Question

56. The Standard Deviation for the Sum of Squared Errors for a data set is$9.8$. What is the cutoff for the vertical distance that a point can be from the line of best fit to be considered an outlier?

Short answer

The cutoff for the vertical distance that a point can be from the line of best fit to be considered an outlier is$18.62$.

Step-by-step solution

Given information

Given in the question that the standard deviation for the Sum of Squared Errors for a data set is $9.8$. And the vertical distance that a point can be from the line of best fit to be considered an outlier.

Explanation

Consider$s$as standard deviation of the sum of squares of residuals.

Then, utilize this standard deviation to check if the point is outlier or not.

If the point is far than$1.9$ standard deviation, then, that point is outlier.
Hence, the standard deviation of sum of squares of residuals is$9.8.$

The point is outlier if it is$1.9$ standard deviation away from fit line.

Now the absolute distance is:
$\begin{array}{r}\text{distance}=1.9\times s\end{array}$
$=1.9\times 9.8$
$=18.62$
So, if the distance one point from fit line is larger than $18.62$this point is considered an outlier. And then clean this outlier and repeat the method to determine all outliers.