Downloaded from https://www.everyspec.com AMCP 70.-19 using linear regreuson analysis. b' p y-axis intercept of the line Regression analysis is a statistical techni- e = standard s-normal variate quo that quantitatively defines the "best" fit of a line through a set of data points. a a - standard deviation of y from j" Correlation is a related technique but con- aldes the interdependence of the variables 57 = "mean" value of y (a function of rather than the dependence of one on an- x'). It is averaged over s. other. The distinction between the two techniques can be rather subtle and Refs.
I = subscript denoting a particular set 24 and 32 or other standard works ought to of measured values (the el is not be consulted. Consider leakage current and actually measured, it is there to life of a transistor. It cannot be said that make an equality) I a- 1, .. N one causes the other (although they may have common causes); so one might be in- E, implies the sum over all N test terested in their correlation. But If one is data interested in prediting the life by measuring the leakage current, then regression is used. N = number of test data pairs As another example consider the ambient temperature and the life of a transistor.
"Best" fit is usually defined as the "least- From a physical point of view, it is not use- squares" fit, iLe,, S:ael -+ a minimum, by ful to speak of life's causing the ambient adjusting m and b'. When # is a standard temperature, only the other way around; so s-normal variate, the maximum likelihood one is interested only in regression, solution Implies the least-squares solution. As used in this chapter, and in many It is convenient to redefine the x' and b' statistical treatments, regression Implies as follows: linear rogression, and correlation implies Uri- ear correlation. Further, this chapter con- a' *(E )/N siders only 2 vwriables, For more extensive treatments, see Rets, 12, 17, 24.
and 32 or X N X' -a' other statistical texts. The problem Is to find the "best" straight line for the test data. xe xa - a' In linear regression, Eqs. 2-55 and 2-56 are b a ma' + b' (2-57) assumed Then the Eqs. 2-55 and 2-56 become y = mX+ V +a •(2-55) y=mx+b+a (2-88) -rmx' + b' (2-56) Y -mx +b (2-89) where y = dependent variablu (a function of The randomness in y can be caused by x') measuring techniques, experimental uncer- taintles, and/or component part variations. independent variable The least-squares solution is M . slope of the line "(Emy)/v (2..60) ,,: ',: