A data scientist is attempting to find the optimal coefficients ($\hat{\beta}$) for a linear model using the equation $\hat{\beta} = (X^{T} X)^{-1} X^{T} y$, where $X$ is the matrix of input features and $y$ is the vector of target values. The calculation fails, returning a 'singular matrix' error. What is the most likely cause of this error in the dataset represented by matrix $X$?

Calculating OLS Coefficients

Impact of an Outlier on OLS Coefficients