Make a table of values to determine the residuals.
Sum for y=x+1.5: 9 Sum for y=x+1.7: 9.72 Better Line of Fit: y=x+1.5
Practice makes perfect
We have been given the following table.
x
1
2
3
4
y
2
5
4
3
We have also been given two possible lines of fit.
Lines of Fit
y=x+1.5
y=x+1.7
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=x+1.5
Residual for y=x+1.5
y Predicted by y=x+1.7
Residual for y=x+1.7
1
2
y= 1+1.5= 2.5
2- 2.5= -0.5
y= 1+1.7= 2.7
2- 2.7= -0.7
2
5
y= 2+1.5= 3.5
5- 3.5= 1.5
y= 2+1.7= 3.7
5- 3.7= 1.3
3
4
y= 3+1.5= 4.5
4- 4.5= -0.5
y= 3+1.7= 4.7
4- 4.7= -0.5
4
3
y= 4+1.5= 5.5
3- 5.5= -2.5
y= 4+1.7= 5.7
3- 5.7= -2.7
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=x+1.5.
