Unit Nine: Inference for Quantitative Data (Slopes)- essential knowledge

What are the two types of variation in points' positions relative to a theoretical line?

Variation can be random or non-random.

What is the appropriate confidence interval for the slope of a regression model?

A t-interval for the slope.

How is the margin of error for the slope of a regression line calculated?

The margin of error is the critical value (t*) times the standard error (SE) of the slope.

What is the point estimate for the slope of a regression model?

The point estimate is the slope of the line of best fit, denoted as bbb.

What is the formula for the interval estimate for the slope of a regression model?

The interval estimate is b±t∗⋅SEb

In repeated random sampling, what percentage of confidence intervals created will capture the true slope of the population regression model?

Approximately C% of the intervals.

What should an interpretation of a confidence interval for the slope of a regression line include?

A reference to the sample taken and details about the population it represents.

What does a confidence interval for the slope of a regression model provide?

An interval of values that may provide sufficient evidence to support a particular claim in context.

How does sample size affect the width of the confidence interval for the slope of a regression model?

The width tends to decrease as the sample size increases.

What is the appropriate test for the slope of a regression model?

A t-test for the slope.

What is the null hypothesis for a t-test for the slope of a regression model?

H0​:β=β0​, where β0​ is the hypothesized value from the null hypothesis.

What is the distribution of the slope of a regression model assuming all conditions are met and the null hypothesis is true?

A t-distribution.

How should the p-value of a significance test for the slope of a regression model be interpreted?

The p-value is computed assuming the null hypothesis is true, meaning the true population slope is equal to the value stated in the null hypothesis.

How is a formal decision made in a significance test for the slope of a regression model?

By comparing the p-value to the significance level α\alphaα. If the p-value ≤α\leq \alpha≤α, reject the null hypothesis; if the p-value >α> \alpha>α, fail to reject the null hypothesis.

How can the results of a significance test for the slope of a regression model be used?

They can support the answer to a research question about the sample being studied.