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

xyz = ???????? y x yz = ???????? y 1 0.2 −1.61 6 2.3 0.83 2 0.3 −1.20 7 2.9 1.06 3 0.5 −0.69 8 4.5 1.50 4 0.5 −0.69 9 8.7 2.16 5 1.3 0.26 10 12.0 2.48

a. Construct a scatterplot of the points (x, y).

b. Should the least-squares line be used to predict the value of y when x = 4.5? If so, compute the leastsquares line and the predicted value. If not, explain why not.

c. Construct a scatterplot of the points (x, z), where z = ln y.

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.

e. Let ẑ denote the predicted value of z computed in part (d). Let ŷ = eẑ

. Explain why ŷ is a reasonable predictor of the value of y when x = 4.5.