A Researcher Wants to Use a Nominal-Level Variable as an Independent

A researcher wants to use a nominal-level variable as an independent variable in a regression equation. It measures the type of school a child attends, and it has three categories: public school, private school, and homeschooled. The researcher creates three variables: one where those who attend public school are coded as 1, one where those who attend private school are coded as 1, and one where those who are homeschooled are coded as 1. The researcher then runs a regression with all three of these variables in the regression equation. Explain what the researcher has done wrong.