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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The trend line is just the closest fitting line you can find. So you can say "on average" the relationship is 2x or whatever, but with such low r, most people are either much above or much below the average. With higher r, we could say that more people would be closer to that avg
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this means that there *is* a relationship between the trendline and the correlation? or hte predictions u can make off it? like if u have a near-flat trendline with high variance on both ends, but then u keep the same variance and make the trendline steep
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like i feel like in both cases, the r would be the same, but the predictions i could make are more interesting in the latter case? i'm trying to figure out how trendlines impact prediction, i guess. maybe its the same amount of prediction as the flat line anyway idk
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So in both cases the points are spread out in a cloud and look somewhat similar. Imagine drawing different trend lines with all different slopes on the same data set and computing r for that line. Maybe the best fit line has r=.08 and m=0 but theres also a line with r=.07 and m=2
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