Page 123 - Standard Handbook Of Petroleum & Natural Gas Engineering

108 Mathematics

The confidence interval for a line of m ppints may be plotted by computing
the confidence limits Ycl at each point, (Xxt, Y',,, i = 1,2, . . .,m) of the regression
line when

where ?,,, = Y + b,(X,x, - x)
-
F = F statistic obtained for (2,n - 2) degrees of freedom and a level of
significance a = 1 - y, y being the level of confidence.
The confidence interval for a single point, say X<,, can be computed using
the interval
1
1) 5

where t,, = value of random variable having a t distribution with (n - 2) degrees
cf freedom akd a level of confidence a = 1 - y
9 = Y + b,(X<, - X)

The confidence interval for a future value X, is given by

where +=Y+b,(X,-X)

COMPUTER APPLICATIONS
See References 29-40 for additional information.
Some areas of digital computer use that are highly applicable to the engineer-
ing field include
Numerical computations for design and modeling
Information storage and retrieval
Data sorting and reduction
Computer-aided graphics for illustration, as well as for design
Word processing
Communication networks and database access
The rapid increase in computer applications is partly attributable to both the
decreasing costs of hardware and software and to the increasing costs of human
labor. This shift has given rise to a productivity factor assigned to various tasks
performed by computers versus people. One figure recently quoted was a
minimum factor of 4 to 5 for CAD (computer aided design), that is, one
draftsman with a CAD system can replace 4 to 5 manual draftsmen.