Page 120 - Standard Handbook Of Petroleum & Natural Gas Engineering

Applied Statistics 105

where s = standard deviation of sample
ta, t,,? = values of variables having a t distribution with v = n - 1, and a %
of distribution cut off in one tail and a/2 % in both tails = F
s/& = measure of dispersion

The confidence interval on the variance is computed by

= values of a random variable with a chi-square distribution
cutting off a/2 % and a %, respectively, of the right tail
= values of a random variable with a chi-square distribution
cutting off (1 - a/2) % and (1 - a) %, respectively, of the
left tail
S2 = KCu
X2 values = distribution factors

Correlation
Correlation analysis quantifies the degree to which the value of one variable
can be used to predict the value of another. The most frequently used method
is the Pearson product-moment correlation coefficient.
The coefficient of determination is the fraction of the variation that is explained
by a linear relationship between two variables and is given by

where Y = observation on the random variable
Y = value of Y estimated from the best linear relationship with the second
variable X
y = mean of the observations on Y
and R is the correlation coefficient. A perfect association is indicated by R = 1
for a direct relationship and R = -1 for an inverse relationship. R = 0 indicates
no linear association between X and Y.