# I have variance of response. How can I find it's MSE?

## Main Question or Discussion Point

To All,

I did a study and my response is defined as y = b1x1 + b2x2 + e where e ~N(0,1).
I have y~N(4,33). In my data results, I did an ordinary least squares regression model
for y = b1x1+b2x2+ e. The ANOVA is telling me the mean of y is 4, but MSE is 1.

So here is my question. If I know y~N(4,33). How can I determine the ANOVA MSE
is going to be 1?

Thanks,
HF08

Related Set Theory, Logic, Probability, Statistics News on Phys.org
I think you are getting a bit confused here. $$\underline{y}=X\underline{\beta} + \underline{\epsilon}$$ is your model? There is no way that $$y$$ could be $$N(4,33)$$ when your $$\epsilon_i$$ are $$N(0,1)$$. Also that ANOVA does not make sense if you have $$\epsilon_i$$ as there is no variance to analyse. In this case ANOVA is right. As
$$Var(y_i)=Var(\mu_i+\epsilon_i)=Var(\epsilon_i)=1$$.

What sofware are you using for this? Try using R. Don't bother with saying that $$\epsilon_i$$ are $$N(0,1)$$ unless you have a very good reason to know this. Usualy $$\epsilon_i$$ are $$N(0,\sigma^2)$$ where you will have to estimate $$\sigma^2$$. In R the model you have can be set up by lm(y~b1+b2-1,data=dataname).

Hope this helps