WILEYPLUS ASSIGMENT

DECIDE FOR YOURSELF DOES A REGRESSION EQUATION ALWAYS MAKE SENSE? Regression is a very powerful statistical tool. However, like any Looking at this scatterplot, it seems reasonable to use a regres- other tool, a failure to understand both its uses as well as its limita- sion line to explain the relationship between the year of Olympics tions can lead to ridiculous, if not disastrous, results. To demon- and the winning time in the 100 meter dash. Specifically, the equa- strate this, we took the data on two variables-the year of the tion of that regression line is Olympics from 1928 to 2004 as the independent variable and win- ner's time (in seconds) in the men's 100 meter dash (race) as a Seconds = 31.1 - .0106 Year dependent variable. Figure 13.26 shows the scatterplot and the To calculate this regression line, we used the actual years of the regression line for these data. Olympiad for the independent variable. Theoretically, we could use this regression equation to estimate the winning times for the years when Olympics are not held. We could also use it to predict the future Scatterplot of Seconds vs Year winning times or to calculate what would have happened in the past. Answer the following questions to see how reasonable this process is. 10.8 1. Based on this regression equation, what is the change in the winning 10.6 time per Olympic period (4 years)? Does the change represent an increase or a decrease? Seconds 10.4 2. Find the predicted winning times for the years 2200, 2600, and 3000. Using these predicted times, determine the winners' speeds (in miles 10.2 per hour) for the years 2200 and 2600. Does it make sense to believe that this pattern will continue in the future? Explain. 10.0 3. A similar analysis could be done in the reverse direction. A 2005 scientific discovery stated that fossils from 35,000-year-old modern 9.8 humans were found in Transylvania (http://www.theglobeandmail 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 com/servlet/story/RTGAM.20040306.wfossil0306/BNStory/ Year specialScienceandHealth/). Using the above regression equation, calculate the winning time for the 100 meter dash at this point Figure 13.26 Scatterplot and regression line. in history. Does this number make sense? Why or why not