An Introduction to Econometrics, 2nd Edition by A. A. Walters (auth.)

By A. A. Walters (auth.)

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Example text

It involves no new concepts of probability; the chances that appear in this approach are simply the probabilities of getting specified evidence given the hypothesis is true. The second group of critics, however, do depart quite radically from the orthodox concepts of probability. So far we have argued that one cannot attach a probability to a hypothesis; for a hypothesis is either true or it isn't. A hypothesis is a statement about the state of nature and cannot be interpreted as being true 'on the average x per cent times ~ METHODOLOGY, PROBABILITY AND SAMPLING in a long series of trials'.

Instead of dividing the sum of squares by n the number of observations, STATISTICAL INFERENCE 41 we divide instead by the number of degrees offreedom (n- 1). The concept of degrees of freedom replaces the number of observations as the critical denominator in the variance estimator. To interpret the degrees of freedom, examine the case of two observations x1 and x2• We find the sum of squares of deviations from the mean. The first deviation is (x 1 -x). But ifwe knew this deviation we would know also the value of (x~- x).

The concept of degrees of freedom replaces the number of observations as the critical denominator in the variance estimator. To interpret the degrees of freedom, examine the case of two observations x1 and x2• We find the sum of squares of deviations from the mean. The first deviation is (x 1 -x). But ifwe knew this deviation we would know also the value of (x~- x). Since x= (x 1 +x 2)/2 knowledge of x and x1 is sufficient to calculate x2• Thus we conclude that there is only one degree offreedom in this estimate of the variance.

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