Forming ANOVA table without observed values.












0












$begingroup$


regression analysis



Need some help in forming the ANOVA table without observed values.
I only managed to find SST with the first line of hint, but do not know how to proceed to find SSTreatment or SSError.
Any hint/solution will be greatly appreciated.






regression linear-regression







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$endgroup$

















    0












    $begingroup$


    regression analysis



    Need some help in forming the ANOVA table without observed values.
    I only managed to find SST with the first line of hint, but do not know how to proceed to find SSTreatment or SSError.
    Any hint/solution will be greatly appreciated.






    regression linear-regression







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      regression analysis



      Need some help in forming the ANOVA table without observed values.
      I only managed to find SST with the first line of hint, but do not know how to proceed to find SSTreatment or SSError.
      Any hint/solution will be greatly appreciated.






      regression linear-regression







      share|cite|improve this question









      $endgroup$




      regression analysis



      Need some help in forming the ANOVA table without observed values.
      I only managed to find SST with the first line of hint, but do not know how to proceed to find SSTreatment or SSError.
      Any hint/solution will be greatly appreciated.






      regression linear-regression




      regression linear-regression






      share|cite|improve this question













      share|cite|improve this question











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      asked Feb 2 at 0:43









      jaclynxjaclynx

      4916




      4916






















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          $begingroup$

          First set up the error funcion



          $$F(beta_0, beta_1) =sum_{i=1}^{N}[y_i-beta_0-beta_1x_i]^2.$$



          Differentiate with respect to $beta_0$ and $beta_1$ and set the derivatives equal to $0$ to obtain.



          $$sum_{i=1}^Ny_i-Nbeta_0-left[sum_{i=1}^{N}x_iright]beta_1=0$$
          $$sum_{i=1}^Ny_ix_i-left[sum_{i=1}^{N}x_iright]beta_0-left[sum_{i=1}^{N}x^2_iright]beta_1=0.$$



          The first equation can be rewritten as



          $$Nbar{y}-Nbeta_0-Nbar{x}beta_1=0 implies beta_0 = bar{y}-2bar{x}=0.$$



          From the second equaiton we can obtain



          $$150-15cdot 2cdot 0 - left[sum_{i=1}^{15}x^2_iright]beta_1=0$$
          $$implies sum_{i=1}^{15}x^2_i=37.5$$



          We know that the correlation $r$ is given by



          $$r= dfrac{1/Nsum_{i=1}^{15}x_iy_i-bar{x}bar{y}}{s_x s_y}$$



          We have to determine $s_x$ in order to calculate $r$:
          $$s_x = dfrac{1}{15-1}sum_{i=1}^{15}(x_i-bar{x})^2$$
          $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2bar{x}sum_{i=1}^{15}x_i+sum_{i=1}^{15}bar{x}^2right]$$
          $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2cdot 15cdotbar{x}^2+15bar{x}^2right]$$
          $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-15cdotbar{x}^2right].$$



          Finally, we know that $text{SSTotal}=sum_{i=1}^{15}left[y_i-bar{y}right]^2$ and



          $$r^2 = dfrac{text{SSTreatment}}{text{SSTotal}}=dfrac{text{SSTreatment}}{sum_{i=1}^{15}left[y_i-bar{y}right]^2}=dfrac{text{SSTreatment}}{(15-1)s^2_y}$$
          $$implies text{SSTreatment} =(15-1),r^2,s^2_y$$






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            0












            $begingroup$

            First set up the error funcion



            $$F(beta_0, beta_1) =sum_{i=1}^{N}[y_i-beta_0-beta_1x_i]^2.$$



            Differentiate with respect to $beta_0$ and $beta_1$ and set the derivatives equal to $0$ to obtain.



            $$sum_{i=1}^Ny_i-Nbeta_0-left[sum_{i=1}^{N}x_iright]beta_1=0$$
            $$sum_{i=1}^Ny_ix_i-left[sum_{i=1}^{N}x_iright]beta_0-left[sum_{i=1}^{N}x^2_iright]beta_1=0.$$



