Understanding Confidence Interval
When you look at a linear regression $y_i = \beta_0 + \beta_1 x_i + u_i$, you can estimate the (ex ante unknown) coefficients $\beta$ using matrix algebra $(X'X)^{-1} X'y = \hat{\beta}$.
A point estimate would be the &quot;best guess&quot; $\hat{y}=\hat{\beta} X$.
Each $\hat{\beta}$ is associated with uncertainty about the estimate, expressed by the standard error of the coefficient (see this post). The confidence interval intuitively says that you want to find the range in which the true $\hat{\beta}$ is with 95% likelyhood (assuming a normal distribution). In this case, you can calculate a confidence interval (for $\hat{\beta}$) by:
$$ CI_{0.95}^{\beta} = [\hat{\beta_i} - 1.96*SE(\hat{\beta_i}), \hat{\beta_i} + 1.96*SE(\hat{\beta_i})].$$
So you can say (under some assumptions) that the true value of the estimated $\hat{\beta}$ is within the confidence band with 95% probability. Note that in linear regression, when you say a coefficient is &quot;statistically significant&quot;, this coincides with &quot;the confidence band is strictly positive or negative&quot; (does not cross zero).
Example in R:
Linear regression:
library(&quot;ISLR&quot;)
auto = ISLR::Auto
ols = lm(mpg~horsepower,data=auto)
summary(ols)

Result:
Coefficients:
             Estimate Std. Error t value Pr(&gt;|t|)    
(Intercept) 39.935861   0.717499   55.66   &lt;2e-16 ***
horsepower  -0.157845   0.006446  -24.49   &lt;2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.906 on 390 degrees of freedom
Multiple R-squared:  0.6059,    Adjusted R-squared:  0.6049 
F-statistic: 599.7 on 1 and 390 DF,  p-value: &lt; 2.2e-16

This tells us that when horsepower goes up by one unit, mpg goes down by -0.158 (point estimate). Now when we ask, what is the true effect (under quite some assumtions) with 95% probability, we look at the CI.
# Confodence interval
confint(ols)

Which gives:
                2.5 %     97.5 %
(Intercept) 38.525212 41.3465103
horsepower  -0.170517 -0.1451725

We can do this &quot;manually&quot; using:
# Get standard errors
sqrt(diag(vcov(ols)))

(Intercept)  horsepower 
0.717498656 0.006445501

And we can calculate the CIs:
# Lower CI
-0.157845 - 1.96*0.006445501

# Upper CI
-0.157845 + 1.96*0.006445501

Which yields:
[1] -0.1704782
[1] -0.1452118

So we could say that the true effect of horsepower on mpg is between -0.17 and -0.15 (and since the CI does not &quot;cross&quot; zero, the effect is statistically significant, meaning p-value &lt; 0.05).