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

  1. Jun 17, 2008 #1
    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
     
  2. jcsd
  3. Jul 16, 2008 #2
    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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