# 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 $x$ be our estimate of the value of $B$, then the SSE corresponding to x is:

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

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

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 $x$ be our estimate of the value of $B$, then the SSE corresponding to x is:

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

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

CB