The article “Application of Radial Basis Function Neural Networks in Optimization of Hard Turning of AISI D2 ColdWorked Tool Steel with a Ceramic Tool” (S. Basak, U. Dixit, and J. Davim, Journal of Engineering Manufacture, 2007:987–998) presents the results of an experiment in which the surface roughness (in ????m) was measured for 27 D2 steel specimens and compared with the roughness predicted by a neural network model. The results are presented in the following table.

True Predicted True Predicted True Predicted Value (x) Value (y) Value (x) Value (y) Value (x) Value (y)

0.45 0.42 0.52 0.51 0.57 0.55 0.82 0.70 1.02 0.91 1.14 1.01 0.54 0.52 0.60 0.71 0.74 0.81 0.41 0.39 0.58 0.50 0.62 0.66 0.77 0.74 0.87 0.91 1.15 1.06 0.79 0.78 1.06 1.04 1.27 1.31 0.25 0.27 0.45 0.52 1.31 1.40 0.62 0.60 1.09 0.97 1.33 1.41 0.91 0.87 1.35 1.29 1.46 1.46 To check the accuracy of the prediction method, the linear model y = ????0 + ????1x + ???? is fit. If the prediction method is accurate, the value of ????0 will be 0 and the value of ????1 will be 1.

a. Compute the least-squares estimates ????̂

0 and ????̂

1.

b. Can you reject the null hypothesis H0 : ????0 = 0?

c. Can you reject the null hypothesis H0 : ????1 = 1?

d. Do the data provide sufficient evidence to conclude that the prediction method is not accurate?

e. Compute a 95% confidence interval for the mean prediction when the true roughness is 0.8 ????m.