The accompanying Minitab regression output is based on data that appeared in the article “Application of Design of Experiments for Modeling Surface Roughness in Ultrasonic Vibration Turning” (J. of Engr. Manuf., 2009: 641–652).

The response variable is surface roughness (mm), and the independent variables are vibration amplitude (mm), depth of cut (mm), feed rate (mm/rev), and cutting speed (m/min), respectively.

a. How many observations were there in the data set?

b. Interpret the coefficient of multiple determination.

c. Carry out a test of hypotheses to decide if the model specifies a useful relationship between the response variable and at least one of the predictors.

d. Interpret the number 18.2602 that appears in the Coef column

e. At significance level .10, can any single one of the predictors be eliminated from the model provided that all of the other predictors are retained?

f. The estimated SD of when the values of the four predictors are 10, .5, .25, and 50, respectively, is .1178.
Calculate both a CI for true average roughness and a PI for the roughness of a single specimen, and compare these two intervals.
The regression equation is Predictor Coef SE Coef T P Constant 0.9723 0.3923 2.48 0.015 a 0.03117 0.01864 1.67 0.099 d 0.5568 0.3185 1.75 0.084 f 18.2602 0.7536 24.23 0.000 v 0.002822 0.003977 0.71 0.480 Source DF SS MS F P Regression 4 401.02 100.25 148.35 0.000 Residual Error 76 51.36 0.68 Total 80 452.38