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Provide some discussions on potential issues of using a small sample (in a multiple regression model)...

Provide some discussions on potential issues of using a small sample (in a multiple regression model) from the econometric viewpoint.

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Small sample size is extremely problematic for regression analysis as it reduces the power of the test. The power of the test is its ability to identify type II errors. A small sample size increases the probability of a type II error ( false acceptance) and reduces the power of the test. This will also lead to an inflated effect size estimation. It is very common to use the following formula for finding the ideal sample size:

Sample size = (Z-score)2 x SD x (1-SD)/ME2

Thus, we see that as sample size reduces, the margin of error increases (ME and sample size are inversely proportional) and the z-score increases (increased type II error)

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