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I have two equations with this format: $Ds= A+A^2+\alpha_1\tag{1}$ and $Ds= M+M^2+\alpha_2 \tag{2}$

Knowing that $(1)$ explains 72% of $Ds$ and $(2)$ 20%. I want to combine these two equations into one and know how much this equation explains. Something like:

$Ds= A+A^2+\alpha_1+M+M^2+\alpha_2$ (I know it cannot be a sum, but I don't know how to combine this).

Thank you for your answers.

SOSA

P.D: I don't have good notion in mathematics, and I'm not sure about the tag for this question.

Sorry for my bad explanation.

The facts are: I have two factors Age (A) and matrilineal link (M) I have a parameter the David score (Ds, hierarchy rank) I made a quadratic regression with the factor A, and I found that this regression explains 72% of Ds. I did the same thing with the factor M and I found that this regression explains 20% of Ds. So now I want to combine these two equations to explain the parameter Ds with these two factors.

Thank you again for your help

I have this idea: Ds=[(Ds= A+A^2+alpha1) + (Ds= M+M^2+alpha2)]/2

Is it correct? But How can I say how much they explain Ds?

SOSA

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    Sorry for my bad explanation. The facts are: I have two factors Age (A) and matrilineal link (M) I have a parameter the David score (Ds, hierarchy rank) I made a quadratic regression with the factor A, and I found that this regression explains 72% of Ds. I did the same thing with the factor M and I found that this regression explains 20% of Ds. So now I want to combine these two equations to explain the parameter Ds with these two factors. Thank you again for your help SOSA2012-12-18

1 Answers 1

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I do not think you have enough information at this point. The reason is the you want to fit the surface

$ Ds(A,M) = \begin{pmatrix}1\\A\\A^2\end{pmatrix}^\top \begin{vmatrix} K_{11} & K_{12} & K_{13} \\ K_{21} & K_{22} & K_{23} \\ K_{31} & K_{32} & K_{33} \end{vmatrix} \begin{pmatrix}1\\M\\M^2\end{pmatrix}$

$ Ds(A,M) = K_{11} + K_{12} M + K_{13} M^2 + K_{21} A + K_{22} A M + K_{23} A M^2 + K_{31} A^2 + K_{32} A^2 M + K_{33} A^2 M^2 $

and you have only sampled a constant $M=M_\star$ varying $A$ giving you

$Ds = (K_{11}+K_{12}M_\star+K_{13} M_\star^2) \\ + (K_{21}+K_{22}M_\star+K_{23} M_\star^2) A \\ + (K_{31}+K_{32}M_\star+K_{33} M_\star^2) A^2 \\ = \alpha_1 + \beta_1 A + \gamma_1 A^2$

and a constant $A=A_\star$ varying $M$ giving you

$Ds = (K_{11}+K_{21}A_\star+K_{31} A_\star^2) \\ + (K_{12}+K_{22}A_\star+K_{32} A_\star^2) M \\ + (K_{13}+K_{23}A_\star+K_{33} A_\star^2) M^2 \\ = \alpha_2 + \beta_2 M + \gamma_2 M^2$

Equating your regression coefficients $\alpha_1$, $\beta_1$, $\gamma_1$ and $\alpha_2$, $\beta_2$, $\gamma_2$ to the coefficients $K_{ij}$ of the 3x3 matrix you have 6 equations and 9 unknowns.

You can assume some of the coefficients are zero like $K_{32}=K_{23}=K_{33}=0$ (by ignoring the cross effects of $A$ and $M$) to give you.

$Ds = (K_{11}+K_{12}M_\star+K_{13} M_\star^2) + (K_{21}+K_{22}M_\star) A + (K_{31}) A^2 \\ = \alpha_1 + \beta_1 A + \gamma_1 A^2$

and

$Ds = (K_{11}+K_{21}A_\star+K_{31} A_\star^2) + (K_{12}+K_{22}A_\star) M + (K_{13}) M^2 \\ = \alpha_2 + \beta_2 M + \gamma_2 M^2$

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    OK, thank you Ja72 I will look for a forum. I noticed an important detail. The constant α1+β1A+γ1A2 are given by SPSS, the only thing is that I don't know how to interpret them (but it's another problem i will try to fix next week). I think the problem changed, I have for my two equations all the data, but the problem now is to combine them. How can I do that? Thank you in advance SOSA Sebastian2012-12-20