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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this sounds like the variance within each category is high and the variance between the means of each category is low
can you do a violin plot of butter consumption after binning the data by how much ppl liked ice cream? what does that look like?
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what the correlation tells you is how much of the variability in butter consumption is explained by how much ppl like ice cream (well, not quite because it's linear but it's kind of like this)
so it tells you the size of the effect relative to natural variability in some sense
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correlation feels pretty intuitive to me here, but i think im getting some intuitive confusion cause to me, correlation is "about prediction," but then i think that the trendline is "about prediction" too. how do i conceive of the impact of the trendline separately?
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i don't think that's quite the right framing
if your model is B = alpha + beta*I + noise where B is butter consumption and I is how much ppl like ice cream, then the slope of the trend line is your estimate of beta
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