Karl Pearson’s coefficient of correlation (r) is strictly invariant to:

Let U = (X - a)/h and V = (Y - b)/k, where a and b are the new origins and h and k are the scale factors, both positive. Cov(U, V) = Cov(X, Y)/(h × k) σ_U = σ_X/h and σ_V = σ_Y/k r_UV = [Cov(X, Y)/(h × k)] / [(σ_X/h) × (σ_Y/k)] = Cov(X, Y)/(σ_X × σ_Y) = r_XY So subtracting constants (change of origin) and dividing by positive constants (change of scale) does not alter r. If h and k have opposite signs, the magnitude of r is unchanged but its sign is reversed, which is why the condition on the sign of the scale factor is stated. Options (A) and (B) are incomplete, because r is independent of both. Options (D) and (E) involve non-linear transformations, which in general change the value of r. Hence the correct option is (C).