# Article analysis example essay

Because the 2016 plan is a smaller static tax cut overall than the 2015 plan, the changes in after-tax income for many taxpayers have become relatively smaller. The 2015 plan would have increased mean after-tax personal incomes by percent, while the 2016 plan would increase them by only percent under the higher-rate assumption, or percent under the lower-rate assumption (Table 9). This large change is mostly attributable to the fact that more income is taxable under the 2016 plan, and secondarily attributable to the fact that the rates on taxable income are higher.

The parameters and variables of factor analysis can be given a geometrical interpretation. The data ( z a i {\displaystyle z_{ai}} ), the factors ( F p i {\displaystyle F_{pi}} ) and the errors ( ε a i {\displaystyle \varepsilon _{ai}} ) can be viewed as vectors in an N i {\displaystyle N_{i}} -dimensional Euclidean space (sample space), represented as z a {\displaystyle \mathbf {z} _{a}} , F p {\displaystyle \mathbf {F} _{p}} and ε a {\displaystyle {\boldsymbol {\varepsilon }}_{a}} respectively. Since the data are standardized, the data vectors are of unit length ( z a ⋅ z a = 1 {\displaystyle \mathbf {z} _{a}\cdot \mathbf {z} _{a}=1} ). The factor vectors define an N p {\displaystyle N_{p}} -dimensional linear subspace (. a hyperplane) in this space, upon which the data vectors are projected orthogonally. This follows from the model equation