Gauss and the Method of Least Squares. Teddy Petrou Hongxiao Zhu. Outline. Who was Gauss? Why was there controversy in finding the method of least squares? Gauss ’ treatment of error Gauss ’ derivation of the method of least squares Gauss ’ derivation by modern matrix notation
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Teddy Petrou Hongxiao Zhu
Born:1777 Brunswick, Germany
Died: February 23, 1855, Göttingen, Germany
By the age of eight during arithmetic class he astonished his teachers by being able to instantly find the sum of the first hundred integers.
If then variance equals .
Suppose we have independent random variables with standard deviation 1 and expected value 0. The linear function of total errors is given by
Now the variance of E is given as
This is assuming every error falls within standard deviations from the mean
Gauss’ Derivation of the Method of Least Squares
How do these results relate with the least squares estimation?
Gauss’ results are equivalent to the following lemma: