Exercise
From an investigation of the residuals of fitting a linear regression by ordinary least squares it is clear that the spread of the residuals increases as the predicted values increase. Observed values of the dependent variable range from 0 to 100. Determine which of the following statements is/are true with regard to transforming the dependent variable to make the variance of the residuals more constant.
- Taking the logarithm of one plus the value of the dependent variable may make the variance of the residuals more constant.
- A square root transformation may make the variance of the residuals more constant.
- A logit transformation may make the variance of the residuals more constant.
- None
- I and II only
- I and III only
- II and III only
- The correct answer is not given by (A), (B), (C), or (D).
Key: B
Adding a constant to the dependent variable avoids the problem of the logarithm of zero being negative infinity. In general, a log transformation may make the variance constant. Hence I is true.
Power transformations with the power less than one, such as the square root transformation, may make the variance constant. Hence II is true.
A logit transformation requires that the variable take on values between 0 and 1 and hence cannot be used here.