A Researcher Had a Categorical Variable That They Wanted to Include

A researcher had a categorical variable that they wanted to include as a predictor in a regression equation. The researcher was trying to predict the success of a back pain intervention, and the categorical variable was the duration of the back pain prior to treatment, with 4 categories: less than 6 months, 6-12 months, 1-2 years, more than 2 years. They needed to code these variables into dummy variables for the regression using less than 6 months as their control category. Which of the following represents the correct coding scheme?

A) $$\begin{array} { | l | l | r | r | r | } \hline\quad\quad\quad\quad & \quad\quad\begin{array} { c } \\\\\\ \text { Duration of Pain } \\\end{array} & \begin{array} { c } \text { Dummy 1 } \\\text { (Under 6 } \\\text { Months vs } \\\text { 6-12 Months) }\end{array} & \begin{array} { c } \text { Dummy 2 } \\\text { (Under 6 } \\\text { Months vs } \\1 - 2 \text { Years) }\end{array} & \begin{array} { c } \text { Dummy 3 } \\\text { (Under 6 } \\\text { Months vs } \\\text { Over 2 Years) }\end{array} \\\hline & \text { Under 6 Months } & 1 & 1 & 1 \\& \text { 6-12 Months } &1 & 0 & 0\\& 1 - 2 \text { Years }& 0 & 1 & 0 \\&\text { More Than 2 Years }& 0 & 0 & 1\\ \hline\end{array}$$
B) $$\begin{array} { | l | l | r | r | r | } \hline\quad\quad\quad\quad & \quad\quad\begin{array} { c } \\\\\\ \text { Duration of Pain } \\\end{array} & \begin{array} { c } \text { Dummy 1 } \\\text { (Under 6 } \\\text { Months vs } \\\text { 6-12 Months) }\end{array} & \begin{array} { c } \text { Dummy 2 } \\\text { (Under 6 } \\\text { Months vs } \\1 - 2 \text { Years) }\end{array} & \begin{array} { c } \text { Dummy 3 } \\\text { (Under 6 } \\\text { Months vs } \\\text { Over 2 Years) }\end{array} \\\hline & \text { Under 6 Months } & 0 & 0 & 0 \\& \text { 6-12 Months } &1 & 0 & 0\\& 1 - 2 \text { Years }& 0 & 1 & 0 \\&\text { More Than 2 Years }& 0 & 0 & 1\\ \hline\end{array}$$
C) $$\begin{array} { | l | l | r | r | r | } \hline\quad\quad\quad\quad & \quad\quad\begin{array} { c } \\\\\\ \text { Duration of Pain } \\\end{array} & \begin{array} { c } \text { Dummy 1 } \\\text { (Under 6 } \\\text { Months vs } \\\text { 6-12 Months) }\end{array} & \begin{array} { c } \text { Dummy 2 } \\\text { (Under 6 } \\\text { Months vs } \\1 - 2 \text { Years) }\end{array} & \begin{array} { c } \text { Dummy 3 } \\\text { (Under 6 } \\\text { Months vs } \\\text { Over 2 Years) }\end{array} \\\hline & \text { Under 6 Months } & 0 & 0 & 0 \\& \text { 6-12 Months } &0 &1 & 1\\& 1 - 2 \text { Years }& 1 & 0 & 1 \\&\text { More Than 2 Years }& 1 &1&0\\ \hline\end{array}$$

D) $$\begin{array} { | l | l | r | r | r | } \hline\quad\quad\quad\quad & \quad\quad\begin{array} { c } \\\\\\ \text { Duration of Pain } \\\end{array} & \begin{array} { c } \text { Dummy 1 } \\\text { (Under 6 } \\\text { Months vs } \\ \text { 6-12 Months) }\end{array} & \begin{array} { c } \text { Dummy 2 } \\\text { (Under 6 } \\\text { Months vs } \\1 - 2 \text { Years) }\end{array} & \begin{array} { c } \text { Dummy 3 } \\\text { (Under 6 } \\\text { Months vs } \\\text { Over 2 Years) }\end{array} \\\hline & \text { Under 6 Months } & 0 & 0 & 0 \\& \text { 6-12 Months } &0 &1 & 1\\& 1 - 2 \text { Years }& 1 & 0 & 1 \\&\text { More Than 2 Years }& 1 &1&0\\ \hline\end{array}$$