Number of observations in regression analysis is considered as
Answers
If you are using just one predictor variable, choice of sample size can be made relative to the size of the correlation between the X predictor and Y outcome.
People generally want power to be at least 80% (that is, 80% chance of obtaining a statistically significant outcome when the true effect is not zero). That corresponds to beta, risk of Type II error, of .20.
It is necessary to state the criterion for significance. For the test of a regression coefficient, alpha = .05 two-tailed is a common choice.
Then you need to make a ball park guess for effect size (the absolute magnitude of the correlation).
In this instance, you can do power analysis for the correlation to find out sample size for a regression with just one predictor; for multiple predictors, it’s more complicated.
Using this information you can use an on line calculator such as the one at
Correlation sample size - Sample Size Calculators
For the example below I set:
Significance criterion alpha = .05, two tailed
Risk of Type II error = beta = .20 (power = .80)
Guess at correlation/ strength of association = .30
In order to have power of .80, a sample size of at least N = 85 is needed.
If you have multiple predictor variables in a regression, here is advice from Tabachnick & Fidell, Using Multivariate Statistics (k is the number of predictors)
a minimum N > 50 + (8*k) for tests of multiple R
a minimum N > 104 + k for tests of individual predictors
In general, for publishable results, N should be over 100.
Much research in the social sciences is “under powered”, that is, the sample sizes are too small