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Data-Centric Statistical Inference Using R and Tidyverse

Interpreting Regression Tables-II

Explore how to interpret the lower and upper bounds of 95% confidence intervals in regression tables. Understand what these intervals imply about population slopes and the relationship between variables. Discover how standard errors contribute to interval calculations and the assumptions behind theory-based inference methods in regression.

We'll cover the following...

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

Previously Seen Regression Table

Term

estimate

std_error

statistic

p_value

lower_ci

upper_ci

Intercept

3.880

0.076

50.96

0

3.731

4.030

bty_avg

0.067

0.016

4.09

0

0.035

0.099

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 β1\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 β1\beta_1 of (0.035, 0.099) can be thought of as a range of plausible values for the population slope β1\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 β1\beta_1 ...