4.7: Residuals & Correlation

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What is a residual in statistics?

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A residual is the difference between the observed value and the predicted value in a regression analysis.

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CCSS.HSS.ID.B.6B

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How do you calculate a residual?

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Residual = Observed Value - Predicted Value.

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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.

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CCSS.HSS.ID.B.6B

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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.

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CCSS.HSS.ID.B.6B

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What is a residual plot?

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A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis.

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CCSS.HSS.ID.B.6B

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What does it mean if a residual plot shows no pattern?

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If a residual plot shows no pattern, it suggests that the linear regression model is appropriate for the data.

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CCSS.HSS.ID.B.6B

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What is the correlation coefficient?

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The correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables.

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What is the range of the correlation coefficient?

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The correlation coefficient ranges from -1 to 1.

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What does a correlation coefficient of -1 indicate?

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A correlation coefficient of -1 indicates a perfect negative linear relationship between two variables.

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CCSS.HSS.ID.B.5

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What does a correlation coefficient of 1 indicate?

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A correlation coefficient of 1 indicates a perfect positive linear relationship between two variables.

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CCSS.HSS.ID.B.5