There are some lines in this chapter that caused me some confusion, but want to make sure others agree or can explain before I propose a change.
There are some lines on residual from prediction of $T$ (treatment) from the other features $X{1i}, ..., X{ki}$
a) "where $\tilde{Ti}$ is the residual from a regression of all other covariates $X{1i} + ... + X_{ki}$ on $Ti$" (under Regression Theory). Should this mean regression of $T$ on $X{1}, ..., X_{k}$ - not a sum? Since treatment is being predicted from the covariates?
b) "where $\delta_{A}$ is the vector of coefficients from the regression of $A$ on $Educ$" (under Regression for Non-Random Data)? Again should this be regression of $Educ$ on $A$?
There are some lines in this chapter that caused me some confusion, but want to make sure others agree or can explain before I propose a change.
There are some lines on residual from prediction of $T$ (treatment) from the other features $X{1i}, ..., X{ki}$
a) "where $\tilde{Ti}$ is the residual from a regression of all other covariates $X{1i} + ... + X_{ki}$ on $Ti$" (under Regression Theory). Should this mean regression of $T$ on $X{1}, ..., X_{k}$ - not a sum? Since treatment is being predicted from the covariates?
b) "where $\delta_{A}$ is the vector of coefficients from the regression of $A$ on $Educ$" (under Regression for Non-Random Data)? Again should this be regression of $Educ$ on $A$?
Thanks!