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Hypothsis Testing refers to the ability to make statistical statements of certainty or precision about parameter estimates based on the assumptions of statistical distributions such as normality. This is one of the main advantages of regression analysis. Let's say sales revenue is a function of advertising dollars and the price of your product. You could estimate the following regression equation if you collected sufficient data:

Sales $$ = Constant + B1(Advertising $$) - B2(Price)

Sales $$ = 12212 + .00133 * Advertising - .02 * Price

How sure can we be -.02 is really a good estimate for price, and not just a result of sampling error or data collection? Regression packages compute the standard errors (precision measures) of each parameter estimate. By using the concept of hypothesis testing, we can test to see if those errors are sufficiently large or small enough to make confidence statements about our results.

One common hypothesis test, the t-test, tells us if the -.02 price estimate is significantly different than zero. In other words, if the test indicates that the -.02 estimate is really no different than zero, than the sampling error was so big that we should have little confidence that fluctuations in price over time had anything to do with trends or shifts in sales revenue. This particular test is computed by dividing the estimated price coefficient by its standard error. This ratio can be compared to a value in a statistical table (given the sample size and degree of certainty you wish) to determine if sampling error played too big a role in coming up with your estimate. For this type of test, the rule of thumb is that the ratio should be greater than 2.0 (in absolute value) to be of much value.

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