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 of a data point in a regression analysis.

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CCSS.HSS.ID.B.6B

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How do you interpret a positive residual?

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A positive residual indicates that the observed value is greater than the predicted value, suggesting that the model underestimates the actual data point.

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CCSS.HSS.ID.B.6B

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How do you interpret a negative residual?

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A negative residual indicates that the observed value is less than the predicted value, suggesting that the model overestimates the actual data point.

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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 displays the residuals on the vertical axis and the independent variable on the horizontal axis, helping to assess the fit of a regression model.

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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 regression model is appropriate for the data.

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CCSS.HSS.ID.B.6B

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What does a positive correlation indicate?

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A positive correlation indicates that as one variable increases, the other variable also tends to increase.

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CCSS.HSS.ID.B.5

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What does a negative correlation indicate?

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A negative correlation indicates that as one variable increases, the other variable tends to decrease.

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CCSS.HSS.ID.B.5

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What does it mean if there is no correlation between two variables?

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No correlation means that there is no predictable relationship between the two variables; changes in one do not affect the other.

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CCSS.HSS.ID.B.5

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How can you determine the strength of a correlation?

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The strength of a correlation can be determined by the correlation coefficient, which ranges from -1 to 1. Values closer to -1 or 1 indicate stronger correlations.

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CCSS.HSS.ID.B.5

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What is the correlation coefficient?

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

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CCSS.HSS.ID.C.8