# Significance of the slope of a straight line fit

I know the significance of the slope of a LMS linear regression can be calculated using the r2 coefficient of determination and looking up the appropriate value in an F table. However, I was thinking of perhaps making this "more robust" by replacing the LMS linear regression with a repeated median straight line fit, and perhaps even replacing the average value used to calculate r2 with the median value of the data. Is there any reason why this would NOT be a valid approach? Maybe the values in an F table are predicated on using LMS and averages, for example?

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No, F tests are based on the assumption that lowest sum of residual squares is optimal. It does not hold in case of robust regression, where the criterion is different.
For instance, effectively one may consider robust regression as least squares on data stripped from outliers; using $r^2$ on all data in this case adds non-culpable penalty for high residuals of outliers.

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No need to reinvent the wheel. There is an alternative, robust, R^2 measure with very good statistical properties:

A robust coefficient of determination for regression, O Renauda

Edit: *Is there any reason why this would NOT be a valid approach? * For one this does not make your method any more robust. There is a large literature on this issue, and fortunatly, good tools have been designed to adress these points.

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