Interpreting Regression Tables-II

Let’s now explore the remaining columns, the lower_ci and upper_ci, in the table below:

Confidence interval

The two rightmost columns of the regression table above (lower_ci and upper_ci) correspond to the endpoints of the 95% confidence interval for the population slope $\beta_1$. Recall our analogy “nets are to fish what confidence intervals are to population parameters” from the Understanding Confidence Intervals lesson. The resulting 95% confidence interval for $\beta_1$ of (0.035, 0.099) can be thought of as a range of plausible values for the population slope $\beta_1$ of the linear relationship between teaching and beauty scores.

As we introduced earlier on the precise and shorthand interpretation of confidence intervals, the statistically precise interpretation of this confidence interval is: If we repeated this sampling procedure a large number of times, we expect about 95% of the resulting confidence intervals to capture the value of the population slope $\beta_1$ ...