I ran a linear regression with one dependent and one explanatory variable. The data covers log returns of an index and log returns of a stock (natural logarithm). log return of stock = Alpha + Beta + log return of index + error

The p value for the Beta estimate is <2e-16. I googled the meaning of this number, which means that the p value is extremely close to zero, but it does not equal to zero.

Now I am confused, since values below 0.01 show significant results, but what if the p value is practically zero? Does it mean that the regression provides a perfect fit?

  • 4
    $\begingroup$ It certainly doesn't represent a perfect fit. WIth a large enough sample even the noisiest and weakest of sample relationships can have extremely small p-values. $\endgroup$
    – Glen_b
    Commented Sep 25, 2017 at 10:31
  • $\begingroup$ Please explain terms in the model incuding alpha, beta. What is log-return of index ? $\endgroup$
    – user10619
    Commented Sep 27, 2017 at 6:41