Question

A linear regression was conducted on the following data points.

A(1, 11) B(3, 7) C(5, 2) D(7, 1) E(9, -2)

The residual for which point has the largest absolute value?

Answer 1

Using MS Excel, we plot the data points and find the trend line. The equation of the line is y=-1.6x+11.8. The equation of the line has no r2 of 1 which means there is a discrepancy of the values. W predict the y-value for each x through substitution.
y(1)=10.2; y(3)=7; y(5)=3.8; y(7)=0.6 and y(9)=-2.6

Residual = Observed - Predicted
Hence for each y,
11-10.2 = .8
7-7 = 0
3.8 - 2 = 1.8
1-0.6=0.4
2.6 - 2 = 0.6
The largest absolute value is 1.8 from the point C(5,2).