Thread: Simple proof to minimize SSE

1. Simple proof to minimize SSE

If I have a simple model where Yi equals some constant plus an error term like

Yi = B + Ei

To minimize the SSE of this model, I would use the mean value of Y for B. How can I prove that the mean of Y minimizes the SSE?

2. Re: Simple proof to minimize SSE

Originally Posted by DannyOcean
If I have a simple model where Yi equals some constant plus an error term like

Yi = B + Ei

To minimize the SSE of this model, I would use the mean value of Y for B. How can I prove that the mean of Y minimizes the SSE?
Let $\displaystyle x$ be our estimate of the value of $\displaystyle B$, then the SSE corresponding to x is:

$\displaystyle SSE(x)=\sum_i (Y_i - x)^2$

differentiate and set to zero to find the $\displaystyle x$ that minimises $\displaystyle SSE(X)$.

CB

3. Re: Simple proof to minimize SSE

Originally Posted by DannyOcean
If I have a simple model where Yi equals some constant plus an error term like

Yi = B + Ei

To minimize the SSE of this model, I would use the mean value of Y for B. How can I prove that the mean of Y minimizes the SSE?
Let $\displaystyle x$ be our estimate of the value of $\displaystyle B$, then the SSE corresponding to x is:

$\displaystyle SSE(x)=\sum_i (Y_i - x)^2$

differentiate and set to zero to find the $\displaystyle x$ that minimises $\displaystyle SSE(x)$.

CB