Confidence interval and random chance I wonder what the relationship between confidence interval and random chance is. Let me elaborate a bit.
Say, I have the following linear relationship between two variables of $X$ and $Y:$
\begin{align}
Y&=\alpha+\beta_1 X_1+ \varepsilon.
\end{align}
Now, say, I get a  $\beta_1 $ of $10 $ which is statistically significant at $5\%.$
This means there is a $95\%$ probability that the relationship is correct and $5\%$ that it might be incorrect. More specifically, in my case, it means that with every unit increase in $X,$ my $Y $ increases by $10\%.$
Question: Can I interpret my result by saying, given that the coefficient is $10\%, $ my outcome is $5\%$ more than the random chance? Does it even work like this?
So, say, if I take the significance level of $10\%$ to account and my coefficient is hypothetically still $10,$ then is my result basically random and not strong enough to draw any meaningful conclusion from?

No, having a significant result at 5% does not mean that the result is correct 95%.
In linear regression you get a confidence interval on all the coefficients. Usually having a significant result means that the coefficient value of zero, that is $\beta_1=0$ is not in the confidence interval of the coefficient at a 5% level.
The way to interpret it  is that under the assumptions of the model, the chance of $\beta_1$ being zero given the data is less than 5%.
