I am looking into the method to calculate the sample size if we would want the specific coefficient significantly different from zero. I have 4 independent variables and 1 dependent variable. And I have 50 observations so far. I would like to know how many more observations do I need to get one of the coefficients significant because it's trending.
I have read this paper from Ken Kelley and Scott E. Maxwell, "Sample Size for Multiple Regression: Obtaining Regression Coefficients That Are Accurate, Not Simply Significant". And they have this formula to estimate sample size.
$N = \Big(\frac{z_{(1-\alpha/2)}}{w}\Big)^2\Big(\frac{1-R^2}{1-R^2_{XX_j}}\Big) + p + 1$
where $R^2$ represents the population multiple correlation coefficient predicting the criterion (dependent) variable $Y$ from the $p$ predictor variables and $R^2_{XX_j}$ represents the population multiple correlation coefficient predicting the $j$th predictor from the remaining $p − 1$ predictors. The calculated $N$ should be rounded to the next larger integer for sample size. The $w$ in the above equation is the desired half-width of the confidence interval.
$R^2$ is easy to calculate. But I don't know how to calculate $R^2_{XX_j}$ for this. Do you guys have any idea?