1. The problem statement, all variables and given/known data Hello to everyone that's reading this. :) For this linear least-squares regression problem (typed below and also), I correctly find the value of g (which is what the problem statement wants to have found), but I was curious about the value of ##a_0## (and that's what this entire thread is about). Problem statement (Alternatively, one can view this PDF: http://docdro.id/GmeGXNr): "To measure g (the acceleration due to gravity) the following experiment is carried out. A ball is dropped from the top of a 30-m-tall building. As the object is falling down, its speed v is measured at various heights by sensors that are attached to the building. The data measured in the experiment is given in the table. x (m), v (m/s) 0, 0 5, 9.85 10, 14.32 15, 17.63 20, 19.34 25, 22.41 In terms of the coordinates shown in the figure (positive down), the speed of the ball v as a function of the distance x is given by ##v^2 = 2gx##. Using linear regression, determine the experimental value of g." 2. Relevant equations ##a_1 = (n Sxy - Sx Sy) / (n Sxx - (Sx)^2)## ##a_0 = (Sxx Sy - Sxy Sx) / (n Sxx - (Sx)^2)## 3. The attempt at a solution The solution in the PDF: "The equation v^2 = 2gx can be transformed into linear form by setting Y = v^2. The resulting equation Y = 2gx, is linear in Y and x with m = 2g and b = 0. Therefore, once m is determined, g can be calculated using g = m/s. The calculations are done by executing the following MATLAB program (script file): Code (Text): clear all; clc; x=[0 5 10 15 20 25]; y=[0 9.85 14.32 17.63 19.34 22.41]; Y=y.^2; X=x; % Equation 5-13 SX=sum(X); SY=sum(Y); SXY=sum(X.*Y); SXX=sum(X.*X); % Equation 5-14 n=length(X); a1=(n*SXY-SX*SY)/(n*SXX-SX^2) a0=(SXX*SY-SXY*SX)/(n*SXX-SX^2) m=a1 b=a0 g=m/2 When the program is executed, the following values are displayed in the Command Window: a1 = 19.7019 a0 = 1.9170 m = 19.7019 b = 1.9170 g = 9.8510 Thus, the measured value of g is 9.8510 m/s^2." Basically, what's I'd like to know is: Should the value of ##a_0## be 0 or 1.9170380952380952381? What "wins"? The ##a_0 = (Sxx Sy - Sxy Sx) / (n Sxx - (Sx)^2)## formula or the zero term in v^2 = 2gx + 0? Any input would be greatly appreciated!