Simple Linear regression Slope and Intercept

Question

Why do we find confidence interval for slope and intercept in Simple Linear Regression Model ? What does it indicate?

Answer 1

For the slope parameter, the CI is useful as another way to measure the strength of the relationship between the dependent and independent variable. If zero is not included in the 95% CI we can say we are 95% confident that there is a true relationship between dependent and independent variable. The confidence interval complements a t-stat and p-value testing if the coefficient is significantly different from zero, that is, a relationship exists.

As for intercept, it is not usually as useful in practice and we don't usually concern ourselves too much about the intercept CI.