Make a table of values to determine the residuals.
Sum for y=2x+3.1: 18.44 Sum for y=2x+3.5: 21 Better Line of Fit: y=2x+3.1
Practice makes perfect
We have been given the following table.
x
1
2
3
4
y
2
9
7
12
We have also been given two possible lines of fit.
Lines of Fit
y=2x+3.1
y=2x+3.5
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=2x+3.1
Residual for y=2x+3.1
y Predicted by y=2x+3.5
Residual for y=2x+3.5
1
2
y=2( 1)+3.1= 5.1
2- 5.1= -3.1
y=2( 1)+3.5= 5.5
2- 5.5= -3.5
2
9
y=2( 2)+3.1= 7.1
9- 7.1= 1.9
y=2( 2)+3.5= 7.5
9- 7.5= 1.5
3
7
y=2( 3)+3.1= 9.1
7- 9.1= -2.1
y=2( 3)+3.5= 9.5
7- 9.5= -2.5
4
12
y=2( 4)+3.1= 11.1
12- 11.1= 0.9
y=2( 4)+3.5= 11.5
12- 11.5= 0.5
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=2x+3.1.
