Their correlation coefficients will be the same, since the correlation coefficient is unitless.

Question

BlackTom AI · Accepted Answer

The statement asks whether the correlation coefficients will be the same because the correlation coefficient is unitless.
Option 1: True. The claim that correlation is unitless is accurate in the sense that r does not have units and typically ranges from -1 to 1. However, this alone does not guarantee that the correlation coefficients for different data sets, variable pairs, or samples will be identical. The value of r reflects the strength and direction of a linear relationship, which can vary between data sets or across repeated samples; unitlessness does not enforce equality across cases.
Option 2: False. The core reason this is incorrect is that unitlessness only tells us that r lacks units, not that it must take the same value across different situations. Two separate variable pairs can have different linear relationships, leading to different r values. Even if you are looking at the same two variables in different samples or under different transformations (that do not affect linearity, such as linear scaling), sampling variability or slight changes in the data can produce different correlation coefficients. Therefore, it is not guaranteed that their correlation coefficients will be the same.

In summary, while the correlation coefficient is unitless, that property does not ensure equality of r across different datasets or conditions; hence the statement is not generally true.

FA25_QTM_100_3 8.10: Guess the correlation.

Their correlation coefficients will be the same, since the correlation coefficient is unitless.

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类似问题

Of the following, the correlation coefficient that indicates the weakest relationship between the two variables being measured is ______________.

The correlation in between mobile usage and exam score of a person found to be -2.2. What is your inference from the above statement.

The correlation between temperature in ◦F and age in weeks was r = −0.70. If we converted the temperature to ◦C and age to months, what would the 29 correlation be?

r = −0.85

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