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Graphical Residual Analysis
Example: The data in the table below represent the per capita gross domestic product of randomly selected countries in Western Europe, the life expectancy of residents of the country, and the residuals. Construct a residual plot and boxplot of the residuals and comment on the appropriateness of the least-squares regression model.
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Using the data in table above, enter the X-values, (GDP), into L1 and the Y-values, (life expectancy), into L2. Press STAT, highlight CALC and select 4:LinReg(ax+b) and press ENTER.
To plot the residuals, first make sure that there is nothing stored in the Y-registers. Press Y= and check the Y-registers. If any of them contain a function, move the cursor to that Y-register and press CLEAR.
Press 2nd
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,
select 1:Plot 1 and press ENTER. For a Type of graph, select the scatter plot
which is the first selection. Press ENTER. Enter L1 for Xlist. Move the cursor
to Ylist. Press 2nd
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and
select 7:Resid. Highlight the first selection, the small square, for the type of
Mark. Press ENTER. Press ZOOM and 9 to select ZoomStat.
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There is no discernable pattern in the plot of the residuals. This indicates support for the linear model that we need to calculate the regression equation.
The next step in analyzing the residuals is to construct a boxplot to determine if there are any unusual residuals values (called outliers.)
Press 2nd
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,
select 1:Plot1, turn ON plot 1 and press ENTER. For Type of graph, select the
boxplot with outliers, which is the first selection in the second row. Press
ENTER. Enter L1 for Xlist. Move the cursor to Freq and set this equal to 1.
Highlight the first selection, the small square, for the type of Mark. Press
ZOOM and 9 to select ZoomStat.
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In this example, there are no outliers. This further supports the use of the linear model that was selected for the dataset.