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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i KNOW the slope of the line isn't correlation, im asking if there's a relationship at all
like is it possible for there to be a steep slope with no correlation
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and im asking what information i can take from the slope, like can i make predictions about my data with the slope
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you can make predictions about the data from the slope, the correlation just tells you how "tight" the data are around the trend line
if the correlation is r = 1.0, then the "predictions" from the line are perfect (within the original data)
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You can make a confidence interval using the slope and the standard deviations. Low R^2 just means that's a much wider range. So slope matters yes, just how much it matters depends on your R^2
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Slope of the line would be used to predict Y given X (or to see how much a change in Y is associated with a 1 unit change in X). Correlation is a measure of how accurate that prediction is
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Yes you absolutely can make predictions from your data with the slope you have (you'll want to use the slope + intercept to make the prediction). I just suspect the predictions will not be very precise.
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