Residual Calculations

Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?

• a straight line is not a good model for the data

• the correlation must be 0

• the correlation must be positive

• outliers must be present

• The regression line might or might not be a good model for the data, depending on the extent of the curve.

When calculating a residual, we do the following:

• Predicted - Observed

• Observed - Predicted

• Predicted + Observed

• Observed + Predicted

Suppose you predict that Mrs. Mack's age is 38, but you later discover that her actual age is 44. What is the residual?

• 6

• -6

• -5

• 5

The residual for one of your calculations is 12. If your prediction is 100, what is the value for your actual observation?

• -88

• -112

• 88

• 112

If an observation is on the prediction line, then we say that the residual

• Positive

• Negative

• Zero

• Cannot be determined

• This residual plot represents a linear fit.
• This residual plot represents a nonlinear fit.
• This residual plot represents no fit.

I predicted someone would score a 78% on their test, but they actually scored an 81%. What's the residual?

• 81 - 78 = 3

• 78 - 81 = -3

• What's residual?

Residuals are . . . 

• possible models not explored by the researcher

• variation in the response variable that is explained by the model

• the difference between the observed response and the values predicted by the model

• data collected from individuals that is not consistent with the rest of the group