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LSRL Regression Inference

LSRL Regression Inference. LSRL Review. Good runners take more steps per second as they speed up. Here are the average number of steps per second for a group of top female runners at different speeds. What is the equation of the LSRL? What is the correlation coefficient and what does it mean?

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LSRL Regression Inference

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  1. LSRL Regression Inference

  2. LSRL Review • Good runners take more steps per second as they speed up. Here are the average number of steps per second for a group of top female runners at different speeds. What is the equation of the LSRL? What is the correlation coefficient and what does it mean? Fill in the residuals

  3. LSRL Review Answers

  4. Residuals • Residual = observed – predicted • Residual = • Easily done on calculator

  5. Big Question Big Question: If we took another sample of 10 runners would we get the same LSRL?

  6. LSRL is from a sample • Our LSRL is constructed from a single sample • Overall for the population there is a line of best fit: Remember we use sample statistics to estimate population parameters

  7. Computer Print out Mr. Hopkins was interested in how the number of hours a student studied for the chapter 13 exam was related to the student’s score. Below is a printout of the regression run using mini-tab: S = 3.879 R-sq = 46.1% R-sq(adj) = 35.4% What is the equation of the LSRL? If we studied 3 hours and received a 68, what is the residual?

  8. Computer printout solution

  9. The true LSRL for the population For each specific x-value: We assume the distribution of y-values is normal The mean of the y-values is on the true LSRL Standard deviation of y-values about the line( ) is unknown.

  10. Standard Deviation • Standard deviation: • Measure of how far points are from the true LSRL • Unknown (just like population standard deviation was unknown for most tests) We need to estimate the standard deviation. What did we do before when we used the t-test for standard deviation?

  11. Standard Error • is an estimate of the true LSRL. • We estimate the standard deviation by using the residuals • Remember: residual is just the distance from the point to the line n = # of observations

  12. Example • Running speed predicts foot speed • X(Explanatory) : running speed • Y(Response) : foot speed • Remember we got:

  13. Calculating Standard Error • Use the lists!

  14. Confidence Interval for the slope • True LSRL: • We don’t know the slope but we can construct a confidence interval for it using our sample! • Our sample gives us:

  15. CI for regression slope

  16. CI for slope in • Let’s construct a 95% CI for the slope of the true LSRL • We already found s = .0494 • To find we need

  17. Interpreting this CI • This is a confidence interval for in • Remember x: running speed y: foot speed We are 95% confident, that foot speed increases between .0861 and .0941 steps/sec for each additional increase in running speed.

  18. Print-out • Finding SEb is a pain. Trust me, that wasn’t much fun! • Usually you get a printout of a regression which makes finding SEb much easier

  19. Example • We will predict BAC(blood alcohol content) using the number of beers an individual drinks. • We run a regression and get the following print out

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