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

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The discussion centers on the calculation of Mean Squared Error (MSE) in the context of an ordinary least squares regression model defined as y = b1x1 + b2x2 + e, where e follows a normal distribution N(0,1). The participant notes that their response variable y is distributed as N(4,33) and questions the consistency of the ANOVA results showing MSE as 1. A key conclusion is that the variance of y is equal to the variance of the error term, leading to the correct MSE calculation of 1, as confirmed by the ANOVA analysis.

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HF08
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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
 
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I think you are getting a bit confused here. [tex]\underline{y}=X\underline{\beta} + \underline{\epsilon}[/tex] is your model? There is no way that [tex]y[/tex] could be [tex]N(4,33)[/tex] when your [tex]\epsilon_i[/tex] are [tex]N(0,1)[/tex]. Also that ANOVA does not make sense if you have [tex]\epsilon_i[/tex] as there is no variance to analyse. In this case ANOVA is right. As
[tex]Var(y_i)=Var(\mu_i+\epsilon_i)=Var(\epsilon_i)=1[/tex].


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

Hope this helps
 

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