Download presentation

Presentation is loading. Please wait.

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

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google