Which one of the following statements about Principal Component Regression (PCR) is FALSE?

The statement that the first principal component direction does not consider variance is false because the very purpose of principal component analysis (PCA), from which PCR is derived, is to maximize the variance captured by the principal components. In PCA, the first principal component is defined as the direction in the feature space along which the data varies the most. This process involves calculating the eigenvectors of the covariance matrix of the data, where the eigenvalues represent the amount of variance captured by each principal component. Therefore, PCR, which uses these principal components for regression, inherently relies on the concept of variance to inform its model structure.

In contrast, standardizing predictors before generating principal components is a common practice to ensure that measurement scales do not distort the results, and PCR can aid in feature selection by highlighting the most informative components. However, it assumes that the directions of maximum variance relate to the underlying structure of the target variable, making the notion that the first principal component does not consider variance contradictory to the fundamental principles of PCA and PCR.