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?

This is incorrect, significance at 5% level does not mean that you have 95% chance of being correct. Hence, the rest of reasoning does not hold.
I do not follow the rest of your question but you cannot multiply coefficients by significance level, it’s comparing apples to oranges, meaningless. Significance level is also not  something that you pick based on your results to “make” them significant, this would lead to flawed results.
