I want to apply linear regression or multiple regression to see the correlation between dependent and independent variables, I have 4 time for each factor, that means I have 16 observations for all predictors, the number of observations is an acceptable?
Hi Mahar
Not easy to say. A rule of thumb is 5-10 respondents or each variable. But it depends on a couple of things.
Take a look at: www.researchgate.net/post/How_large_should_a_sample_size_be_for_multiple_regression_What_is_the_minimum/amp
And
https://stats.stackexchange.com/questions/10079/rules-of-thumb-for-minimum-sample-size-for-multiple-regression
Soms sources are mentioned
Please check Hair et al. [Hair, Black, Babin, Anderson & Tatham. (2014). Multivariate Data Analysis, 7th Edition]. See discussion on sample size in pages 573-574, 10:1 is desirable.
many rule of thumbs recommended required sample size for linear regression analysis based on predictor variables or participant number (e.g. above 50 participants) or both ( 5 participants/ten participants for each predictor variable) However, most obvious answer is It depends on your studied sample or sample characteristics. If you are working on a rare disease probably, none of the below rules did not work for that sample. However, One commonly used rule of thumb is Green (1991) recommendation N ≥ 50 + 8 m for the multiple regression or N ≥104 + m for testing importance of predictors where m is number of predictor variables. Lastly, most approximate way to calculate required sample size is using prior power calculation as suggest by Sofia. For g power
follow below steps.
G*Power:
- F-test
- Linear multiple regression: fixed model R2 deviation from zero
(R2 increase would be for hierarchical regression)
Above calculation give you wer determine ( you can use f2 = 0.15 (maybe .02 or .35))
or Rho = estimate based on r2
- Alpha = .05 (minimum)
- Beta = .80 (minimum), (.95 preferable)
- Number of predictors = number of IVs.
Above calculation give you required sample size for different effect sizes.
Have a good work.
The rule of thumb is usually 10 subjects per predictor.
I'm going to dissent slightly. There is no correct answer because it depends on the size of the effects you want to able to detect (or specifically the size of their unique contribution to the regression relative to error/noise). Common rules of thumb are either plucked from thin area or taken from papers that assume a certain size of effect and a certain pattern of correlations between predictors (e.g., see Green, 1991).
Also your model is repeated measures and thus you need to look at statistical power to detect effects in a multilevel or repeated measures regression. Using a calculator like PANGEA to explore power might be useful:
https://jakewestfall.shinyapps.io/pangea/
one of the Assumptions of multiple regression is sample size = 100 respondents or more. Besides linearity , co-linearity, normality, and multi co-linearity.
Dr. Mansour Lotayif
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