Introduction to Probability and Statistics for Engineers and Scientists

432 Chapter 9: Regression

x 1 x 2 x 3 y

7.1 .68 4 41.53

9.9 .64 1 63.75

3.6 .58 1 16.38

9.3 .21 3 45.54

2.3 .89 5 15.52

4.6 .00 8 28.55

.2 .37 5 5.65

5.4 .11 3 25.02

8.2 .87 4 52.49

7.1 .00 6 38.05

4.7 .76 0 30.76

5.4 .87 8 39.69

1.7 .52 1 17.59

1.9 .31 3 13.22

9.2 .19 5 50.98

48.The tensile strength of a certain synthetic fiber is thought to be related tox 1 , the

percentage of cotton in the fiber, andx 2 , the drying time of the fiber. A test of 10

pieces of fiber produced under different conditions yielded the following results.

Y=Tensile x 1 =Percentage x 2 =Drying

Strength of Cotton Time

213 13 2.1

220 15 2.3

216 14 2.2

225 18 2.5

235 19 3.2

218 20 2.4

239 22 3.4

243 17 4.1

233 16 4.0

240 18 4.3

(a) Fit a multiple regression equation.

(b) Determine a 90 percent confidence interval for the mean tensile strength of

a synthetic fiber having 21 percent cotton whose drying time is 3.6.

49.The time to failure of a machine component is related to the operating volt-

age (x 1 ), the motor speed in revolutions per minute (x 2 ), and the operating

temperature (x 3 ).