Example: Midterm Grades

In the file MidtermsRegression.html, we looked at the relationship between midterm 1 and midterm 2 grades for students in introductory statistics.

exams <- read.csv('http://people.hsc.edu/faculty-staff/blins/StatsExamples/midtermRegressionS13_F15.csv')
myLM <- lm(Midterm2 ~ Midterm1, data = exams)

Prediction intervals for y-values

predict(myLM, data.frame(Midterm1 = c(50,75,100)), interval = "prediction", level = 0.95)
##        fit      lwr       upr
## 1 58.64292 36.71148  80.57436
## 2 73.13604 51.40805  94.86404
## 3 87.62917 65.74822 109.51012

Confidence intervals for y-values

predict(myLM, data.frame(Midterm1 = c(50,75,100)), interval = "confidence", level = 0.95)
##        fit      lwr      upr
## 1 58.64292 55.24737 62.03847
## 2 73.13604 71.50895 74.76314
## 3 87.62917 84.57666 90.68168

Confidence intervals for other parameters

confint(myLM, level = 0.95)
##                  2.5 %     97.5 %
## (Intercept) 20.9415856 38.3717603
## Midterm1     0.4681803  0.6912696