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

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

z = In y z= In y 0.2 -1.61 6. 2.3 0.83 -1.20 -0.69 0.3 2.9 1.06 3 0.5 4.5 1.50 0.5 -0.69 8.7 2.16 1.3 10 12.0 2.48 0.26