· Perform a significance test about the slope of the population (true) regression line.
Activity: How Does GPA Relate to ACT Score?
Perform a significance test. Easy!
This is where all of our hard work training students with the 4-step process really pays off. The general formula for a confidence interval is always the same:
test statistic = (statistic - parameter) / (SD statistic)
The specific formula for this test statistics is easy if you know what you're trying to estimate (slope):
t = (b - BETA) / (SEb)
The only new idea students need to know here is that df = n - 2.
The relationship between confidence intervals and
When debriefing this activity, we conclude that there is convincing evidence of a positive linear relationship between GPA and ACT. We ask students to think about what the confidence interval for the true population slope would look like based on our data. Of course, we know the confidence interval would contain only positive values (would NOT contain 0). This means that the null hypothesis value (slope = 0) is not plausible and we have convincing evidence to reject this claim.