MATLAB: Calculate Sum of Square Error

linear regression

% Extract Data from Excel sheet to  Metrix
Metrix = xlsread('D:\data.xlsx');
% X represent annual franchise fee and Y represent start up cost ($1000) for a pizza franchise
X = Metrix(:,1);
Y = Metrix(:,2);
%  as we know regression line eq is ---> y = wx+b where w is slope and b is y-intercept
SUMxy = sum(X.*Y);
SUMx = sum(X);
SUMy = sum(Y);
n = length(X);
SUMx2 = sum(X.*X);
SUMxthen2 = SUMx*SUMx;
slope_W = (((n)*(SUMxy)) - (SUMx*SUMy))/((n*SUMx2)-(SUMxthen2));
YIntercept_B = (SUMy/n)-(slope_W*(SUMx/n));
x=linspace(0,2000);
eq_y = slope_W*x+YIntercept_B;
scatter(X,Y,'*');
hold on;
plot(x,eq_y);
hold off;
as we know SSE = (y-y_bar)^2 .. but i have not a y_bar values how to i extract y_bar values in Matrix ?

Best Answer

You get the yhat values by plugging your observed X-values into the equation determined by your regression fit. You have an equation that comes from estimating the slope and the intercept.
yhat = slope*x+intercept
You have a vector of X-values, the values you used in determining the model fit in the first place. So you just plug that vector in your fitted equation and you will get a vector of yhat values equal in length to your observations, then just use the code I gave you above.
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