Calculating Residuals

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What is a residual in the context of regression analysis?

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A residual is the difference between the observed value and the predicted value (y - yhat) for a given data point.

Tags

CCSS.HSS.ID.B.6B

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How do you calculate a residual?

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Residual = Observed value (y) - Predicted value (yhat) from the regression line.

Tags

CCSS.HSS.ID.B.6B

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yhat = -0.3 + 1.7(5.1) = 8.37.

Tags

CCSS.8.EE.C.8C

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If a student predicted a score of 78% but the actual score was 81%, what is the residual?

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Residual = 81 - 78 = 3.

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What does a negative residual indicate?

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A negative residual indicates that the observed value is less than the predicted value.

Tags

CCSS.HSS.ID.B.6B

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What does a positive residual indicate?

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A positive residual indicates that the observed value is greater than the predicted value.

Tags

CCSS.HSS.ID.B.6B

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Back

Residual = 26 - (20 + 0.5(3)) = 4.5.

Tags

CCSS.HSS.ID.B.6B

Front

True or False: A residual is the slope in your line of best fit.

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False.

Tags

CCSS.HSS.ID.B.6B

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Back

Residual = 2 - (15 - 3(11)) = -20.

Tags

CCSS.HSS.ID.B.6B

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What is the significance of residuals in regression analysis?

Back

Residuals help assess the accuracy of the regression model; smaller residuals indicate a better fit.

Tags

CCSS.HSS.ID.B.6B