Question

The method of least squares dictates that we choose a regression line where the sum of the square of deviations of the points from the line is:
A) Maximum
B) Minimum
C) Zero
D) Positive

Answer 1

Hint: We have to choose the correct option for the given definition from the particular given options. For that we have to know about the given concept in the question. It will help us to choose the correct option. After analyzing the concept with all options we will get the final required answer.

Complete step-by-step solution:
The least squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plottes curve. Least squares regression is used to predict the behaviour of dependent variables.
The method of least squared dictates that we choose a regression line where the sum of the square of deviation of the points from the line is minimum.
A process by which we estimate the value of a dependent variable on the basis of one or more independent variables is regression.
More specifically, regression analysis helps one understand how the typical value of the dependent variable (or criterion variable) changes when any one of the independent variables is varied, while the other independent variables are held fixed.
$\therefore $ The method of least squares dictates that we choose a regression line where the sum of the square of deviations of the points from the line is: Minimum.

Option B is the correct answer.

Note: The least square method provides the overall rationale for the placement of the line of best fit among the data points being studied. The most common application of this method, which is sometimes referred to as “linear” or “ordinary”, aims to create a straight line that minimizes the sum of the squares of the errors that are generated by the results of the associated equations, such as the squared residuals resulting from differences in the observed value, and the value anticipated, based on the model.