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what is the difference between regression lines and regression equations?
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Regression lines are drawn on the basis of regression equations. That's the difference.
are regerssion lines are free lines drawn with hand.
No, they are based on regression equations. Basically, in a scatter diagram, we, statisticians, generally select a line that would not only represent the collection of (x, y) values but also when extrapolated would give almost accurate answers. By the method of least square, we find the regression equations, with a definite slope and definite intercept. Then we draw the regression lines.
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