1 / 18

Chapter 12

Chapter 12. Inference for Linear Regression. Reminder of Linear Regression. First thing you should do is examine your data… Look at your scatterplot. Does it appear linear? Are there outliers? What direction is it going in? Is there a strong relationship? LSR: y-hat = a + bx

johnsmartinez
Download Presentation

Chapter 12

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 12 Inference for Linear Regression

  2. Reminder of Linear Regression • First thing you should do is examine your data… • Look at your scatterplot. Does it appear linear? Are there outliers? What direction is it going in? Is there a strong relationship? • LSR: y-hat = a + bx • a = y-intercept; b= slope • Slope is the rate of change in y for every one x.

  3. Statistics versus parameters • a and b are statistics (estimates of y-intercept and slope). • α and β are unknown parameters • a is an unbiased estimator of α and b is an unbiased estimator of β

  4. We are interested in β • We are going to look at inference for β (slope). • Confidence Intervals and Hypothesis tests.

  5. Confidence Intervals • These will be t-tests • What is the basic formula for confidence intervals? • Estimate +/- margin of error • Estimate +/- t-statistic*Standard Error • For inference for the true mean slope (β) • b +/- t*(SE)

  6. Standard Error and DF • You will either be given this information or you can get your calculator to give it to you! • Degrees of freedom = n – 2 • Why?

  7. Computer Output • Look with me pg 770 • Remember, under coefficient… • Constant = y-intercept • Variable definition = slope • Standard error is the second row under STDev

  8. Hypothesis Tests • Generally, • H0 = 0 • This says that the true slope is zero, which means there is no change in y. This can be different if the context of the problem would mean that no change is not zero…

  9. Calculator! • Put your data in List 1 and List 2 • In your calculator, you go to LinRegTTest under Stat, Test

  10. Example • How well does the number of beers a student drinks predict his or her blood alcohol level? Sixteen student volunteers at Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC).

  11. The Data

  12. Conditions • Observations are independent • You don’t observe the same person multiple times • The true relationship is linear • Check residual plot for scatter. Look at scatter plot.

  13. Conditions Continued • The spread is uniform • The residual plot does not have a cone like appearance. • The residuals have a normal distribution. • Graph residuals

  14. Residuals • Since almost all the conditions deal with residuals, we should probably review • Residual = observed – predicted • y – (y-hat) • In you calculator: Define L3 as L2 – Y1(L1) • You can look at a scatter plot of L1 vs. L3 to see residual plot. • To determine normality, look at a histogram of L3

  15. Example of Ohio State University • Check your conditions for the previous problem. • Let’s finish the problem now.

  16. Example of when H0 is not β = 0

  17. Homework: • Read Chapter 12. Do questions #9, 10, 14, 18, MC 21-26(explain)

  18. CONGRATULATIONS!!!! You have now finished all of your AP Statistics Course work!!!!!!!

More Related