How is the best-fitting line between the points in a scatterplot defined? A. the

Question

How is the best-fitting line between the points in a scatterplot defined?

A. the line that gives the largest sum of the vertical distances between each point and the line

B. The line that gives the smallest sum of the squared verticle distances between each point and the line

C. The line that gives the smallest sum of the vertical distances between each point and the line.

D. The line that has a sum of the squared vertical distances between each point and the line of 0

The line that gives the largest sum of the squared verticle distances between each point and the line

Explanation / Answer

B is a correct answer

the least squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.

A quantity related to the regression output is "r2".   When r2 is close to 0 the regression line is NOT a good model for the data.  When r2 is close to 1, the line would fit the data well. r2 has a technical name, the coefficient of determination, and represents the fraction of the variation in the values of y that is explained by least squares regression of y on x.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.