Which one of the statements is true regarding residuals in regression analysis? Mean of residuals is always 0 Mean of residuals is always < 0 Mean of residuals is always > 0 There is no such rule for residuals
Question
Which one of the statements is true regarding residuals in regression analysis? Mean of residuals is always 0 Mean of residuals is always < 0 Mean of residuals is always > 0 There is no such rule for residuals
Solution
The true statement regarding residuals in regression analysis is: Mean of residuals is always 0.
Here's why:
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Residuals are the difference between the observed and predicted values in a regression analysis.
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The line of best fit in a regression analysis is calculated in such a way that it minimizes the sum of the squared residuals.
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Because of this, the positive and negative residuals will balance each other out, leading to a mean of 0.
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Therefore, the mean of residuals is always 0 in regression analysis.
The other statements are incorrect. The mean of residuals is not always less than 0 or greater than 0, and there is indeed a rule for residuals - that their mean is 0.
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