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A statistician wishes to know the sample size needed in a multiple regression study. She has...

A statistician wishes to know the sample size needed in a multiple regression study. She has four predictors and can tolerate at most a .10 drop-off in predictive power. But she wants this to be the case with .95 probability. From previous related research, the estimated squared population multiple correlation is .62. How many subjects are needed?

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Solution: A statistician wishes to know the sample size needed in a multiple regression study. She has four predictors and can tolerate at most a 0.10 drop-off in predictive power. But she wants this to be the case with 0.95 probability. From previous related research, the estimated squared population multiple correlation is 0.62. How many subjects are needed?

Answer: To find the sample size, we use the below formula:

We are given:

is the critical value at 0.05 significance level and can be found using the standard normal table:

Therefore, there are 91 subjects needed.

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