Appendix A. Introduction to statistics and analytic concepts 231
A.1.10 Interpolation
Interpolation simply means to calculate a new value in between two known
values. Linear interpolation uses the output of a linear regression to arrive at new
values of a dependent variable based on the input of an independent variable
value in to the linear regression model. That is, interpolation is the creation new
values at equal distances along a line between two known values.
A.1.11 Extrapolation
Extrapolation involved projecting out to new values outside the range of known
values based on a regression model. In general, extrapolation is not very reliable
and the results so obtained are to be viewed with a healthy scepticism. In order
for extrapolation to be at all reliable, the original data must be very consistent.
A.1.12 Probability
The probability of an event is the likelihood of it occurring, and is expressed as a
number between 0 (certainty that the event will not occur) and 1 (certainty that
the event will occur).
In a situation where all outcomes of an experiment are equally likely, then the
probability of an event is equal to the number of outcomes corresponding to that
event divided by the total number of possible outcomes.
In a deck of 52 playing cards, the probability of drawing a KING would be 4/52,
since there are 4 KINGs in the deck. The probability of drawing KINGS or
QUEENS would be 8/52. The probability of not drawing a KING or QUEEN would
be 44/52.
If A and B represent events, the some properties of probabilities include:
Pr(not A) = 1 - Pr(A)
Pr (A or B) = Pr(A) + Pr(B) if A & B are mutually exclusive events
Pr (A or B) = Pr(A) + Pr(B) - Pr(A and B) for any 2 events
Pr (A and B) = Pr(A) x Pr(B) if A and B are independent events
A.1.12.1 Conditional probability
Given 2 events A and B, the conditional probability of A given B is the probability
that A will occur, given that B has occurred. If B has nonzero probability, then the
condition probability of A given B is:
Pr(A|B) = Pr(A and B) / Pr(B)
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