The article "Behavioural Effects of Mobile Telephone Use During Simulated Driving"† reported that for a sample of 20 experimental subjects, the sample correlation coefficient for x = age and y = time since the subject had acquired a driving license (yr) was 0.97. Why do you think the value of r is so close to 1? (The article's authors give an explanation.)

Step-by-step explanation:

Sample size N is equal to 20 experimental subjects (small sample size). Sample correlation coefficient r = 0.97

The variables are:

X = Age of subject (in years)

Y = Time since subject acquired a driving license (in years)

The general reason why the value of r for 2 variables will be very close to 1 is that the magnitude of the effect of the phenomenon-of-interest (behavioural effects of mobile telephone use during simulated driving) is very large.

r = 0.97 is a positive figure also. This implies that the phenomenon-of-interest in variable X and in variable Y move in the same direction or increase simultaneously.

For the r of 0.97, the behavioural effect of mobile telephone use during simulated driving as related to the age of the experimental subjects, IS ALMOST THE SAME MAGNITUDE as the behavioural effect of mobile telephone use during simulated driving as related to the time (in years) since subjects acquired a driving license.

This is the reason why the correlation coefficient here is very close to 1.

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1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.