myData = read.csv("midtermRegressionS13_F15.csv")

head(myData)

	Midterm.1	Midterm.2
1	52	54
2	70	73
3	86	89
4	73	62
5	92	85
6	47	72

summary(myData)
cor(myData) # For a data.frame, cor() returns the correlation matrix.

   Midterm.1       Midterm.2     
 Min.   :33.00   Min.   : 19.00  
 1st Qu.:67.00   1st Qu.: 65.75  
 Median :79.00   Median : 75.00  
 Mean   :76.78   Mean   : 74.17  
 3rd Qu.:88.00   3rd Qu.: 84.00  
 Max.   :99.00   Max.   :100.00  

	Midterm.1	Midterm.2
Midterm.1	1.0000000	0.6094617
Midterm.2	0.6094617	1.0000000

x = myData$Midterm.1
y = myData$Midterm.2
devx = x-mean(x)
devy = y-mean(y)
sum(devx*devy)/(sqrt(sum(devx^2))*sqrt(sum(devy^2)))
cor(x,y) # For two vectors, cor() just gives the Pearson correlation coefficient.

0.609461666031633

0.609461666031632

plot(myData)
abline(lm(y~x)) # Note that order matters in the command lm(). The y variable must come first

# The slope of the regression line is: r s_y/s_x:
cor(x,y)*sd(y)/sd(x)

0.57972495435538

# To see the details of the least squared regression line:
myLinearModel = lm(y~x)
myLinearModel

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
    29.6567       0.5797  

plot(resid(myLinearModel))
abline(0,0) # This command adds a line with y-intercept = 0 and slope = 0 to the plot.