An analyst wants to determine the relationship between speed, in miles per hour, and the time, in hours, it takes to drive 5 miles. Twenty trials are completed and the correlation coefficient between speed and time is determined to be -0.276. Therefore, slower speed was related to greater time. How is the correlation affected if the units for time are changed from hours to minutes?

Answer below:

Step-by-step explanation:

SPEED (in miles/hour),  TIME (in hours)

This analyst determined the relationship between the 2 measures above, using 20 trials.

The correlation coefficient between both factors was -0.276

Now, correlation coefficient is a figure that shows the strength and direction of two quantities. The quantities here are speed and time.

The minus sign in this correlation coefficient shows a negative movement of one quantity against the other. In other words, as one quantity moves up, the other goes down, and vice versa. An increase in magnitude of speed will result in a decrease in magnitude of time spent driving. Vice versa.

If you plot speed against time, the graph (that joins each point of intersection of speed and time together) will slope downwards showing the opposing movements of time and speed.

How is the correlation affected if the units for time (time only, not speed) are changed from hours to minutes?

If the units for each time measured are changed to minutes while that of speed is left in hours, the magnitude of each time measured will increase by 60.

For example, if three of the twenty trials have the following values for time -  1.5 hours,  2.3 hours,  3.6 hours

then they will be multiplied by 60, in order to change to minutes. The new values are shown below:

90 minutes,  138 minutes,  216 minutes

THIS CHANGE ON THE VARIABLE TIME ALONE, WILL CAUSE IT TO CARRY MORE MAGNITUDE WHILE THE TIME IN THE MEASUREMENT OF SPEED REMAINS THE SAME.

WHAT THIS WILL DO TO THE CORRELATION COEFFICIENT IS: to lower the value of the figure from 0.276 to a value like 0.043

The minus sign will still remain, as speed and time are still moving in opposite directions.

The value of the correlation coefficient will drop!

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step-by-step explanation:

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