P Statistics teachers from across the country meet annually in Kansas City to score AP Statistics exams. One social event that many teachers participate in is the annual Prediction Fun Run. Prior to the race, the teachers predict how long it will take them to complete the 1.96-mile long course. During the event, they are timed and their actual finishing times are paired with their predicted times. Here is a scatterplot of the results. 3,000 2,500 2,000 1,500 1,000
500 0
0 500
1,000 1,500 2,000 2,500
Predicted Time (Seconds)
3,000
The winner of the race is not the fastest runner, but the most accurate runner.
a) Let x = the runner’s predicted time (in seconds) and y = the runner’s actual time (in seconds). Provide the equation of the line that can be used to assess how accurate the runners were. Plot this line on the graph above. Clearly label two points you are using to plot the line.
b) Is the line you drew in part (a) a least-squares regression line for these data? Explain.
c) While many runners were quite good at predicting their race time, some runners did very poorly at this task. Circle the point of the runner who had the largest error in prediction. Justify your choice. Was this runner faster or slower than predicted?
d) Describe the relationship between predicted time and actual time. Are all runners able to predict