Interpreting Regression Tables-I

We’ve so far focused only on the two leftmost columns of the regression table—term and estimate. Let’s now shift our attention to the remaining columns, which are the std_error, statistic, p_value, lower_ci and upper_ci in the table below:

Given the lack of practical interpretation for the fitted intercept $b_0$, we’ll focus only on the second row of the table corresponding to the fitted slope $b_1$. We’ll first interpret the std_error, statistic, p_value, lower_ci and upper_ci columns.

Standard error

The third column of the regression table above is std_error and it corresponds to the standard error of our estimates.

Note: The standard error is the standard deviation of any point estimate computed from a sample.

So what does this mean in terms of the fitted slope $𝑏_1$= 0.067? This value is just one possible value of the fitted slope resulting from this particular sample of $n$ = 463 pairs of teaching and beauty scores. However, if we collected a different sample of $n$ = 463 pairs of teaching and beauty scores, we’ll almost certainly obtain a different fitted slope $𝑏_1$. This is due to sampling variability.

Lets say we hypothetically collected 1,000 such samples of pairs of teaching and beauty scores, computed the 1,000 resulting values of the fitted slope $b_1$, and visualized them in a histogram. This will be a visualization of the sampling distribution of $b_1.$ ...