0

I have a multilinear regression model with 4 parameters and 164 observations. I want to determine the confidence intervals for each coefficient of the multilinear regression. I have the covariance matrix for the 4 parameters. The formula for calculating the confidence intervals for βᵢ, the coefficient corresponding to parameter xᵢ, is given by:

$IC = [βᵢ ± t_{α/2}^{n-p-1} \sqrt{Var(βᵢ)/(n-p)}]$

Here, n represents the number of observations (164 in my case), p represents the number of parameters (4 in my case). $Var(βᵢ)$ refers to the corresponding element of the covariance matrix.

My question is should I divide by the (n-p) in the $\sqrt{Var(βᵢ)/(n-p)}$ or not, i find different versions of it on the internet.

Ay Jab
  • 1
  • 1
    It depends, because "$Var(\beta_i)$" is either zero or undefined (because $\beta_i$ is not a random variable: it's a parameter in the model). Some formulas will refer to the residual variance, others to the error variance, and yet others to the sampling variance of the estimate of $\beta_i.$ Could you please tell us, then, exactly how you interpret "$Var(\beta_i)$"? – whuber Jul 05 '23 at 17:28
  • The thing I don't know exactly how they are calculated, all I know that model is a multilinear regression and in the output i have the covariance matrix with correlations of variables and their standard deviations, so I assume it's a classic covariance matrix that normally is calculated in a multilinear regression model as: $\hat{\Gamma}n=\frac{1}{n-1} \sum{k=1}^n\left(X_k-\bar{X}_n\right)^t\left(X_k-\bar{X}_n\right) .$ – Ay Jab Jul 07 '23 at 12:27
  • Please visit the results of this site search for multiple regression variance matrix. – whuber Jul 07 '23 at 13:27

0 Answers0