Residuals and Residual Plots

Front

What is a residual?

Back

A residual is the difference between the observed value and the predicted value in a regression analysis, calculated as Observed - Predicted.

Tags

CCSS.HSS.ID.B.6B

Front

What does a random residual plot indicate?

Back

A random residual plot indicates that the model is a good fit for the data, as there are no discernible patterns.

Tags

CCSS.HSS.ID.B.6B

Front

What is the purpose of a residual plot?

Back

The purpose of a residual plot is to assess the goodness of fit of a regression model by visualizing the residuals.

Tags

CCSS.HSS.ID.B.6B

Front

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

Back

If a residual plot shows a distinct pattern, it suggests that the model may not be capturing all the information in the data, indicating a poor fit.

Tags

CCSS.HSS.ID.B.6B

Front

How do you interpret a negative residual?

Back

A negative residual indicates that the observed value is less than the predicted value, meaning the model overestimated the outcome.

Tags

CCSS.HSS.ID.B.6B

Front

How do you interpret a positive residual?

Back

A positive residual indicates that the observed value is greater than the predicted value, meaning the model underestimated the outcome.

Tags

CCSS.HSS.ID.B.6B

Front

What is the formula for calculating a residual?

Back

Residual = Observed Value - Predicted Value.

Tags

CCSS.HSS.ID.B.6B

Front

What does it mean if the correlation coefficient (r) is close to 1 or -1?

Back

If r is close to 1, it indicates a strong positive linear relationship; if r is close to -1, it indicates a strong negative linear relationship.

Tags

CCSS.HSS.ID.C.8

Front

What is the range of possible values for the correlation coefficient (r)?

Back

The correlation coefficient (r) ranges from -1 to 1.

Tags

CCSS.HSS.ID.B.5

Front

What is the difference between a scatter plot and a residual plot?

Back

A scatter plot shows the relationship between two variables, while a residual plot shows the residuals on the vertical axis and the independent variable on the horizontal axis.

Tags

CCSS.HSS.ID.B.6B