Calculating Residuals

Front

What is a residual in the context of regression analysis?

Back

A residual is the difference between the observed value and the predicted value (y - yhat) for a given data point.

Front

How do you calculate a residual?

Back

Residual = Observed value (y) - Predicted value (yhat) from the regression line.

Front

Back

yhat = -0.3 + 1.7(5.1) = 8.37.

Front

If a student predicted a score of 78% but the actual score was 81%, what is the residual?

Back

Residual = 81 - 78 = 3.

Front

What does a negative residual indicate?

Back

A negative residual indicates that the observed value is less than the predicted value.

Front

What does a positive residual indicate?

Back

A positive residual indicates that the observed value is greater than the predicted value.

Front

Back

Residual = 26 - (20 + 0.5(3)) = 4.5.

Front

True or False: A residual is the slope in your line of best fit.

Back

False.

Front

Back

Residual = 2 - (15 - 3(11)) = -20.

Front

What is the significance of residuals in regression analysis?

Back

Residuals help assess the accuracy of the regression model; smaller residuals indicate a better fit.