Make a table of values to determine the residuals.
Sum for y=3x+1.2: 829.56 Sum for y=3x+1: 809 Better Line of Fit: y=3x+1
Practice makes perfect
We have been given the following table.
x
2
4
6
8
y
1
5
4
3
We have also been given two possible lines of fit.
Lines of Fit
y=3x+1.2
y=3x+1
In order to determine which line of fit is better, let's calculate the residuals for both lines.
x
y (Actual)
y Predicted by y=3x+1.2
Residual for y=3x+1.2
y Predicted by y=3x+1
Residual for y=3x+1
2
1
y=3( 2)+1.2= 7.2
1- 7.2= -6.2
y=3( 2)+1= 7
1- 7= -6
4
5
y=3( 4)+1.2= 13.2
5- 13.2= -8.2
y=3( 4)+1= 13
5- 13= -8
6
4
y=3( 6)+1.2= 19.2
4- 19.2= -15.2
y=3( 6)+1= 19
4- 19= -15
8
3
y=3( 8)+1.2= 25.2
3- 25.2= -22.2
y=3( 8)+1= 25
3- 25= -22
Now, we will square the residuals and find their sum s for each line so that we can compare which line is a better fit. Let's start with the line y=3x+1.2.
