3. A group of researchers wanted to understand what factors contribute to running performance. To study this, they recruited a random sample of 43 male experienced marathon runners to see which factors could predict marathon performance. Each athlete performed a progressive maximal treadmill test to exhaustion where they began running at 6 km/h and the treadmill speed was increased every minute until exhaustion. The maximum speed each person was able to sustain for one minute was recorded. Oxygen consumption was measured during the test and the maximum oxygen consumption rate (VO2 max) was recorded. Each athlete's best marathon time from the past three months was noted as well. The file 'Assignment5-marathon.cav' contains the maximum treadmill speed (km/h), VO2 max (mL/kg/min), and best marathon completion time (min) for each participant in this study. a. Create a scatterplot to show the relationship between VO2 max and marathon time. Show the least squares line on the plot. [/3] b. Find the equation to predict marathon time based on VO2 max. State how you found the equation (i.e., which software) and include a screenshot of any software used. Write an interpretation of the slope. [/3] c. Check that the conditions for least squares linear regression are met for the regression model. [/4] d. Find the R' value for the linear regression model. Another regression was performed to predict marathon completion time based on maximum treadmill speed and the R for this regression was 0.782. Is VO2 max or maximum treadmill speed a better predictor of marathon completion time? Why? [/2] e. The scatterplot and least squares regression line for the maximum treadmill speed model is shown below. The regression equation is ? = -9.40x + 364.79 Someone who is just learning to run performs the maximal treadmill test and gets a maximum treadmill speed of 8.5 km/h. What would you predict their marathon completion time to be using the regression model? What are two problems with using the equation in this situation? [/3] 220 200 180 Marathon Completion Time (min 160 140 120 16 18 20 22 24 Maximum Treadmill Speed (km/h)