Residual practice

Front

What is a residual plot?

Back

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.

Front

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

Back

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

Back

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

Front

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.

Front

What characteristics should a good residual plot exhibit?

Back

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.

Front

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

Back

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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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.

Front

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.

Front

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

Back

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

Front

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

Back

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