Question

After running a regression, you plotted the residual against the predicted value. You observed that the residuals seem to increase (in absolute value) as the predicted value increases. You therefore transformed the dependent variable by taking the natural logarithm of it.?After the transformation is applied you now should see that.. A. the error term has a constant variance. B. the residuals have a constant spread around the predicted value. C. the residuals are all close to zero. D. the residuals decrease (in absolute value) as the predicted value increases.

Answer 1

A. the error term has a constant variance

Explanation:

Firstly, note that it is observed the residuals increase as the predicted value increases. Now the natural logarithm transformation will change will change a skewed variable into a normal distributed value, which leads to a linear regression between the both variables, since they (the independent and dependent variables) are normal. A key assumption of linear regression is Homoscedasticity, therefore the error term obtains the same finite variance.

So as soon as the transformation is applied, the error term will therefore have a constant variance.