Linear-log regression model (curve fitting)

Dear all

I reask this question with more details

I have this data

x= [50;81;73;77;127;140;122;125;140;145;180;185;178;96;83;192;182;120;127];

y= [122;126;121;123;135;130;117;119;125;125;135;135;140;140;147;147;144;141;139];

y(x) = α + β10 log10(x) + ξ, : ξ ~ N(0, σ^2), random variable that accounts for shadowing variation modeled with normal distribution and standard deviation (Specifically, is a random variable that accounts for shadowing variation modeled with normal distribution and standard deviation σ, assumed equal to the standard deviation of the regression residuals).

How can I use curve fitting to find the values of α, β and ξ,

Expected Output fitting plot

Answer 1

[Ameer Hamza]

Try this

x = [50;81;73;77;127;140;122;125;140;145;180;185;178;96;83;192;182;120;127];
y = [122;126;121;123;135;130;117;119;125;125;135;135;140;140;147;147;144;141;139];

[x, idx] = sort(x);
y = y(idx);

log_x = 10*log10(x);

X = [ones(size(x)) log_x];
param = X\y;
y_est = X*param;
y_err = y - y_est;
sigma = std(y_err);

plot(x, y, 'r+', x, y_est, 'b-')

[Ahmad Hani]

Thanks Ameer Hamza,

[Ameer Hamza]

I am glad to be of help!