Question

to investigate the influence of distracted driving, 13 volunteers were asked to participate in a study involving a driving simulator. the participants drove at a safe speed but were told to stop the car at a random moment during the simulation. the scatterplot shows the reaction time and the simulated cars stopping distance (in feet) for each volunteer. the value of r for the scatterplot is 0.936. how would the correlation change if the stopping distances were recorded in meters, rather than feet? the value of the correlation coefficient would not change. since the points would be more spread out, the value of the correlation coefficient would decrease. since the number of meters would be less than the number of feet, the value of the correlation coefficient would increase. since the number of meters would be less than the number of feet, the value of the correlation coefficient would decrease.

Explanation:

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. It is not affected by changes in the units of measurement. Whether the stopping distance is measured in feet or meters (a simple linear transformation \( y = kx\), where \( k\) is a positive constant, as \( 1\) meter \( \approx 3.28\) feet), the relative positions of the data points (the pattern of the scatter - plot) in terms of the linear relationship does not change.

Answer:

The value of the correlation coefficient would not change.