2.1 Regression

#install.packages("AER")

library("AER")

data("CASchools")

teacher_stu_ratio <- CASchools$students/CASchools$teachers
lm_math <- lm(CASchools$math ~ teacher_stu_ratio)
resid<- lm_math$residuals
plot(teacher_stu_ratio, resid, 
     ylab="Residuals", xlab="teacher_stu_ratio", 
     main="Residual Plot - Math") 
abline(0, 0, col="red")                  # the horizon

lm_read <- lm(CASchools$read ~ teacher_stu_ratio)
resid<- lm_read$residuals
plot(teacher_stu_ratio, resid, 
     ylab="Residuals", xlab="teacher_stu_ratio", 
     main="Residual Plot - Read") 
abline(0, 0, col="red")                  # the horizon

Regression:

plot(CASchools$math ~ teacher_stu_ratio)
regLine(lm_math)

summary(lm_math)

Call:
lm(formula = CASchools$math ~ teacher_stu_ratio)

Residuals:
    Min      1Q  Median      3Q     Max 
-44.615 -13.374  -0.828  12.728  52.711 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)       691.4174     9.3825  73.692  < 2e-16 ***
teacher_stu_ratio  -1.9386     0.4755  -4.077 5.47e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 18.41 on 418 degrees of freedom
Multiple R-squared:  0.03824,   Adjusted R-squared:  0.03594 
F-statistic: 16.62 on 1 and 418 DF,  p-value: 5.467e-05

plot(CASchools$read ~ teacher_stu_ratio)
regLine(lm_read)

summary(lm_read)

Call:
lm(formula = CASchools$read ~ teacher_stu_ratio)

Residuals:
    Min      1Q  Median      3Q     Max 
-50.839 -14.479   1.121  14.495  44.370 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)       706.4485     9.9410  71.064  < 2e-16 ***
teacher_stu_ratio  -2.6210     0.5038  -5.202 3.09e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 19.51 on 418 degrees of freedom
Multiple R-squared:  0.06081,   Adjusted R-squared:  0.05856 
F-statistic: 27.06 on 1 and 418 DF,  p-value: 3.091e-07