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Week #29 – Goodness-of-fit

is hypothesized to describe the observed distribution.  For example, if you were picking 12 birthdays randomly from the days in the year, the expectation is that the 12 months would be approximately equally represented.  We would be surprised if all 12 picks were from the same month.  There would be some random variation, of course, so we would also be surprised if each month was represented once.  Goodness-of-fit measures the extent to which the actual picks depart from the theoretical uniform distribution, and a goodness-of-fit test measures the extent to which this departure might be random.  Goodness of fit tests are used, for example, in regression analysis to determine measure how well a regression model fits the observed data. .