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
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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The regression coefficients is Covariance(X,Y)/Variance(X), the correlation is Covariance(X,Y)/Std(X)*Std(Y)
There’s a very close relationship but you can have the correlation and slope differ arbitrarily depending on the variances of the dataset
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With correlation = 0, no, but if you have a small positive or small negative correlation, you can certainly get a statistically significant slope. "Steep" is a little ambiguous because I don't know much about your data, but I suspect no you wouldn't get a steep slope.
The slope = correlation * (stdev in y / stdev in x). So correlation times the ratio of the amount y varies vs the amount x varies. You can simulate and plot a multi variate normal with any correlation and stdev (therefore slope) you want and then plot it to get an intuition.
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If the data is normalized and you’re doing univariate linear regression, then the correlation actually *is* the same as the slope. So if the non-standardized slope is “steep” but the correlation is low, that just means that the variance in y is high or that in x is low
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