# Dummies that take only one non-zero value

According to this blog post in the section «2. Dummies That Take Only One Non-Zero Value», the author states that when the dummy has only 1 observation where it's different from zero, then we can drop that observation without altering the OLS estimates for the remaining coefficients... Why is this true?

I've tried doing some calculations, and it will always depend on the dummy(I've interchanged some columns and rows so that the first column represents the dummy, and the 1st row the observation where the dummy is non-null.) The OLS estimates seems to depend on 1st row...

My design matrix is $\begin{bmatrix} D & X \end{bmatrix}$. For OLS estimates I get $\hat\beta=\begin{bmatrix} 1 & -x_{1}(X'X)^{-1} \\ -(X'X)^{-1} x_{1}' & (X'X)^{-1} \end{bmatrix}\begin{bmatrix} y_1 \\ X'Y \end{bmatrix}$,where $x_1$ is the 1st row of $X$ matrix.

Any help would be appreciated

• Maybe if you could show us your calculations we could point out what's wrong. Possible: This statement is conditional on having a constant in your model. Intuitively: if you observe that older people walk slower, how could that observation be altered if I told you that they all have had 3 hip replacements. If there was variation in the number of hip replacements, you might check for (and find) a link between that number and the walking pace. If not, then not
– sheß
Commented May 20, 2016 at 8:24
• @sheß I've added my calculations. Commented May 20, 2016 at 8:44