Concept explainers
Expand Your Knowledge: Residual Plot The least-squares line usually does not go through all the sample data points (x, y). In fact, for a specified x value from a data pair (x, y), there is usually a difference between the predicted value and the y value paired with x. This difference is called the residual.
The residual is the difference between the y value in a specified data pair (x, y) and the value
One way to assess how well a least-squares line serves as a model for the data is a residual plot. To make a residual plot, we pull the x values in order on the horizontal axis and plot the corresponding residuals
Residual | |||||||
X | y |
|
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6 | 15 | 12.6 | 2.4 | ||||
20 | 31 | 26.8 | 4.2 | ||||
0 | 10 | 6.6 | 3.4 | ||||
14 | 16 | 20.7 | -4.7 | ||||
25 | 28 | 31.8 | -3.8 | ||||
Residual | |||||||
X | y |
|
|
||||
16 | 20 | 22.7 | -2.7 | ||||
28 | 40 | 34.8 | 5.2 | ||||
18 | 25 | 24.7 | 0.3 | ||||
10 | 12 | 16.7 | -4.7 | ||||
8 | 15 | 14.6 | 0.4 |
If the least-squares line provides a reasonable model for the data, the pattern of points in the plot will seem random and unstructured about the horizontal line at 0. Is this the case for the residual plot?
If a point on the residual plot seems far outside the pattern of other points, it might reflect an unusual data point (x. y), called an outlier. Such points may have quite an influence on the least-squares model. Do there appear to be any outliers in the data for the residual plot?
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Chapter 4 Solutions
Understanding Basic Statistics
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