The data to the right represent the time (in seconds) to complete a 400-meter race while a wind is blowing 2 meters per second in different directions. The wind direction is measured from the finishing straight (so 180 degrees is a head on wind). See the figure. The wind speed of 2 meters per second is the strongest wind speed allowed for a world record to be recorded withoutthe notation "wind assisted."

(a) Draw a scatter diagram of the data. What type of relation appears to exist between x and y?
(b) Find the quadratic regression equation yn = b0 + b1x + b2x2.
(c) Draw a residual plot against the fitted values, x, and x2. Also, draw a boxplot of the residuals. Are there any problems with the model?

Group start 10,000 m 400 m, 800 m, 2000 m 4x 100 m relay 4x 200 m relay 4 x 400 m relay staggered start Finish 123 45678 Line Track length of 400 m is measured 300 mm from inneredge of Lane 1 (radius of actual track measurement is 36.8 m radius) Length of straight 84.39 m 200 meter staggeed start Group 100 m 1/2j3 j4i516ii, start start 3000 and 5000 m Wind Direction Time Wind Direction Time (degrees), x (degrees), x (seconds), y (seconds), y 180 42.85 43.03 30 43.04 210 42.82 43.01 60 240 42.82 90 42.97 270 42.86 42.92 120 300 42.92 150 42.88 330 42.99