Thread: Hypothesis test involving regression coefficient

I'm working on a problem and was hoping I could get either confirmation that I'm doing it correctly, or help in learning the correct way. I used Excel to calculate a stock's Beta, comparing percentage changes in the stock price to that of the S&P 500. I am now tasked with implanting a hypothesis test testing whether the population Beta is greater than 1. My understanding of how to work this problem is that I will subtract 1 from my regression coefficient, and then divide that by the standard error of the regression coefficient to arrive at my t-statistic. I will then use a one tail t-test to arrive at my p-value. Is this correct? If not, how would I go about conducting this test? Thank you very much for your time and help.

Hey Ironlionzion.

What is this Beta? Is this some kind of mean (Since you mention a t-test, this is used primarily for means)?

The idea that you have for getting a statistic and a p-value for the null hypothesis is the way to do it, but the only thing that I am not clear on is what this Beta actually is and how its calculated from your sample.

Chiro,

Thank you for your reply. Beta is just my regression coefficient from my regression equation. It measures a stock's volatility versus the market. So, basically I'm being tasked with testing whether the regression coefficient for my population would be greater than 1. Thank you again for your time and help.

It will depend on your model and your data, but essentially the whole thing boils down to what the distribution of your Beta's are.

I did a quick search, and the following seems like a good place to start reading:

http://www.google.com.au/url?sa=t&rc...ZO8zKw&cad=rja

The key thing is finding a distribution for your Beta's and then using that to get p-values or intervals for a significance level to test hypotheses in the exact same way you do it in a t-test, or an F-test.

The other way that is derived from scratch is the Bayesian Inference technique that puts priors on the parameters and gets a distribution for the coeffecients which is a t-distribution (multi-variate) with the point estimates being the normal ones calculated from Least Squares with a covariance matrix given also by the LSE approach sigma_hat^2 * (X'X)^(-1) where X' is the transpose of the design matrix X and sigma_hat^2 is the estimate of sigma^2).

You should be able to use this result and you can look it up either on Google or in a textbook (my resources are from university notes which I can't share unfortunately).