quick question on linear regression...

[roadvirusss]

I probably should know this, but in terms of determining correlation between two data series, how do the coefficient of determination (r^2) and the t-statistic (r * sqrt( ( N - 2 ) / ( 1 - r^2)) compare?

I did a linear regression where the r^2 value turned out to be around .2, which is not nearly indicative of a linear relationship. However, since the sample size N was 30, my t-statistic turned out to be about 2.6, which translates to a .015 value of p when cross referenced to 28 degrees of freedom.

Question is: what does the t-statistic actually mean? There was no obvious linear relationship, but the low value of p implies that the results are significant. Does this mean that they are correlated in some other way? Thanks in advance...

 

[galactus]

With 28 degrees of freedom you are very close to the standard normal

distribution. From what I remember, the lower the degrees of freedom,

the 'flatter' the distribution curve. The t-statistic, like the z-statistic, is

telling you that you are 2.6 standard deviations from the mean with about

98.5% confidence. The p-value is the lowest level of significance for which

you can reject the null hypothesis.