Calculate Sum of Square Error

% 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 ?

[Image Analyst]

Please attach your spreadsheet so we can run your code.

[Muhammad]

done ... now u run it

[Azzi Abdelmalek]

There is no y_bar in your code

[Muhammad]

i know ! my question is this how to i calculate y_bar ?

Answer 1

[Wayne King]

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.

[Muhammad]

now i understand and feeling Stupid ! Thank u for u help :)

[Carolyn]

y_bar is basically yhat, right?

Answer 2

[Wayne King]

The sum of square error in regression is the 2-norm squared of the residuals, so if yhat are your fitted values, and y are the original observations, then

 r = y-yhat;
 SSE = norm(r,2)^2;

[Muhammad]

how to i calculate yhat ?

[Wayne King]

yhat are your fitted values. You have a regression equation, it's your eq_y the values of that equation are your predicted values

[Muhammad]

i knw bro ! but how to i get these fitted values from eq_y ?