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04-20-2011 Linear Regression

04-20-2011 Linear Regression - Lecture 23 Chapter 12 Today...

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•4/20/2011 •1 Lecture 23: April 20, 2011 Chapter 12: Today: bottom page 504-bottom page 515 Connect Quiz 3: Chapter 12 Pages 488- 503 (i.e., through R 2 ) Opens Thursday, April 21 by 11:00 a.m. Closes Monday, April 25 at 1:00 p.m. You have 2 two-hour sessions of your choosing to complete the quiz. This will be six or seven problems. Watch for Quiz 4. It deals with material for today. It will close Wednesday, April 27 at 6:00 p.m. Homework No. 13 on material for today New Worked-Out Problem on the Web Site: Simple Regression Slope, Intercept, R-Squared, Standard Error of the Estimate Discussion Session 13: Friday, April 22 First item of business: You will be dealing with text problem 12.21 on page 510. Your tasks rely heavily on sum-of-squares calculations. Here they are: SS xy = 2130, SS xx = 350, SS yy = 15318, and SSE = 2355. You really should calculate these on your own before you attend discussion. I will ask you to do one or more similar calculations on the final exam. Second item of business: Calculate the regression slope coefficient b 1 using Formula (12.13) on page 500. Next, make use of Formula (12.19) on page 504 and Formula (12.21) on page 505 to construct a confidence interval for β 1 . Third item of business: Perform a two-tailed hypothesis test on the slope coefficient . Make use of the steps in hypothesis testing that we’ve been using. The set-up and testing procedure will be similar to testing a single population mean, which we did long ago. If you need a refresher on the steps, go to the Handouts menu on the course web site. Click on Revised Steps in Hypothesis Testing . Fourth item of business: You will be testing the overall significance of the regression . This turns out to be an F test, and you will be applying your skills from ANOVA about how to do the test. Effectively, you will be using Formula (12.27) on page 512 to get F. This F is based entirely on the ANOVA table for a simple regression . This is Table 12.8 found at the bottom of page 511. Fifth item of business: You will be constructing a prediction interval for an individual value of Y . The prediction itself – call it Y-hat – is a random variable , and we will construct an interval around it. There are some rather complicated formulas relating to prediction intervals. We will not go this route. Instead, we will use an approximation to the true formula. This is Formula (12.31) on page 517. It is called the Quick Prediction Interval for Individual Y . Sixth item of business: Get into Minitab and run the regression. My suggestion is that you run Minitab before you do any of the tasks above. Match the Minitab output with your calculations or use the Minitab output to help you get a calculation.
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