Residuals

Why Do You Need to Look at the Residual Plot? Because a linear regression model is not always appropriate for the data Can I just look at the scatterplot? – A plot may look linear in one scale, but not in another – You may not have enough data to see the actual pattern (if any) My r value is close to -1 or 1 – The r value may indicate a strong correlation, but r values are only good if we know the data is linear enough Great, so now what? – Evaluate the appropriateness of the model by defining residuals and examining residual plots

What is a Residual? Formula: Residual = Observed value - Predicted value Tells us how far off our prediction is Tells us if our prediction was too high or too low Both the sum and the mean of the residuals are equal to zero

What Does the Residual Plot Tell Us? Random pattern of residuals supports a linear model Non-random pattern supports a non-linear model

In the context of regression analysis, which of the following statements are true?regression analysis I.When the sum of the residuals is greater than zero, the data set is nonlinear. II.A random pattern of residuals supports a linear model. III.A random pattern of residuals supports a non- linear model. Solution The correct answer is II only.

Directions for TI-83/84 Residuals If we know the data is linear enough, the r value tells us the direction and strength. The r value does not tell us the data is linear