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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.
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