            The first equation can be rewritten as



            $$Nbar{y}-Nbeta_0-Nbar{x}beta_1=0 implies beta_0 = bar{y}-2bar{x}=0.$$



            From the second equaiton we can obtain



            $$150-15cdot 2cdot 0 - left[sum_{i=1}^{15}x^2_iright]beta_1=0$$
            $$implies sum_{i=1}^{15}x^2_i=37.5$$



            We know that the correlation $r$ is given by



            $$r= dfrac{1/Nsum_{i=1}^{15}x_iy_i-bar{x}bar{y}}{s_x s_y}$$



            We have to determine $s_x$ in order to calculate $r$:
            $$s_x = dfrac{1}{15-1}sum_{i=1}^{15}(x_i-bar{x})^2$$
            $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2bar{x}sum_{i=1}^{15}x_i+sum_{i=1}^{15}bar{x}^2right]$$
            $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2cdot 15cdotbar{x}^2+15bar{x}^2right]$$
            $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-15cdotbar{x}^2right].$$



            Finally, we know that $text{SSTotal}=sum_{i=1}^{15}left[y_i-bar{y}right]^2$ and



            $$r^2 = dfrac{text{SSTreatment}}{text{SSTotal}}=dfrac{text{SSTreatment}}{sum_{i=1}^{15}left[y_i-bar{y}right]^2}=dfrac{text{SSTreatment}}{(15-1)s^2_y}$$
            $$implies text{SSTreatment} =(15-1),r^2,s^2_y$$






            share|cite|improve this answer









            $endgroup$


















              0












              $begingroup$

              First set up the error funcion



              $$F(beta_0, beta_1) =sum_{i=1}^{N}[y_i-beta_0-beta_1x_i]^2.$$



              Differentiate with respect to $beta_0$ and $beta_1$ and set the derivatives equal to $0$ to obtain.



              $$sum_{i=1}^Ny_i-Nbeta_0-left[sum_{i=1}^{N}x_iright]beta_1=0$$
              $$sum_{i=1}^Ny_ix_i-left[sum_{i=1}^{N}x_iright]beta_0-left[sum_{i=1}^{N}x^2_iright]beta_1=0.$$



              The first equation can be rewritten as



              $$Nbar{y}-Nbeta_0-Nbar{x}beta_1=0 implies beta_0 = bar{y}-2bar{x}=0.$$



              From the second equaiton we can obtain



              $$150-15cdot 2cdot 0 - left[sum_{i=1}^{15}x^2_iright]beta_1=0$$
              $$implies sum_{i=1}^{15}x^2_i=37.5$$



              We know that the correlation $r$ is given by



              $$r= dfrac{1/Nsum_{i=1}^{15}x_iy_i-bar{x}bar{y}}{s_x s_y}$$



              We have to determine $s_x$ in order to calculate $r$:
              $$s_x = dfrac{1}{15-1}sum_{i=1}^{15}(x_i-bar{x})^2$$
              $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2bar{x}sum_{i=1}^{15}x_i+sum_{i=1}^{15}bar{x}^2right]$$
              $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2cdot 15cdotbar{x}^2+15bar{x}^2right]$$
              $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-15cdotbar{x}^2right].$$



              Finally, we know that $text{SSTotal}=sum_{i=1}^{15}left[y_i-bar{y}right]^2$ and



              $$r^2 = dfrac{text{SSTreatment}}{text{SSTotal}}=dfrac{text{SSTreatment}}{sum_{i=1}^{15}left[y_i-bar{y}right]^2}=dfrac{text{SSTreatment}}{(15-1)s^2_y}$$
              $$implies text{SSTreatment} =(15-1),r^2,s^2_y$$






              share|cite|improve this answer









              $endgroup$
















                0












                0








                0





                $begingroup$

                First set up the error funcion



                $$F(beta_0, beta_1) =sum_{i=1}^{N}[y_i-beta_0-beta_1x_i]^2.$$



                Differentiate with respect to $beta_0$ and $beta_1$ and set the derivatives equal to $0$ to obtain.



