A range of values likely to contain the true population parameter.

The single best estimate of a population parameter, like the sample slope.

The 'buffer zone' around the point estimate, calculated using the t-score and standard error.

The differences between observed y-values and y-values predicted by the regression line.

Measures the spread of data points around the regression line; also known as the standard error of the estimate.

The percentage of times that the confidence interval will contain the true population parameter if the study is repeated many times.

Ensures the t-interval is valid and the results are reliable. Violating conditions can lead to inaccurate conclusions.

Larger sample sizes generally lead to narrower (more precise) confidence intervals.

A larger standard deviation of residuals leads to a wider (less precise) confidence interval.

Higher confidence levels lead to wider confidence intervals because you need a larger range to be more confident you've captured the true population parameter.

$SE(b) = \frac{s}{\sqrt{\sum(x_i - \bar{x})^2}}$, where s is the standard deviation of the residuals.

Margin of Error = t-score * Standard Error of the slope.

Point Estimate ± Margin of Error

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

Sample Slope ± (t-critical value * Standard Error of the slope)