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Statistical Methods in Economics

Notes is said to be positive. If the values of two variables move in the opposite directions i.e., an
increase in the value of one variable is associated with fall in other, or vice versa, the correlation
is said to be negative. For example, the price and supply are positively correlated but price and
demand are negatively correlated.
(2) Linear and non-linear correlation: If, in response to a unit change in the value of one variable,
there is a constant change in the value of the other variable, the correlation between them is
said to be linear. This means, the relation between variables fits in Y = a + bX. But when no
constant change in variable is registered for a given unit change in other variable, non-linear or
curvilinear correlation is said to exist.
(3) Simple, multiple and partial correlation: When relation between two variables is studied, it is
simple correlation. When three or more factors are studied together to find relationships, it is
called multiple correlation. In partial correlation, two or more factors are agreed to be involved
but correlation is studied between only two factors, considering other factors to be constant.
9.2 Application of Correlation for Economists

The cause and effect relation existing between economic events is especially difficult to ascertain
because of the presence of innumerable variable elements. In solving his problems the economist can
not, like the physicist or chemist, eliminate all causes except one and then by experiment determine
the effect of that one. Causes must be dealt with en masse. Since any effect is the result of many
combined causes the economist is never sure that a given effect will follow a given cause. In stating
an economic law he always has to postulate “other things remaining the same,” with, perhaps, little
appreciation of what the other things may be. It is rarely, if ever, possible for the economist to state
more than “such and such a cause tends to produce such and such an effect.” Events can only be
stated to be more or less probable. He is dealing mainly, therefore, with correlation and not with
simple causation.
The problems of economics are similar to certain problems of biology, such as the effect of environment
and heredity upon the individual. In dealing with the question of heredity Karl Pearson says: “Taking
our stand then on the observed fact that a knowledge neither of parents nor of the whole ancestry
will enable us to predict with certainty in a variety of important cases the character of the individual
offspring we ask: What is the correct method of dealing with the problem of heredity in such cases ?
The causes A, B, C, D, E , . . . which we have as yet succeeded in isolating and defining are not always
followed by the effect X, but by any one of the effects U, V, W, X, Y, Z. We are therefore not dealing
with causation but correlation, and there is therefore only one method of procedure possible; we
must collect statistics of the frequency with which U, V, W, X, Y, Z, respectively, follow on A, B, C, D,
E . . . From these statistics we know the most probable result of the causes A, B, C, D, E and the
frequency of each deviation from this most probable result. The recognition that in the existing state
of our knowledge the true method of approaching the problem of heredity is from the statistical side,
and that the most that we can hope at present to do is to give the probable character of the offspring of
a given ancestry, is one of the great services of Francis Galton to biometry.”
Just as the biologists cannot predict a man’s height or color of eyes or temper or combativeness by
knowing those qualities in his ancestors, so economists cannot predict that a definite call rate in Wall
Street will go with a given percentage of reserves to deposits in New York banks or that a given
supply of wheat will result in a definite price per bushel. But, on the other hand, just as it has been
observed that there is a relation existing between a man’s stature and the stature of his ancestors, so
it has been observed that a relation does exist between bank reserves and call rates and between
supply of wheat and its price per bushel.
In order to deal in a satisfactory way with such questions as those given above it is necessary to
accumulate statistics of the supposedly related phenomena. In order to have those statistics indicate
anything it is necessary to obtain a method of measuring the extent of correlation between the phenomena.
The commonly used method of measuring the amount of correlation between any two series of
economic statistics is to represent the two series graphically upon the same sheet of cross-section
paper and then compare the fluctuations of one series with those of the other. The quantity theory of

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