How do you interpret a 95% CI for a regression coefficient?

How do you interpret a 95% CI for a regression coefficient?

• A. The interval guarantees the true coefficient lies in that range for 95% of samples
• B. The interval is the same as the p-value being 0.05
• C. The interval estimates the range in which the true coefficient lies with 95% confidence; if includes zero, not statistically significant at 0.05
• D. The interval indicates the probability that the coefficient is exactly equal to the point estimate

Answer: (C)

Interpreting a 95% CI for a regression coefficient is about the range of plausible values for the true population slope based on the data and the model. The 95% confidence level means that if you repeated the study many times and computed a CI from each sample, about 95% of those intervals would contain the true coefficient. If zero lies inside this interval, there’s not enough evidence at the 5% significance level to claim a real effect; the relationship could be null. This interpretation is about long-run behavior of the method, not a guarantee for a single sample. It’s also not a statement about the probability that the coefficient equals the point estimate, nor is it identical to the p-value—though they are related: if the interval excludes zero, the p-value would be below 0.05; if it includes zero, the p-value is above 0.05.

Interpreting a 95% CI for a regression coefficient is about the range of plausible values for the true population slope based on the data and the model.

The 95% confidence level means that if you repeated the study many times and computed a CI from each sample, about 95% of those intervals would contain the true coefficient. If zero lies inside this interval, there’s not enough evidence at the 5% significance level to claim a real effect; the relationship could be null.

This interpretation is about long-run behavior of the method, not a guarantee for a single sample. It’s also not a statement about the probability that the coefficient equals the point estimate, nor is it identical to the p-value—though they are related: if the interval excludes zero, the p-value would be below 0.05; if it includes zero, the p-value is above 0.05.