What is the difference between least squares and reduced chi-squared? For me they look nearly exactly the same, with the difference, that in chi-squared everything is divided by the variance. But despite from that, they are both identical?

  • $\begingroup$ Check out this lecture; the direct answer to your question is on slide 5. In short: $\chi^2$ if $y$ are from a Gaussian distribution, if not – it's least squares (because then the resulting distribution is not $\chi^2$). $\endgroup$ – corey979 Mar 3 at 11:54
  • $\begingroup$ Why the downvote? Seems a perfectly valid question to me. $\endgroup$ – corey979 Mar 3 at 11:55
  • $\begingroup$ @corey979 Do I understand it right, that they use least squares to minimize chi-squared? I'm now even more confused as they also involve MLE there in the same context.. $\endgroup$ – Ben Mar 3 at 12:03

$R^2$ is used in order to understand the amount of variability in the data that is explained by your model. A $R^2$ of $90\%$ means that the $90\%$ of the variance of the data is explained by the model, that is a good value. On practice you cannot rely only on the $R^2$, but is a type of measure that you can find.

The Chi-Square goodness of feat instead determines if your data matches a population, is a test in order to understand what kind of distribution follow your data. Instead, the Chi Square statistic is commonly used for testing relationships between categorical variables.

There are other posts in this forum that explain this difference, and there are many sites that explain these two variable.


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