Page 122 - Standard Handbook Of Petroleum & Natural Gas Engineering

Applied Statistics 107

and

and by solution of the set, b,, and b, can be obtained.
The standard deviation Sy gives the accuracy of prediction. If Y is related to
one 01- more predictor variables, the error of prediction is reduced to the
Ftnndurd crror of ertimute Se (the standard deviation of the errors), where

where v = degrees of freedom, or sample size - number of unknowns. For the
general linear model with an intercept, there are (p + 1) unknowns
and v = n - (p + 1)

If Sc = 0, then R = 1, and if Se = Sv, then R = 0.
The sta?adurdized partial regresszok coeffzcient t is a measure of the relative
importance of the corresponding predictor and is given by

t = (b,S,)/S,
whei-r -1 < t < 1 for rational models

The two-sided confidence intervals for the coefficients b<, and b,, when p, and
PI are random variables having t distributions with (n - 2) degrees of freedom
and error variances of

spcx;
Se(b,,) =
nC(X, - X)?
and

are (if a is the level of significance)