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I have a series of actual price and predicted price. Values of which are given below. Now when I try to find the correlation coefficient using the R function cor(actual price,predicted price) I get 0.6769881. But when I try to find the mean square error the value comes 3.634382e-05, which I believe is a bit low for the corresponding correlation coefficient. Is there something I am doing wrong

     **predicted Price**                            **Actual Price** 
        4.760972                                      4.780 
        4.767296                                      4.779
        4.776825                                      4.775
        4.776761                                      4.776
        4.775952                                      4.779
        4.776835                                      4.777
        4.772703                                      4.776
        4.774033                                      4.778
        4.774343                                      4.779
        4.778052                                      4.783
        4.779570                                      4.779
        4.774922                                      4.781
        4.777020                                      4.779
        4.780514                                      4.786
        4.784221                                      4.784
        4.780591                                      4.780 
        4.782547                                      4.784
        4.783528                                      4.785
        4.784811                                      4.783
        4.787684                                      4.787
        4.790639                                      4.787
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The correlation coefficient and the MSE measure two different things.

  • The correlation coefficient essentially measures how well you can approximate your Actual Price by an affine linear function of Predicted Price. Plot Actual Price against Predicted Price, put a regression line through the scatterplot - the correlation coefficient will essentially tell you how much your points scatter around the line.

  • The MSE calculates... well, the mean squared error. In the scatterplot mentioned above, draw a vertical line from each dot to the regression line, then average the areas of the squares over those vertical lines. That's your MSE.

Both measures will increase if your scatterplot goes "farther away" from the regression line, but that's really all the relationship they have. (For instance, multiply all prices by 100, so you measure them in cents instead of in dollars. Then your MSE will increase by a factor of 10,000, but the correlation will stay unchanged. And in your scatterplot, all that will change is the axis scaling.) So you shouldn't be surprised at not finding a relationship between the correlation and the MSE, because there really is no reason to expect one.

(Incidentally, it's not obvious what a "large" or "small" correlation or MSE would be in this context. And you seem to be doing forecasting/prediction; this book chapter about assessing forecast accuracy may be helpful.)

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