A range of plausible values for the true population parameter (e.g., slope).

The slope of the line of best fit, denoted by b.

The percentage of confidence intervals that would contain the true parameter if we took many samples.

Degrees of freedom (df) = n - 2, where n is the sample size.

A measure of the variability of the sample slope estimates around the true population slope.

b ± t* (SE of b), where b is the sample slope, t* is the t-critical value, and SE of b is the standard error of the slope.

df = n - 2, where n is the sample size.

As sample size increases, the width of the confidence interval decreases because a larger sample size reduces the standard error.

As the confidence level increases, the width of the interval increases. A higher confidence level requires a wider interval to capture the true parameter with greater certainty.

If 0 is contained in the confidence interval, it is plausible that the true slope is 0, meaning there is no linear correlation. If 0 is not contained in the interval, there is evidence of a linear correlation.

If we created several random samples of the same size from the same population, 95% of the resulting confidence intervals would contain the true slope of the population regression model.

If the entire confidence interval is positive, there is evidence of a positive correlation. If the entire confidence interval is negative, there is evidence of a negative correlation.