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#1 Posted : Friday, July 07, 2017 12:36:52 AM
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In classroom companion, page 58 of the psych/soc book, it says: "the square of the correlation, r^2 is the fraction of the variation in the y-values that is explained by the least squares regression of y on x. "

i'm kind of confused as to what r^2 is. Is it how well the y values can be predicted based on x?
#2 Posted : Thursday, July 13, 2017 3:56:49 AM
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Hi Michelle,
My name is Rachael (I'm an instructor with PREP101).
So by no means would I consider myself a statistician, but the good news is that for the MCAT you don’t need to be!
Essentially what r-squared is showing you is a measure of how close the data (y-values) are to the fitted regression line.
Put another way,
r^2 is a percentage (so between 0 and 100%) of the y-value (or response variable) that is explained by the linear model. So the higher the r^2 value, the better the model fits your data.
In relation to the graphs you see, the closer the observed y-values sit to the regression line the better the regression model explains the variation in the data.
So all your little dots on the plotted graph are the observed data and the closer those dots are bunched up to the regression line running across your chart, the higher your r^2 value. In theory, if you could ever get a model that explained 100% of the variance, then the fitted values would equal the observed values and you would have all of your data points falling along the regression line.

Does that help?
For more info this is a relatively user friendly site I have found that does a nice job explaining. blog.minitab.com
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