I Need Help Obtaining The Values C1,c2.c3 From A Least Squares Fit Of ...

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I need help obtaining the values c1,c2.c3 from a least squares fit of the data. Follow 7 views (last 30 days) Show older comments Lovie Reid on 29 Jul 2020

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Edited: James Tursa on 30 Jul 2020 I need help obtaining the values c1,c2.c3 from a least squares fit of the data.

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James Tursa on 29 Jul 2020 ×

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What have you done so far? What specific problems are you having with your code? Lovie Reid on 29 Jul 2020 ×

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Ive plug inK = [76.5 80.4 83.3 85.7 88.1 90.2 92.0 93.6 95.1 96.5 98.9];MPa = [0.08 0.12 0.16 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.60];y=log(MPa/3.77);beyond this im confused as how to properly write out z

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James Tursa on 29 Jul 2020

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Edited: James Tursa on 29 Jul 2020 Open in MATLAB Online It appears to me that your equation is linear in c1, c2, c3. Just make a matrix equation out of this and then apply your least squares technique to the matrix. That is, you know everything in that equation except the c1, c2, c3. So just calculate all the values for each set of data and that will give you a matrix equation of the form:b = A*cwhere each elemet of b is calculated from your data (the ln(Psat/Pc) values) each row of A is calculated from your data corresponding to the element of b (the x, x^2, ln(Tsat/Tc) values) c is simply the unknown column vector [c1;c2;c3]Then use your least squares technique to solve for c.

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Lovie Reid on 29 Jul 2020 ×

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okay so far I've plugged in K = [76.5 80.4 83.3 85.7 88.1 90.2 92.0 93.6 95.1 96.5 98.9 101 103 106.3 109.2 111.8 114.2 116.4 118.4 122.9 127.0];MPa = [0.08 0.12 0.16 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.50 3.00];y = log(MPa./3.77);x = (1./132.5 - 1./K);z = [x x.^2 log(K./132.5) ones(size(x))];Am I on the right track with this? James Tursa on 29 Jul 2020 ×

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Edited: James Tursa on 30 Jul 2020 Open in MATLAB Online Make K and MPa column vectors instead of row vectors.And good programming practice is to avoid "magic" numbers in your code like the 3.77 and the 132.5 values. Instead, use named variables with comments. E.g.,Pc = 3.77; % Critical Pressure (MPa)Tc = 132.5; % Critical Temperature (K)Then use Pc and Tc downstream in your code. It seems a simple thing, but it really helps with the readability and maintainability of your code. And put comments with description and units on every line that has values.What is the ones(size(x)) for? James Tursa on 30 Jul 2020 ×

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Lovie Reid Answer moved here:I've removed the ones(size(x)) I was just using other examples to help, but would this be right for the least squaresa = polyfit(x,y,2); James Tursa on 30 Jul 2020 ×

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Edited: James Tursa on 30 Jul 2020 Open in MATLAB Online polyfit(x,y,2) would be used if you had a set of x,y coordinates and you wanted to fit that with a 2nd degree polynomial. But you don't have that situation. You have a linear matrix equation with three variables that you are trying to fit. It is linear in the c1,c2,c3 terms. Using your variable names, you have this matrix equation (assuming you make y and x column vectors as I suggested):y = z * cYou have three unknowns, the c = [c1;c2;c3], and 21 equations. An overdetermined linear system of equations where you know y and z. You are being asked to produce the least squares solution for c.

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