FAQ: Statistical Thinking - Variable Relationships

This community-built FAQ covers the “Variable Relationships” exercise from the lesson “Statistical Thinking”.

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FAQs on the exercise Variable Relationships

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One thing I don’t understand is that in the learning environment, a correlation coefficient of 0 is considered a weak correlation, while 0.5 and -0.5 are unlabelled.

I was wondering why 0 would be considered weak rather than no correlation entirely, and why 0.5 and -0.5 are not labelled as weak.

Most likely a mistake - if you search more on this topic online, it is consistent that 0 means NO Correlation, and between 0.25 to 0.5 is considered a weak correlation. I would say anything below 0.25 is much too weak to be able to say there is a correlation at all.

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The text says “The farther the coefficient is from 0, the stronger the relationship.” For some reason, my brain found it easier to think of it as "the closer it is to +1 (positive coefficient) or -1 (negative coefficient) the stronger the correlation. However, is that thinking flawed?

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I am confused about the difference between slope and correlation coefficient. Could someone please check my understanding?

The correlation coefficient mimics how close to a linear relationship that 2 variables have.

The actual slope of said linear relationship could be any amount of steepness (not like it has to be y=x, in other words 1 for a positive coefficient)

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Good question.
I think you are correct.
A slope is about a line. Whereas a correlation is about a scatter, a set of points in two dimensional space.
The correlation coefficient is computationally “normalized”, such that the size of the slope, if there is one, does not affect the correlation coefficient.

Thanks ramtob

Does normalize mean the steepness difference between a gradient of 2 and 5 is ignored and it simply highlights how close to a linear relationship the variables have (be it 2 or 5)?

So a perfect linear relationship of 2 or 5 would appear the same on a scatter?

You’re welcome.
No, in general 2 and 5 will not look the same on a scatter. The size of the (accurate or approximate) slope does affect the scatter. But the correlation coefficient will be the same.

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