Recap: Inference for Regression

Theory-based inference for regression

When we interpreted the regression table, we mentioned that R doesn’t compute its values using simulation-based methods for constructing confidence intervals and conducting hypothesis tests using the infer package. Rather, R uses a theory-based approach using mathematical formulas, similar to theory-based confidence intervals and theory-based hypothesis tests. These formulas were derived in a time when computers didn’t exist, so it would’ve been incredibly labor-intensive to run extensive simulations.

In particular, there’s a formula for the standard error of the fitted slope $𝑏_1$:

There are many formulas in statistics, so let’s break down what each symbol represents. First, $s_x$ and $s_y$ are the sample standard deviations of the explanatory variable bty_avg and the response variable score, respectively. Second, $r$ ...