Question

i Problem 10: Interpolation, least squares, and finite difference Consider the following data table: 0 2 0.2 2.018 0.4 2.104 0.6 [2.306 If the Sum of the Squares of the errors for the linear least-squares fit for the above problem is computed as SSE = 8.679 x 10-3 and the sum of the squares of the deviation from their mean is computed as SS, = 0.059, then the R2 value for the linear least fit and the standard error Sxy are 3 R2-0.90 and Sxy-0.05 R2-0.85 and Sxy-0.05 R2-3.55 and Sxy-1.72 R? - 1.85 and Sxy0.06 None of the above

Answer 1

The problem was solved in Octave/Matlab.

The answer is none of the above.

clear;
clc;

x = [0 0.2 0.4 0.6];
y = [2 2.018 2.104 2.306];
n = numel(y);

yBar = mean(y);
SSE = 8.579e-3;
SS0 = 0.059;
SST = sum((y - yBar).^2);

R2 = 1 - SSE/SST;

Sxy = (sqrt(SS0/(n-1)))/sqrt(n);

fprintf(sprintf('R^2 = %.2f and S_{xy} = %.2f\n',round(R2,2),round(Sxy,2)))

Output

= 0.07 R^2 = 0.85 and s_{xy} >> |