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Multiple Choice
Which of the following patterns in a residual plot indicates that the line of best fit is appropriate for the data?
A
The residuals show a funnel shape, with increasing spread as the fitted values increase.
B
The residuals are randomly scattered around the horizontal axis with no apparent pattern.
C
The residuals form a clear curved pattern.
D
The residuals increase or decrease systematically as the fitted values increase.
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1
Understand that a residual plot displays the residuals (differences between observed and predicted values) on the vertical axis and the fitted values on the horizontal axis.
Recall that the purpose of examining a residual plot is to check if the assumptions of linear regression are met, especially the assumption of linearity and constant variance.
Recognize that if the line of best fit is appropriate, the residuals should be randomly scattered around the horizontal axis (residual = 0) without any systematic pattern.
Identify that patterns such as a funnel shape, curved pattern, or systematic increase/decrease in residuals indicate problems like heteroscedasticity or non-linearity, meaning the line of best fit may not be appropriate.
Conclude that the correct pattern indicating an appropriate line of best fit is when residuals are randomly scattered around the horizontal axis with no apparent pattern.