Orthogonal means:

Orthogonal means:

• A. Means variables are perfectly correlated
• B. Means the variables are the same
• C. Means one variable causes the other
• D. Means perpendicular and independent (uncorrelated)

Answer: (D)

Orthogonal means perpendicular; in statistics that perpendicular idea describes zero linear relationship between variables. When two variables are orthogonal, their standardized relationship has zero correlation, so they don’t share linear information with each other. You can think of them as independent in the sense of not contributing linear overlap to each other, which is why you hear that they are uncorrelated. This is why the best description is a pair that is perpendicular and uncorrelated. It’s not about one variable causing the other, nor about them being the same variable or perfectly correlated. Note that independence is stronger than being uncorrelated in general, though in many introductory contexts orthogonality is treated as uncorrelated, with independence holding in special cases like jointly normal distributions.

Orthogonal means perpendicular; in statistics that perpendicular idea describes zero linear relationship between variables. When two variables are orthogonal, their standardized relationship has zero correlation, so they don’t share linear information with each other. You can think of them as independent in the sense of not contributing linear overlap to each other, which is why you hear that they are uncorrelated. This is why the best description is a pair that is perpendicular and uncorrelated.

It’s not about one variable causing the other, nor about them being the same variable or perfectly correlated. Note that independence is stronger than being uncorrelated in general, though in many introductory contexts orthogonality is treated as uncorrelated, with independence holding in special cases like jointly normal distributions.