One factor in the development of tennis elbow, a malady that strikes fear into the hearts of all serious players of that sport (including one of the authors), is the impact-induced vibration of the racket-and-arm system at ball contact. It is well known that the likelihood of getting tennis elbow depends on various properties of the racket used. Consider the accompanying scatterplot of x = racket resonance frequency (in hertz) and y = sum of peak-to-peak acceleration (a characteristic of arm vibration, in meters per second per second) for n = 23 different rackets. Discuss interesting features of the data and of the scatterplot.
a. There are several observations that have identical or nearly identical x-values yet different y-values. Therefore, the value of y is not determined solely by x, but also by various other factors.
b. There are several observations that have identical or nearly identical x-values yet different y-values.
Therefore, the value of y is not determined by x.
c. There appears to be a general tendency for y to increase in value as x increases in value.
d. There appears to be a general tendency for y to decrease in value as x increases in value.
e. There are two data points which are far removed from the remaining data points. These two data points have large x-values and small y-values. Their presence might have an undue influence on a line fit to the data.
f. There are three data points that are far removed from the remaining data points. These three data points have small x-values and small y-values. Their presence might have an undue influence on a line fit to the data.