For the dataset with points (1,3) and (3,7), the least-squares regression line is y = a + b x.

• A. y = 1 + 2x
• B. y = 2 + x
• C. y = 3 + 2x
• D. y = 0 + 2x

Answer: (A)

With two data points, the least-squares line passes exactly through both points, giving a perfect fit. The slope is the rise over run between the points: (7 − 3) / (3 − 1) = 4 / 2 = 2. Using one point to find the intercept, 3 = 2(1) + a gives a = 1. So the line is y = 1 + 2x, which indeed passes through both points (1,3) and (3,7). The other options do not go through both points, so they would yield nonzero residuals and a worse fit.