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A set of bivariate data was used to create a least squares regression line. Which of the following is minimized by the line
A) the sum of the residuals
B) the sum of the squared residuals
C) the sum of the absolute value of the residuals
D) the influence of outliers
E) the slope

Respuesta :

SaniShahbaz

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.

The only correct option that is minimized by the least squares regression line is;

Option B; the sum of the squared residuals.

We want to find the correct option that minimizes the line. Let's look at the options ;

Option A; This statement is not correct because If you do a summation of the residuals, you would get a value of 0.

Option B; Since error needs to be minimized so that the line is a close to the points as possible and as seen above that the sum of the residuals is zero. Then before we sum them, we need to first of all square the residuals which will always give a positive value. Thus, since the Least Square Regression Line minimizes the sum of residuals, then this option is correct.

Option C; This option is wrong because the sum of the absolute values of the residuals is not a method for in creation of least squares regression line

Option D; This option is wrong because the influence of outliers has nothing to do with the topic in question.

Option E; This option is wrong too because slope has nothing to do with the topic in question.

Read more at; https://brainly.com/question/13464184

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