The professor passed us a homework. The text below has my attempt at solving it.

Question

The professor passed us a homework. The text below has my attempt at solving it. I'm unsure if my answer is correct. Could you please help me verify it?

1. Consider the simple linear regression model yi=0+AX,+u. Given the n observations (Xi,Wh ! = 1,2, , n}, we estimate A as a. Give a geometric interpretation of . B1 takes the slope between every pair of consecutive points, then average them. That is the slope of the line between points {y1,x1) and {y2,X2} is calculated as: Slope 1 = (x2-31) , then this process is repeated for points {y2, X2} and {y3, X3} and so son, until the line between points {yn-1,Xn-13 and fyn, Xn) . The value of every slope is (X2-x1) summed, and then averaged by the multiplier^^ which divides the sum of slopes by the number of line segments. This is equivalent of connecting all consecutive points with a line segment then making a predictive slope that is the average combination of all line segments' slopes n-1

Explanation / Answer

Yes the explanation is indeed correct.

The beta denotes the slope of the regression line which is nothing but the average of the pairwise slope of consecutive points.

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