Chapter 7.2, Problem 14E

An engineer wants to predict the value for y when x = 4.5, using the following data set.

1. a. Construct a scatterplot of the points (x, y).
2. b. Should the least-squares line be used to predict the value of y when x = 4.5? If so. compute the least-squares line and the predicted value. If not, explain why not.
3. c. Construct a scatterplot of the points (x, z), where z = ln y.
4. d. Use the least-squares line to predict the value of z when x = 4.5. Is this an appropriate method of prediction? Explain why or why not.
5. e. Let $\hat{z}$ denote the predicted value of z computed in part (d). Let $\hat{y}=e^{\hat{z}}$ Explain why $\hat{y}$ is a reasonable predictor of the value of y when x = 4.5.