The size of the sample determines the reliability, the extent that the regression analysis result is error free. It determines the statistical power of the significance testing, as well as the generalizability, i.e., the ability to apply the result to the larger population.
As a thumb rule, 15 to 20 observations are required for each independent variable. If the sample is constrained, a bare minimum of 5 observations are required for each independent variable, provided there are at least 20 observations for simple regression, and 50 for multiple regression.
Small samples can detect only the stronger relationships. Moreover, if the ratio of observations to parameters is below norm, you run the risk of “overfitting” – making the results too specific to the sample, thus lacking generalizability. Increasing the degrees of freedom improves generalizability and reliability of the result.
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