dumb stats question i am embarrassed about the basicness of it so im hiding it in thread below, but i would like help understanding
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i think i know roughly how correlations work - if u plot the values, u can get a trendline (the line that minimizes distance from line to all the points). if u then take this line and calculate square root of distance from line to points... something something correlation
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like, if all the points are real far from the line, its low correlation, if all the points are close to the line, its high correlation
but i don't understand the relationship of this to the slope of the line itself?
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like what does it *mean* for there to be a real strong trend slope with an r of 0.02? Or weak with r of .9? is that even possible? what does this even mean about the data?
i conceive of correlations as about predictive power - given knowledge of X, how can we predict Y?
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im getting confused cause i have a data finding where i had ppl select how much they liked... let's call it ice cream, on a 0-3 scale. I also asked... let's say, how much butter did you eat growing up?
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and found that people liked ice cream 3/3, reported double the amount of childhood butter consumption than ppl who like ice cream at 0/3.
This is a *trendline* I'm finding here, right? a consistent increase in avg ice cream preference per degree of childhood butter consumption
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i feel like i should be able to make strongish predictions off of this. If you tell me you're into ice cream 3/3, I should 2x my estimate of how much butter consumption was in your childhood, right? This *feels* like a strong thing to me.
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But my actual correlation for this data is r=0.08, which is very tiny! Is it that correlations aren't supposed to tell me the dramaticness of my prediction, but rather the reliability of it? Should I 2x my estimate of butter consumption but i'm only ~1% more likely to be right?
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I don't even know how to conceive of that, it's breaking my brain. Or is this all impossible and I just probably made a mistake in my data? I kinda feel like I'm asking the wrong question in here somewhere.
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(and to clarify, the trendline is a linear trendline when i graph out the average scores, there's not like a secret bell curve in there to wipe out the correlation for me)
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why am i so triggered by all the responses explaining things to me that i thought i clearly laid out as understanding in my thread
its surprisingly upsetting, i am resisting urges to block everyone
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GUYS I AM AWARE THAT THE SLOPE OF THE LINE IS NOT THE SAME AS CORRELATION, PLEASE STOP TELLING ME THIS
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I'm pretty sure it's this. If the slope is large but the correlation is small, it basically means that whatever factor you're looking at makes a large difference on average, but not necessarily in any particular case.
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oh this phrasing made it feel more intuitive for me, like group A can score 10, and group B can score 20, which is a 2x increase, but the variance can be huge or small?
I'm not sure how to 'fit' this into thinking about data yet though
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this is essentially correct (although I'm not sure what exactly you mean by "1% more likely to get it right")
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correlation isn't about the 'strength' of the relationship nor the 'reliability' of it. it's about how much of the variation in Y can be explained by variation in X. if Y varies wildly all over, despite a strong, reliable background dependence on X, the correlation is low. cheers
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Imagine a magic wand which makes people levitate.
X = wand angle, Y = flight altitude
Slope: how does the altitude relate to the wand angle? E.g. 1 meter per degree.
Correlation: How precise is the effect? Exactly 1m per degree, or roughly 0.5 - 1.5m per degree, or what?
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That’s a very good intuition!
An example of this: the correlation between being kicked in the head and headaches is very small. But the slope is large—being kicked in the head definitely causes headaches, but most headaches are not caused by being kicked in the head.
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