Answer:
(a) The athlete who finished first in the race had the quickest running time of 9.6 seconds
(b) There is a direct proportional relationship between reaction time and running time on average
(c) Long-term assumptions associated with least-squares regression
Limited efficacy in terms of sensitivity to outliers
Challenges in terms of extrapolating data characterizations
Explanation:
It is stated that
Total race time = Reaction time + Running Time
The winner is the athlete with the minimum total race time, which equates to the runner who has the lowest (Reaction time + Running Time)
Analyzing the scatter plot indicates that the winner corresponds to the lowest sum of x + y coordinates, placing the winner near the origin.
The three closest to the origin yielded the following x + y values:
0.135 + 9.7 = 9.835
0.145 + 9.7 = 9.845
0.153 + 9.6 = 9.753
Consequently, the athlete with the winning time was the one who achieved a running time of 9.6 seconds
(b) No, as a slight estimate indicates that an increase in running time correlates with an increase in reaction time
(c) Given a reaction time of 0.3 seconds is an outlier, employing a least-squares regression model may not be suitable due to the issues of extended range, limited sensitivity to outliers, and challenges in extrapolation characterization.
