Which of following is true or the most appropriate about a scatterplot with regression line or ordinary least square (OLS) regression?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Which of following is true or the most appropriate about a scatterplot with regression line or ordinary least square (OLS) regression?

 

Question 18 options:

 

No matter how you decide to draw your straight line, in general, all will will fall directly on the line.   

 

Any data point that does not fall directly on the line will have a certain amount of distance between the point and the line.

 

If you were to calculate the distance between the data point and the line you have drawn, and then sum the distance, you would have a regression coefficient for the data points

 

OLS is based on an idea that we have seen before: the sum of deviation.

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