                $$sum_{i=1}^Ny_i-Nbeta_0-left[sum_{i=1}^{N}x_iright]beta_1=0$$
                $$sum_{i=1}^Ny_ix_i-left[sum_{i=1}^{N}x_iright]beta_0-left[sum_{i=1}^{N}x^2_iright]beta_1=0.$$



                The first equation can be rewritten as



                $$Nbar{y}-Nbeta_0-Nbar{x}beta_1=0 implies beta_0 = bar{y}-2bar{x}=0.$$



                From the second equaiton we can obtain



                $$150-15cdot 2cdot 0 - left[sum_{i=1}^{15}x^2_iright]beta_1=0$$
                $$implies sum_{i=1}^{15}x^2_i=37.5$$



                We know that the correlation $r$ is given by



                $$r= dfrac{1/Nsum_{i=1}^{15}x_iy_i-bar{x}bar{y}}{s_x s_y}$$



                We have to determine $s_x$ in order to calculate $r$:
                $$s_x = dfrac{1}{15-1}sum_{i=1}^{15}(x_i-bar{x})^2$$
                $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2bar{x}sum_{i=1}^{15}x_i+sum_{i=1}^{15}bar{x}^2right]$$
                $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2cdot 15cdotbar{x}^2+15bar{x}^2right]$$
                $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-15cdotbar{x}^2right].$$



                Finally, we know that $text{SSTotal}=sum_{i=1}^{15}left[y_i-bar{y}right]^2$ and



                $$r^2 = dfrac{text{SSTreatment}}{text{SSTotal}}=dfrac{text{SSTreatment}}{sum_{i=1}^{15}left[y_i-bar{y}right]^2}=dfrac{text{SSTreatment}}{(15-1)s^2_y}$$
                $$implies text{SSTreatment} =(15-1),r^2,s^2_y$$






                share|cite|improve this answer









                $endgroup$



                First set up the error funcion



                $$F(beta_0, beta_1) =sum_{i=1}^{N}[y_i-beta_0-beta_1x_i]^2.$$



                Differentiate with respect to $beta_0$ and $beta_1$ and set the derivatives equal to $0$ to obtain.



                $$sum_{i=1}^Ny_i-Nbeta_0-left[sum_{i=1}^{N}x_iright]beta_1=0$$
                $$sum_{i=1}^Ny_ix_i-left[sum_{i=1}^{N}x_iright]beta_0-left[sum_{i=1}^{N}x^2_iright]beta_1=0.$$



                The first equation can be rewritten as



                $$Nbar{y}-Nbeta_0-Nbar{x}beta_1=0 implies beta_0 = bar{y}-2bar{x}=0.$$



                From the second equaiton we can obtain



                $$150-15cdot 2cdot 0 - left[sum_{i=1}^{15}x^2_iright]beta_1=0$$
                $$implies sum_{i=1}^{15}x^2_i=37.5$$



                We know that the correlation $r$ is given by



                $$r= dfrac{1/Nsum_{i=1}^{15}x_iy_i-bar{x}bar{y}}{s_x s_y}$$



                We have to determine $s_x$ in order to calculate $r$:
                $$s_x = dfrac{1}{15-1}sum_{i=1}^{15}(x_i-bar{x})^2$$
                $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2bar{x}sum_{i=1}^{15}x_i+sum_{i=1}^{15}bar{x}^2right]$$
                $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-2cdot 15cdotbar{x}^2+15bar{x}^2right]$$
                $$= dfrac{1}{15-1}left[sum_{i=1}^{15}x^2_i-15cdotbar{x}^2right].$$



                Finally, we know that $text{SSTotal}=sum_{i=1}^{15}left[y_i-bar{y}right]^2$ and



                $$r^2 = dfrac{text{SSTreatment}}{text{SSTotal}}=dfrac{text{SSTreatment}}{sum_{i=1}^{15}left[y_i-bar{y}right]^2}=dfrac{text{SSTreatment}}{(15-1)s^2_y}$$
                $$implies text{SSTreatment} =(15-1),r^2,s^2_y$$







                share|cite|improve this answer












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                answered Mar 7 at 17:15









                MachineLearnerMachineLearner

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