ANOVA

Discussion in 'CS1' started by ykai, Mar 13, 2023.

  1. ykai

    ykai Ton up Member

    According to SSTOT=SSREG+SSRES and it is come from MSE.
    and
    MSE=E[(g(xunderbar)-theta)^2]=Variance+bias^2
    SSTOT=sum(y_i-ybar)^2
    SSREG=sum(yhat-ybar)^2
    SSRES=sum(y_i-yhat)^2

    Is SSRES=bias^2 ?
    Is SSREG=Variance ?
    I just guess,not sure about it.

    And relationship between Var[m(theta)] and E[s^2(theta)] is respounded to SSREG and SSRES respectively.
    The formal term in Var[m(theta)] is similar to SSTOT.
    Are they equal situation,eg SSREG=Variance=Var[m(theta)],or just have similar relationship?
     
    Last edited: Mar 13, 2023
    ykai, Mar 13, 2023
    #1
  2. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    Hi Ykai

    MSE, mean square error, is from Chapter 8 Point estimation, it is used to compare estimators.

    In Chapter 12 Linear regression we look at MSS, mean sum of squares, it is the sum of squares divided by the degrees of freedom.

    Sample variance is sum(x_i-x_bar)^2/(n-1)

    Sigma_hat^2 is sum(y_i-y_i_hat)^2/(n-2)=SS_RES/(n-2)=MSS_RES

    SS_REG is the variability explained the by model, SS_RES is the remaining unexplained variability.

    I can see where you are coming from but I would keep MSE and MSS separate for CS1.

    Thanks
    Andrea
     
    Andrea Goude, Mar 14, 2023
    #2
  3. ykai

    ykai Ton up Member

    Thank you, it seems that my concept is not complete enough.
     
    ykai, Mar 14, 2023
    #3

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