Introduction to Probability and Statistics for Engineers and Scientists

426 Chapter 9: Regression

Stress N

(thousand psi) (million cycles to failure)

55.0 .223

50.5 .925

43.5 6.75

42.5 18.1

42.0 29.1

41.0 50.5

35.7 126

34.5 215

33.0 445

32.0 420

EstimateAandm.

33.In 1957 the Dutch industrial engineer J. R. DeJong proposed the following model

for the time it takes to perform a simple manual task as a function of the number

of times the task has been practiced:

T≈ts−n

whereTis the time,nis the number of times the task has been practiced, andt

andsare parameters depending on the task and individual. Estimatetandsfor

the following data set.

T 22.4 21.3 19.7 15.6 15.2 13.9 13.7

n 0123456

34.The chlorine residual in a swimming pool at various times after being cleaned is

as given:

Chlorine Residual

Time (hr) (pt/million)

2 1.8

4 1.5

6 1.45

8 1.42

10 1.38

12 1.36

Fit a curve of the form

Y≈ae−bx

What would you predict for the chlorine residual 15 hours after a cleaning?