Question

A set of bivariate data was used to create a least squares regression line. Which of the following is minimized by the line

Answer 1

Answer:

B) The sum of the squared residuals

Step-by-step explanation:

Least Square Regression Line is drawn through a bivariate data(Data in two variables) plotted on a graph to explain the relation between the explanatory variable(x) and the response variable(y).

Not all the points will lie on the Least Square Regression Line in all cases. Some points will be above line and some points will be below the line. The vertical distance between the points and the line is known as residual. Since, some points are above the line and some are below, the sum of residuals is always zero for a Least Square Regression Line.

Since, we want to minimize the overall error(residual) so that our line is as close to the points as possible, considering the sum of residuals wont be helpful as it will always be zero. So we square the residuals first and them sum them. This always gives a positive value. The Least Square Regression Line minimizes this sum of residuals and the result is a line of Best Fit for the bivariate data.

Therefore, option B gives the correct answer.

Answer 2

Answer:

B) the sum of the squared residuals

Step-by-step explanation:

The sum of square of residual is used to check whether or not the regression line that is plotted is best or not.

It calculate the distance between the scatter point and the regression line.

If the square of the distance between the scatter point and the regression line is very small or equal to zero it is said to the best regression line.

Thus, Option (B) is correct.