When I compute the beta coeff between two series how do I find out if there is anything significant in thenumber. I have heard of people using t-stats or t-values or looking at r-square. Could someone pleasetell me in simple terms what these mean and how I should use them or compute them.thanks

I am not a statistician but I will give it a try Since you are talking about two series I guess you run a simple regression with a constant. The output is an alpha coefficient (the constant), a beta coefficient, t-stat values for those two, an R2 value etc.The t-stat tells you whether the value of the coefficient it corresponds to is significant. If not you have to rerun the regression leaving that term out. Once you have a well specified model the R2 value tell you the goodness of fit. I prefer to think of it as how much of the variation in your data is explained by the equation you have formed.Any additions, corrections more than welcome rgds,Dimitris

The mindless approach to regression is to compute Beta and compare the absolute value of the t-statistic to 2. If it's greater then you believe the regression, if it's less you ignore it.The trouble is data analysis requires thinking, not recipes. Betas with high t-statistics should often be ignored, and Betas with low t-statistics are often useful. One key question is whether you're interested in the Beta or the residuals. If it's the Beta, there's some justification for throwing out uncertain values. But the standard of comparison should be the size of the uncertainty, not how close the Beta is to zero. If it's the residual, it's generally good to use any Beta, however uncertain.Another question is whether you are interested in abstract truth, as when writing a journal article, or practical decisions, like how to hedge. Again, in the first case you have to throw out Betas you cannot measure well, but there's seldom anything special about the value zero. In the second case, any Beta can be useful.

QuoteThe trouble is data analysis requires thinking, not recipes.Rarely has a truer word been said - this cannot be over-emphasised.You also need to think about what you're regressing against - a colleague of mine has a theory that there is no alpha in hedge funds, just betas to different benchmarks - I tend to agree.

Where is a Bayesian when you need one?I'm no expert but I think you should look for x(i) = A + B * y(i) + N(0, Cs)(i), where x, y are the returns, by doing a Bayesian analysis, so to obtainP(A, B, C | x, y, I) = P(A, B, C|I) * P(x | A, B, C, y)and if A and C (alpha and sigma residual) are undesired, then integrate to obtain P(B | x, y, I). This gives the whole distribution of B and then you can do what you want with it, i.e. take an estimator with respect to a loss function, get a confidence interval, look at the whole distribution and decide whether it is tight enough to be significant. Oops bracket trouble.

This is a good point, and you don't have to be a Bayesian to profit from it. You can construct a classical confidence interval (what most statistical packages give you automatically) and ask yourself if it is meaningful. This is more useful than asking if the interval contains zero.