Question

Why is a least-squares line given this name? A)It provides the smallest possible slope. B)It provides the smallest possible y-intercept. C)It provides the smallest possible value for r2, which is a squared value. D)It provides the smallest possible sum for the squares of the residuals. E)The power of x is 1, which is smaller than a power of 2, or squared.

Answer 1

Answer: D) It provides the smallest possible sum for the squares of the residuals.

Explanation:

The least square regression line usually employed when fitting linear regression model basically works in other to minimize the sum of square error(residual). The residual or error simply refers to the difference between the actual and predicted value for each point given. The least square regression line can take up different positions between the plotted points, once, depending in the sum of the square of the error values. Hence, the least square regression line will be positioned where the sum of squared error is minimum in other to increase prediction accuracy.