Beginning Scatterplot

Entering the data as vectors

x<-c(10,    35, 19, 16, 40, 32, 14)
y<-c(10,    35, 14, 22, 41, 25, 17)
n<-length(y)

Creating a data frame from the two vectors and view top records:

d<-data.frame(x,y)
head(d)

Calculating the Average of Y

meany<-mean(y)
print(meany)

[1] 23.42857

Producing the Plot

plot(d,pch=20,cex=3,cex.axis=1.5,cex.lab=1.5)

Adding the Mean of Y:

plot(d,pch=20,cex=3,cex.axis=1.5,cex.lab=1.5)
lines(c(0,50),c(meany,meany),col="black",lwd=3)

Adding the Residuals:

plot(d,pch=20,cex=3,cex.axis=1.5,cex.lab=1.5)
mlines<-function(){ for(i in 1:n)
  lines(c(d$x[i],d$x[i]),c(d$y[i],meany),col="red",lwd=3)
}
mlines()

lines(c(0,50),c(meany,meany),col="black",lwd=3)

Produce the Linear equation:

model_y<-lm(y~x)

Show results:

summary(model_y)

Call:
lm(formula = y ~ x)

Residuals:
     1      2      3      4      5      6      7 
-1.269  1.565 -5.249  5.411  3.132 -5.775  2.184 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)   2.4026     4.2352   0.567   0.5950   
x             0.8866     0.1624   5.460   0.0028 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.665 on 5 degrees of freedom
Multiple R-squared:  0.8564,    Adjusted R-squared:  0.8277 
F-statistic: 29.81 on 1 and 5 DF,  p-value: 0.002803

Use model to make prediction

yhat<-predict(model_y)

Redraw Plot and add Linear Regression Line

plot(d,pch=20,cex=3,cex.axis=1.5,cex.lab=1.5)
abline(model_y,col="blue",lwd=3)

Add Residual lines to plot

plot(d,pch=20,cex=3,cex.axis=1.5,cex.lab=1.5)
abline(model_y,col="blue",lwd=3)

plines<-function(){ for(i in 1:length(yhat))
  lines(c(d$x[i],d$x[i]),c(d$y[i],yhat[i]),col="red",lwd=3)
}
plines()