Chapter 12.2, Problem 54E

To determine

To find: the best reason to prefer the least square regression lint which uses $x$ to predict $\log y$

Answer to Problem 54E

The residual plot has more random scatter.

Explanation of Solution

Interested in the best reason to prefer the least-squares regression line that uses x to predict log(y)

1. When the value of $r^2$ is smaller, then this means that less of the variation in log(y) has been described by x compared to the model which predicts $\sqrt{y}$ instead and therefore the model is a worse model. This then means that this is not a good reason to prefer the model which uses x to predict log (y).
2. When the standard deviation of the residuals is not bigger, then there is less variation between the actual values and predicted values and therefore the model is a better model. This then means that this is a good reason to prefer the model that uses x to predict log (y).
3. The largeness of the slope is not affected how good a model is and therefore this is not the best reason to prefer the model that uses $x$ to expect $\log y$
4. A residual figure is having more random scatter is not necessarily imply that the model is better, the reason is that the increased about of scatter could be due to more variation between the expected values and the actual values. Then this means that this is not the best reason to prefer the model that uses $x$ to predict $\log y$ .
5. Normal that the distribution of the residual of the residual is no affect how good a model is . this then means that this is not the best reason to prefer the model that uses $x$ to predict $\log y$

Hence, the correct option is (b)