Residuals and Residual Plots

What is a residual in statistics?

• The residual is the average of the observed and predicted values.

• The residual is the product of the observed and predicted values.

• The residual is the difference between the observed and predicted values.

• The residual is the sum of the observed and predicted values.

How are residuals calculated?

• By adding the predicted values to the actual values in a regression model.

• By multiplying the predicted values with the actual values in a regression model.

• By dividing the predicted values by the actual values in a regression model.

• By subtracting the predicted values from the actual values in a regression model.

What does a positive residual indicate?

• The observed value is lower than the predicted value.

• The observed value is equal to the predicted value.

• The observed value is unrelated to the predicted value.

• The observed value is higher than the predicted value.

What does a negative residual indicate?

• The observed value is higher than the predicted value.

• The observed value is equal to the predicted value.

• The residual is positive.

• The observed value is lower than the predicted value.

What is a residual plot?

• A residual plot is a graph that shows the residuals on the vertical axis and the dependent variable on the horizontal axis.

• A residual plot is a graph that shows the residuals on the horizontal axis and the independent variable on the vertical axis.

• A residual plot is a graph that shows the predicted values on the vertical axis and the independent variable on the horizontal axis.

• A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis.

How is a residual plot used to assess the goodness of fit?

• A residual plot is used to determine the correlation coefficient.

• A residual plot is used to calculate the mean squared error.

• A residual plot is used to estimate the standard deviation of the residuals.

• A residual plot is used to identify patterns or trends in the residuals and assess the goodness of fit.

What does a random pattern in a residual plot indicate?

• A good fit

• Underfitting

• Overfitting

• No relationship

What does a curved pattern in a residual plot indicate?

• There is no relationship between the independent and dependent variables.

• The data is perfectly linear.

• The relationship between the independent and dependent variables is not linear.

• The data is too noisy to determine a relationship.

Tags

CCSS.HSS.ID.B.6

What does a funnel-shaped pattern in a residual plot indicate?

• Homoscedasticity

• Multicollinearity

• Heteroscedasticity

• Autocorrelation

What does an outlier in a residual plot indicate?

• An outlier in a residual plot indicates a perfect fit between the predicted and actual values.

• An outlier in a residual plot indicates a random error in the data.

• An outlier in a residual plot indicates a large deviation from the predicted value.

• An outlier in a residual plot indicates a small deviation from the predicted value.

Tags

CCSS.HSS.ID.A.3