Residuals & Correlation

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What is a residual in statistics?

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A residual is the vertical distance between a data point and a line of fit, representing the difference between the observed value and the predicted value.

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CCSS.HSS.ID.B.6B

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How is a residual calculated?

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Residual = Actual Value - Predicted Value.

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CCSS.HSS.ID.B.6B

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What does a random pattern in a residual plot indicate?

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A random pattern in a residual plot indicates that the linear model is a good fit for the data.

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CCSS.HSS.ID.B.6B

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What does it mean if a residual plot shows a distinct pattern?

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A distinct pattern in a residual plot suggests that the linear model may not be appropriate for the data.

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CCSS.HSS.ID.B.6B

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What is the acronym for the formula Residual = Actual - Predicted?

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RAP.

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CCSS.HSS.ID.B.6B

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How many negative residuals are present if a residual plot shows 5 points below the line of fit?

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5 negative residuals.

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CCSS.HSS.ID.B.6B

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What is the significance of examining a scatter plot of residuals?

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Examining a scatter plot of residuals helps to assess the fit of the regression model and identify any patterns.

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CCSS.HSS.ID.B.6B

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What does it indicate if a scatter plot of residuals shows points evenly distributed around zero?

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It indicates that the model is appropriate and that the errors are randomly distributed.

Tags

CCSS.HSS.ID.B.6B

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What is the purpose of a residual plot?

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A residual plot is used to determine the appropriateness of a regression model by visualizing the residuals.

Tags

CCSS.HSS.ID.B.6B

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If a residual plot shows a curve, what does that imply about the model?

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It implies that a linear model may not be suitable, and a non-linear model might be needed.