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The answer is 33033/80265= 0.4115?

  • $\begingroup$ By definition, $R^2 = 1 - SSE/SST = SSR/SST = 33033/80265$. $\endgroup$
    – Zhanxiong
    Aug 1 at 4:01
  • 1
    $\begingroup$ Welcome to Cross Validated! The model and error sums of squares should add up to the total sum of squares, yet they are unequal. It could be worth asking your professor about this. $\endgroup$
    – Dave
    Aug 1 at 4:07

1 Answer 1


There are many equivalent ways of thinking about $R^2$. The one that makes the most sense to me is comparing the performance of your model to the performance of some baseline model that always predicts the same value: the pooled mean of the response variable $y$.

If we measure model performance by considering the sum of squares, the the “model” sum of squares in the table is the performance of our model.

Then we need the performance of our baseline model. Using the terminology of your table, that comes from the “corrected total” sum of squares. This “total” sum of squares is related to the overall variance of $y$, and this is what leads to $R^2$ being described as the “proportion of variance explained”.

Then we take the ratio to get the $\frac{33033}{80265}$ that you know is the solution.

(Note that it would be more common to use the equivalent definition $R^2=1-\frac{47231}{80265}$, except that the error and model sums of squares do not add up to the total sum of squares. I am convinced that this is a rounding issue.)


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