SOME HYPOTHESES OF INTEREST


We will return to the question of how you can examine your data to see if they violate any of these assumptions, but meanwhile, suppose that the data do satisfy all of the assumptions outlined above. What sorts of hypotheses can we now test? We can test hypotheses about the values of the population slope and the population intercept and hypotheses about how well the regression model fits the population. With the computer, this is no problem. However, one has to watch out for the coefficients of the regression, because instead of thinking of these values as descriptions of the sample, we will now treat them as our best guesses, or estimates, of the unknown population values of the slope and intercept. Another thing you have to watch is the fact that the coefficients and plot values may not be exactly the same, even though they are the same variables . This is because they are not all the same cases. Previously we took a smaller sample so we would not have too many cases to plot. We would expect the slope and intercept in a plot to be better estimates of the population values than the values that we are considering now, since these are now based on more cases.

It is also important to recognize that since both the slope and the intercept are calculated numbers there is variation within them. That variation is identified as the standard error of the slope and intercept. The standard errors are estimates of the standard deviation of the sampling distributions of the slope and the intercept. Remember, the slope and intercept we have calculated are based on one sample from a population. If you took another sample and calculated values for the slope and intercept they would differ . The values of the slope and intercept from repeated samples from the same population have a distribution. The standard deviation of this distribution is called the standard error. It is just like the standard error of the mean.




Six Sigma and Beyond. Statistics and Probability
Six Sigma and Beyond: Statistics and Probability, Volume III
ISBN: 1574443127
EAN: 2147483647
Year: 2003
Pages: 252

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