everyone! I'm kinda new to regression, so as far as I'm concerned, the confidence intervals show us how likely that estimate is to reflect the population, right? However, when it comes to regression, can we affirm that the confidence interval should include our slopes and, then, if they don't, then our estimates are not significant, is that what they mean?
Thanks in advance,
On a non-technical level, a confidence interval is just a "plausible range" for the value of a parameter (eg a regression coefficient). On a technical level, if the study was repeated a large number of times then those confidence intervals will contain the true (unknown) value 95% of the time (for a 95% confidence interval of course).
Note that it is mistake to interpret the confidence interval in terms of the probability of the true parameter value lying inside the interval. Either it does, or it does not. Such an interpretation is treating the parameter as a random variable. It is not. It is the confidence interval that is random. The true parameter is determined, but unknown.
You are correct about the connection between the confidence interval containing the estimate, and statistical significance.