Residual practice

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What is a residual plot?

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A residual plot is a graphical representation that shows the residuals on the vertical axis and the independent variable on the horizontal axis. It helps 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 a random pattern?

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A random pattern in a residual plot indicates that the regression model is appropriate for the data and that the assumptions of linear regression are met.

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CCSS.HSS.ID.B.6B

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What is the significance of the correlation coefficient (r) in regression analysis?

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The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, with values ranging from -1 to 1.

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CCSS.HSS.ID.C.8

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What does an r value of 0.934 indicate?

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An r value of 0.934 indicates a strong positive linear relationship between the two variables being analyzed.

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CCSS.HSS.ID.B.5

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What characteristics should a good residual plot exhibit?

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A good residual plot should exhibit a random scatter of points, indicating that the model fits the data well and that the residuals are randomly distributed.

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CCSS.HSS.ID.B.6B

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What does it imply if a residual plot shows a clear pattern?

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A clear pattern in a residual plot suggests that the regression model may not be appropriate for the data, indicating potential issues such as non-linearity.

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CCSS.HSS.ID.B.6B

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How can you determine if a linear regression model is appropriate using residual plots?

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You can determine if a linear regression model is appropriate by checking if the residuals are randomly scattered around zero in the residual plot.

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What is the purpose of examining residuals in regression analysis?

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Examining residuals helps to validate the assumptions of the regression model, identify outliers, and assess the model's fit.

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CCSS.HSS.ID.B.6B

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What does it mean if a residual plot is fan-shaped?

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A fan-shaped residual plot indicates that the variance of the residuals is not constant (heteroscedasticity), which violates the assumptions of linear regression.

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CCSS.HSS.ID.B.6B

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What is the relationship between residuals and the fitted values in regression analysis?

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Residuals are the differences between the observed values and the fitted values predicted by the regression model.

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CCSS.HSS.ID.B.6B