Which expression represents the sum of the X values squared?

Which expression represents the sum of the X values squared?

• A. ΣX^2
• B. (ΣX)^2
• C. Σ(X^2)
• D. ΣX

Answer: (A)

Sum of squares means you square each data point first, then add them all up. So for observations X1, X2, ..., Xn, the sum of the squares is X1^2 + X2^2 + ... + Xn^2, which is what the notation Σ X^2 (or Σ(X^2)) expresses. This is different from squaring the total sum, (Σ X)^2, which would give extra cross terms from expanding the square of a sum (like 2·X1·X2, etc.). Thus the expression with the square on each X inside the summation is the correct representation of the sum of the X values squared.

Sum of squares means you square each data point first, then add them all up. So for observations X1, X2, ..., Xn, the sum of the squares is X1^2 + X2^2 + ... + Xn^2, which is what the notation Σ X^2 (or Σ(X^2)) expresses. This is different from squaring the total sum, (Σ X)^2, which would give extra cross terms from expanding the square of a sum (like 2·X1·X2, etc.). Thus the expression with the square on each X inside the summation is the correct representation of the sum of the X values squared.