Notation The author conducted an experiment in which the heigh...

Question

Notation The author conducted an experiment in which the height of each student was measured in centimeters and those heights were matched with the same students’ scores on the first statistics test.
c. Does r change if the heights are converted from centimeters to inches?

c. Does r change if the heights are converted from centimeters to inches?

Accepted Answer

All right, hello everyone. So this question says, a researcher conducted a study in which the daily calorie intake of students was recorded and matched with their scores on a physical endurance test. If the calorie intake values are converted from kilocalories to joules, does the correlation coefficient are change and give reason? Now here Here we have 4 different answer choices labeled A through D. Options A and C say yes. And options B and D say no. So first and foremost, what is R? What is the correlation coefficient, and what does it tell you? Well, recall that the correlation coefficient talks about the strength. And also the direction. Of a linear relationship between two different variables. And so what that means. Is that art tells you about whether or not those two valuables. Are related to each other, that is, do they both increase when one is changed? Do they both decrease, or does one increase when the other decreases? It's important to recognize that R is unitless. It only tells you about the relationship between two variables. Therefore, In this particular case, when you're converting data from one unit to another, that's not going to change the correlation between that data. But it's important to recognize that it's going to remain unchanged so long as the variables are converted through a linear transformation. In this case, you're doing that because you're converting kilocalories into joules by multiplying by a constant factor. Therefore, the value of R doesn't change when units are changed. Meaning a correct answer is option B. Which says no because correlation is unitless and measures the same or remains the same rather under a linear transformation. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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