I tried to calculate the minimum sample size for multiple linear regression.

I tried to check the sample size for predictors=4, effect size f=0.2/d=0.2, sig.level =0.05, power=0.8

1. When I checked the power of the entire model (F power) n=304

2. When I checked the power of one coefficient (t power) n=198

2. When I checked the power of one coefficient with Bonferroni correction(t power) n=281 (sig.level =0.05/4)

I probably doing something wrong as I get a smaller sample size when evaluating each coefficient??? (R code below)

You may say regression effect size f and t-test d are not the same. so Low effect is d=0.2 and f=0.14 get even larger sample size with F power.

Thanks

----------------------------------------------------------------------------------------------------------------

Per Green, if you check only for R squared, say the entire model is significant: n=50 + 8*predictors.

and if you try to evaluate the coefficients: n=104+predictors

Code:

```
> pwr.f2.test(u =4, v=(304-4-1), f2=0.04, sig.level =0.05)
Multiple regression power calculation
u = 4
v = 299
f2 = 0.04
sig.level = 0.05
power = 0.8012571
> pwr.t.test(power=0.8, d = 0.2 , sig.level = 0.05 ,alternative="two.sided" , type = "one.sample")
One-sample t test power calculation
n = 198.1508
d = 0.2
sig.level = 0.05
power = 0.8
alternative = two.sided
> pwr.t.test(power=0.8, d = 0.2 , sig.level = 0.05/4 ,alternative="two.sided" , type = "one.sample")
One-sample t test power calculation
n = 281.903
d = 0.2
sig.level = 0.0125
power = 0.8
alternative = two.sided
==============================
> pwr.f2.test(u =4, v=(614-4-1), f2=0.14^2, sig.level =0.05)
Multiple regression power calculation
u = 4
v = 609
f2 = 0.0196
sig.level = 0.05
power = 0.8002173
```