Student Guide (continued) FRQ 1 AP 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 Actual Time (Seconds) 1,500 1,000 500 0 0 500 1,000 1,500 2,000 Predicted Time (Seconds) 2,500 3,000 The winner of the race is not the fastest runner, but the most accurate runner. a) Letx 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 Ine 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 this task. Circle the point of the runner who had the largest error in prediction. Justify your choice Was is runner faster or slower than predicted? d) Describe the nationship between predicted me and actualme Areas to predict 15 Student Guide (continued) FRQ 2 Professional basketball teams have 11 players per team. Salary is dependent upon their scoring average. measured in points per game. A least-squares regression line that describes the relationship between scoring average and salary for one professional basketball team is = 2,671,134.68 + 684,663.08x, where x is the player's scoring average and y is the player's salary. The residuals for this regression are given in the graph below. $2.00.00.000 $1,50,00,000 $1.00.00.000 . 550,00.000 Residual SO 6 10 12 14 18 -$50.00.000 -$1,00,00,000 -5150,00.000 Scoring Average Points per Game) a) Is a line an appropriate model to use for these data? What information tells you this? b) What is the value of the slope of the least-squares regression line? Interpret the slope in the context of this problem. c) What is the predicted salary of the basketball player with 10.9 points per game? d) Approximate the actual salary of the basketball player with 10.9 points per game