4/21/2023

Regression Activities

• Kenyon Tuition activity
• Anscombe's data
• Nonlinear Regression (Use alligator.csv in the Stat106-ElementsofStatistics-S2023\!Class-csv-Rscripts folder on Google Drive)

Inference for regression

• Population regression line
• Estimating the regression parameters
• Confidence intervals and significance tests for the regression slope and intercept
• Confidence interval for a mean response
• Prediction interval for a future response

How well does the number of beers a student drinks predict his or her blood alcohol content? 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). The data are in the file bac.csv in the !Class-csv-Rscripts folder on Google Drive. The students were equally divided between men and women and differed in weight and usual drinking habits. Because of this variation, many students don't believe that the number of drinks predicts blood alcohol well.

• Make a scatterplot of the data. Find the equation of the least-squares regression line for predicting blood alcohol from number of beers and add this line to your plot. What is r-squared for these data? Briefly summarize what your data analysis shows.
• Is there significant evidence that drinking more beers increases blood alcohol on the average in the population of all students? State hypotheses, give a test statistic and P-value, and state your conclusion.
• Does student 3 have the largest residual from the fitted line? Is this observation extreme in the x direction so that it may be influential?
• Do the regression again, omitting student 3. Add the new regression line to your scatterplot. Does removing this observation greatly change predicted BAC? Does r-squared change greatly? Does the P-value of your test change greatly? What do you conclude: did your work above depend heavily on this one student?
• Steve thinks he can drive legally 30 minutes after he drinks 5 beers. The legal limit is BAC = 0.08. Give a 95% confidence interval for Steve's BAC. Can he be confident he won't be arrested if he drives and is stopped?

Please read Section 9.1 for class on Monday.