# Interpreting regression Output for CAPM

I have an interpretation problem. As you can see below there's a linear regression output for the CAPM. I don't know how to interpret the significance level. ExIndex has a very low p-value, but the Significance level is 0. So can I reject H0 or not? The same question for the intercept.

Coefficients:
Estimate     Std. Error  t value  Pr(>|t|)
(Intercept) - 0.003258     0.001560    -2.089       0.0377 *
ExIndex      0.898980     0.106511     8.440     2.3e-15 ***
Signif. codes:   0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02508 on 258 degrees of freedom Multiple

p-values are to some extend based on the readers or the analysts perspective, but the general rule is, the closer your value is to zero the more evidence you have against $H_0$. R uses a star rating system according to commonly used significant (cut-off points) levels,so as to help the readers decision. For example the three stars next to the p-value of ExIndex suggest that there is very strong evidence against the hypothesis that $\beta_1 = 0$, while on the other hand the one star next to the p-value of the intercept suggests that the hypothesis that $\beta_0 = 0$ might be rejected at a cut of point of 5%, while is not rejected at 1% and 0.1% cut of point. It is worth noting that things like practical and statistical significant are to be taken into account when dealing with p-values.