Spacetime as a redshift and analyze the effect in terms of scenarios (b) or (d). In classical mechanics, the state of motion of a particle is characterized by its mass and its velocity. Linear momentum, the product of a particle's mass and velocity, is a vector quantity, possessing the same direction as the velocity: p = "mv". It is a "conserved" quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. In relativistic mechanics, the momentum vector is extended to four dimensions. Added to the momentum vector is a time component that
Linear regression linear relationship between the dependent variable and regressors. Thus the model takes the form where denotes the transpose, so that xβ is the inner product between vectors x and β. Often these "n" equations are stacked together and written in matrix notation as where Some remarks on notation and terminology: Example. Consider a situation where a small ball is being tossed up in the air and then we measure its heights of ascent "h" at various moments in time "t". Physics tells us that, ignoring the drag, the relationship can be modeled as where "β" determines the initial velocity of