1. T-test

2. t
A unitless number with a known distribution, if the assumptions about the errors are true.
The Y values are random variables.
You calculate the least squares slope from the Y values.
Therefore, the slope estimate is a random variable.

3. t The slope has a mean and a variance.
We can calculate those, based on the assumptions about the errors.
The mean of the slope is the true slope. That’s what “unbiased” implies.

4. t The slope has a mean and a variance.
We can calculate those, based on the assumptions about the errors.
The mean of the slope is the true slope. That’s what “unbiased” implies.

5. Standard error of beta-hat

6. T-test
This has the t-distribution with N-2 degrees of freedom. (The beta should be beta-0, your hypothesized value.)

7. t For testing the hypothesis that the true beta is 0:
N-2 degrees of freedom.

8. Types of errors Type I error: Type II error:
Rejecting a hypothesis that is true
Type II error:
Refusing to reject a hypothesis that is false.
The significance level is the probability of a Type I error.

9. T table

10. Next time: Graphs How to tell if the assumptions are plausible.
NOT by standard regression results.

11. Confidence interval for a coefficient
Coefficient ± its standard error × t from table
One calculation (two, really) lets you test many hypothesized values for the true parameter.
If 0 is in the confidence interval, your coefficient is not significantly different from 0.

12. Confidence interval for a coefficient
Coefficient ± its standard error × t from table
95% probability that the true coefficient is in the 95% confidence interval?
If you do a lot of studies, you can expect that, for 95% of them, the true coefficient will be in the 95% confidence interval.

13. Confidence interval for prediction
Hyperbolic outline