Residuals & Correlation

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What are residuals in the context of regression analysis?

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Residuals are the differences between the observed values and the predicted values from a regression model.

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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 negative residual indicate?

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A negative residual indicates that the predicted value is too big.

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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 predicted value is too small.

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CCSS.HSS.ID.B.6B

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What is the purpose of analyzing residuals in regression?

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Analyzing residuals helps to assess the fit of the model and identify any patterns that suggest the model is inappropriate.

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CCSS.HSS.ID.B.6B

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What does a residual plot show?

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A residual plot shows the residuals on the vertical axis and the independent variable on the horizontal axis, helping to visualize the fit of the model.

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CCSS.HSS.ID.B.6B

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What indicates a good linear fit in a residual plot?

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A good linear fit is indicated by residuals that are randomly scattered around zero without any discernible pattern.

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CCSS.HSS.ID.B.6B

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What is correlation?

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

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CCSS.HSS.ID.C.9

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What are the possible values of the correlation coefficient (r)?

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The correlation coefficient (r) can range from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.

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CCSS.HSS.ID.C.8

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How can you rank scatter plots based on correlation strength?

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Scatter plots can be ranked based on how closely the points cluster around a line; the closer they are, the stronger the correlation.

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CCSS.HSF-LE.A.1B