Question

Points and their residual values are shown in the table. Which residual value is the farthest from the line of best fit? 0.19 0.7 2 8

Answer 1

(2, 3.5)

Explanation:

The residual with the largest magnitude is 0.7, indicating the point (2, 3.5) is farthest from the line of best fit.

Answer 2

The residual value which is the farthest from the line of best fit is:

0.7

Explanation:

We are given a table which displays the point and their residual values.

The table is as follows:

x y Residual Absolute Residual value

1 2 -0.4 0.4

2 3.5 0.7 0.7

3 5 -0.2 0.2

4 6.1 0.19 0.19

5 8 -0.6 0.6

The residual value is negative if the point on the scatter plot lie below the regression line and is positive if the point on the scatter plot lie above the regression line.

(Since the residual value is calculated as:

Residual value=Actual y-value(i.e. on scatter plot)-Observed y-value( i.e. on regression line ) )

Now, the residual value is farthest from the line if the absolute value of the residual value is highest.

Hence, the highest absolute residual value is: 0.7