Question

the following scatterplot shows the arm - span (in centimeters) and height (in centimeters) for a random sample of 19 twelfth - graders. the correlation is r = 0.902.
(a) explain why it is incorrect to say that the correlation is 0.902 centimeter.
(b) what would happen to the correlation if height was measured in inches instead of centimeters? explain your answer.
(c) what would happen to the correlation if height was used as the explanatory variable and arm - span was used as the response variable?

Explanation:

Step1: Understand correlation concept

Correlation measures the strength and direction of a linear relationship between two variables. It is a unit - less measure.

Step2: Answer part (a)

Correlation is a unit - less quantity. Changing the units of measurement of the variables does not change the correlation value. So, it is incorrect to say that the correlation depends on the units. The value of correlation ($r = 0.902$) would remain the same regardless of whether height and arm - span are measured in centimeters or inches.

Step3: Answer part (b)

Since correlation is unit - less, if height was measured in inches instead of centimeters, the correlation $r = 0.902$ would remain the same.

Step4: Answer part (c)

The correlation value does not depend on which variable is the explanatory variable and which is the response variable. Correlation measures the strength and direction of the linear association between two variables. So, if height was used as the explanatory variable and arm - span as the response variable, the correlation $r = 0.902$ would remain unchanged.

Answer:

(a) Correlation is unit - less, so changing units does not affect it.
(b) The correlation would remain 0.902.
(c) The correlation would remain 0.902 as it is not affected by which variable is explanatory and which is response.