Lesson 12.6 Outliers

Outliers, in General

Outliers are points far from the line of best fit. The difference between the actual y and the estimated y for an outlier is "large." Outliers should be examined closely. In some cases, they should be deleted from the set of data points. In other cases, they should not be deleted at all because they are the key to the population under study. You must carefully examine what causes a data point to be an outlier.

In this course, you will learn one method for determining outliers. When you take higher level courses in Linear Regression, you will learn other methods for determining outliers.

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Outlier Calculation

To calculate outliers:

• Do linear regression.
• Calculate each (actual y - estimated y) value: Each

These values are called residuals.

• Calculate the SSE which is the sum of the squares of all the (actual y - estimated y) values. SSE =

 

• Calculates, the standard deviation of all the

values (the residuals):

where n - 2 is equal to the number of data points - 2 .

• Multiply 1.9 by s.
• Compare the absolute value of each residual to 1.9s.
•  If the absolute value of any residual is greater than or equal to 1.9s, the corresponding point is an outlier. (If

then the corresponding point is an outlier.)

Example: Linear regression produces the following line of best fit:

The data points are

(1, 2), (3, 1.5), (4, 1), (2, 2), (3, 1), (5, 0.3), (1, 4).

 

The table contains the actual y values, the estimated y values calculated from the line of best fit, and the absolute value of the difference.

y	2	1.5	1	2	1	0.3	4
	2.84	1.49	0.82	2.17	1.49	0.15	2.84
	0.84	0.01	0.18	0.17	0.49	0.15	1.16

SSE = .84² +.01² +.18² + .17² +.49² +.15² +1.16² = 2.38 

n = 7 data points

 

Compare each value in the table below to 1.31.

No value is greater than or equal to 1.31. We do not have any

Therefore, no point is an outlier. 

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Think About It

Please continue to the next section of this lesson.

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Up » 12.1 Linear Equations » 12.2 Scatter Plots » 12.3 The Regression Equation » 12.4 The Correlation Coefficient » 12.5 Prediction » 12.6 Outliers » 12.7 TI-83