
setwd("~/Downloads/Intro to R/Module 10")
enroll <- read.csv("enrollmentForecast.csv")
# Explore the data
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. :3345
# Visualize relationships
plot(enroll$UNEM, enroll$ROLL,
main = "Enrollment vs Unemployment Rate",
xlab = "Unemployment Rate", ylab = "Enrollment")
plot(enroll$HGRAD, enroll$ROLL,
main = "Enrollment vs High School Graduates",
xlab = "High School Graduates", ylab = "Enrollment")
plot(enroll$INC, enroll$ROLL,
main = "Enrollment vs Income",
xlab = "Per Capita Income", ylab = "Enrollment")
# Build first linear model
mod1 <- lm(ROLL ~ UNEM + HGRAD, data = enroll)
summary(mod1)
##
## Call:
## lm(formula = ROLL ~ UNEM + 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) -8.256e+03 2.052e+03 -4.023 0.00044 ***
## UNEM 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-11
anova(mod1)
## Analysis of Variance Table
##
## Response: ROLL
## Df Sum Sq Mean Sq F value Pr(>F)
## UNEM 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 ' ' 1
# Residual plot for model 1
plot(mod1$residuals, main = "Residuals of Model 1", ylab = "Residuals", xlab = "Index")
abline(h = 0, col = "red")
# Predict enrollment for new data
new_data <- data.frame(UNEM = 9, HGRAD = 25000)
predict(mod1, newdata = new_data)
## 1
## 21585.58
# Build second model including income
mod2 <- lm(ROLL ~ UNEM + HGRAD + INC, data = enroll)
summary(mod2)
##
## Call:
## lm(formula = ROLL ~ UNEM + HGRAD + INC, data = enroll)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1148.84 -489.71 -1.88 387.40 1425.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.153e+03 1.053e+03 -8.691 5.02e-09 ***
## UNEM 4.501e+02 1.182e+02 3.809 0.000807 ***
## HGRAD 4.065e-01 7.602e-02 5.347 1.52e-05 ***
## INC 4.275e+00 4.947e-01 8.642 5.59e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 670.4 on 25 degrees of freedom
## Multiple R-squared: 0.9621, Adjusted R-squared: 0.9576
## F-statistic: 211.5 on 3 and 25 DF, p-value: < 2.2e-16
# Compare models
anova(mod1, mod2)
## Analysis of Variance Table
##
## Model 1: ROLL ~ UNEM + HGRAD
## Model 2: ROLL ~ UNEM + HGRAD + INC
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 26 44805568
## 2 25 11237313 1 33568255 74.68 5.594e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1