![]() To be r times the ratio between the sample standardĭeviation in the y direction over the sample standardĭeviation in the x direction. Is a regression line that we're trying to fit to these points. So this, you would literally say y hat, this tells you that this The equation for any line is going to be y is equal to mx plus b, where this is the slope and Intuition for the equation of the least squares line. Their standard deviations, will help us build an And visualizing these means, especially their intersection and also So the mean is three,Īnd this is one sample standard deviation for y above the mean and this is one standardĭeviation for y below the mean. We could do the same thing for the y variables. Sample standard deviation below the mean, and then Sample standard deviation above the mean, this is one Is eight divided by four, which is two, so we have xĮquals two right over here. One plus two plus two plus three divided by four, Here, so the sample mean for x, it's easy to calculate In red so that you know that's what is going on Sample standard deviation for x are here in red, and actually let me box these off We clearly have the fourĭata points plotted, but let's plot the statistics for x. So before I do that, let's just visualize some of the statistics that we have here for these data points. On this video is build on this notion and actuallyĬome up with the equation for the least squares We got an r of 0.946, which means we have a fairly If r is equal to zero, you don't have a correlation, but for this particular bivariate dataset, One, you have a perfect negative correlation, and And as we said, if r is equal to one, you have a perfect positive correlation. The product of the z scores for each of those pairs. In that video we saw all it is is an average of In previous videos, we took this bivariate data and weĬalculated the correlation coefficient, and justĪs a bit of a review, we have the formula here, and it looks a bit intimidating, but
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