Make a table of values to determine the residuals.
Sum for y=1.6x+4: 41.64 Sum for y=1.8x+4: 63.96 Better Line of Fit: y=1.6x+4
Practice makes perfect
We have been given the following table.
x
1
3
5
7
y
2
6
8
13
We have also been given two possible lines of fit.
Lines of Fit
y=1.6x+4
y=1.8x+4
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=1.6x+4
Residual for y=1.6x+4
y Predicted by y=1.8x+4
Residual for y=1.8x+4
1
2
y=1.6( 1)+4= 5.6
2- 5.6= -3.6
y=1.8( 1)+4= 5.8
2- 5.8= -3.8
3
6
y=1.6( 3)+4= 8.8
6- 8.8= -2.8
y=1.8( 3)+4= 9.4
6- 9.4= -3.4
5
8
y=1.6( 5)+4= 12
8- 12= -4
y=1.8( 5)+4= 13
8- 13= -5
7
13
y=1.6( 7)+4= 15.2
13- 15.2= -2.2
y=1.8( 7)+4= 16.6
13- 16.6= -3.6
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=1.6x+4.
