Society of Actuaries (SOA) PA Practice Exam

What graphical method is used to check the linearity assumption in regression analysis?

1. Residuals versus Fitted values graph

2. Normal QQ Plot

3. Scale-Location graph

4. Residuals versus Leverage graph

The correct answer is: Residuals versus Fitted values graph

In regression analysis, the linearity assumption posits that there is a linear relationship between the independent and dependent variables. One effective way to check this assumption is by using a Residuals versus Fitted values graph. When you plot the residuals (the differences between the observed and predicted values) against the fitted values (the predicted values from the regression model), you are looking for patterns in the residuals. If the linearity assumption holds true, the residuals should be randomly scattered around the horizontal axis (the zero line) without any discernible pattern or structure. If you observe a clear pattern, such as a curve or a trend, this indicates that the relationship may not be linear and suggests that a different model or transformation may be needed. Other graphical methods, like the Normal QQ plot, primarily assess the normality of residuals rather than linearity. The Scale-Location graph helps to evaluate homoscedasticity (constant variance of residuals) but does not directly check for linearity. Similarly, the Residuals versus Leverage graph serves to identify influential data points but is not specifically aimed at detecting linearity in the relationship. Thus, the Residuals versus Fitted values graph is the most appropriate choice for assessing