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In $\mathbf{R}^2$ linear dependence implies that one vector is a linear function of the other: $$\textbf{v}_{1}=a\textbf{v}_2.$$ It's clear from this definition that the two variables would move in lock-step, implying a correlation of $1$ or $-1$ depending on the value of $a$. To more fully understand the differences and connections between the concepts, ...