fitting data into a quadratic curve
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Hello,
I have some data that can be fitted into a quadratic curve of y=ax^2 + bx + c. My data passes through the origin, and has a horizontal slope near the origin too. So my question is how do i force b and c to be zero in the qudratic equation ? while doing that i want to estimate the error too, so how do i keep track of the error if i have more than one quadratic equation.
I tried using fittype and polyval, and i am familiar with them, but that doesn't do my task.
I attached my data for better understanding.
Thanks for any help.
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Star Strider
2019-10-4
To force ‘b’ and ‘c’ to be zero:
B = volume_flow_rate1(:).^2 \ influence(:) % Estimate Regression Parameter
vfrv = linspace(min(volume_flow_rate1), max(volume_flow_rate1)); % Vector For Regression Evaluation
inflv = vfrv(:).^2 * B; % Evaluate Regression
figure();
plot(volume_flow_rate1,influence, '--r*' );
hold on
plot(vfrv, inflv, '-.k') % Plot Regression
hold off
xlabel ('Q (uL/s)');
ylabel ('P(Pa)');
legend ('Via');
text(25, 1200, sprintf('y = %.6f\\cdotx^2', B)) % Regression Equation
The regression parameter is:
B =
0.0266527362537937
To force only ‘c’ to be zero:
B = [volume_flow_rate1(:).^2, volume_flow_rate1(:)] \ influence(:); % Estimate Regression Parameters
vfrv = linspace(min(volume_flow_rate1), max(volume_flow_rate1)); % Vector For Regression Evaluation
inflv = [vfrv(:).^2, vfrv(:)] * B; % Evaluate Regression
figure();
plot(volume_flow_rate1,influence, '--r*' );
hold on
plot(vfrv, inflv, '-.k') % Plot Regression
hold off
xlabel ('Q (uL/s)');
ylabel ('P(Pa)');
legend ('Via');
text(25, 1200, sprintf('y = %.6f\\cdotx^2 %+.6f\\cdotx', B)) % Regression Equation
The regression parameter estimates are:
B =
0.0304986880886496
-0.722814145120915
10 个评论
Hadi Data
2019-10-4
Star Strider
2019-10-4
My pleasure.
It depends on what you mean by ‘error’. To calculate the residuals and their standard deviations:
rsd = influence(:) - (volume_flow_rate1(:).^2 * B); % Residuals
std_rsd = std(rsd) % Standard Deviation Of Residuals
Hadi Data
2019-10-7
Star Strider
2019-10-7
As always, my pleasure!
I do not have the Curve Fitting Toolbox, so I cannot help you with any questions related directly to it.
Calculate the residuals by finding the values of the fitted curve at every value of the independent variable, then subtract that value from the data value at the same point.
The term ‘parameter estimation’ is the general term for determining the parameters of a model related to data. That is the only description I have ever encountered. There are several ways to estimate parameters, depending on the technique or algorithm used. Most of them minimise the squared distance between the data and the estimated model at each data value, although there are other methods of comparing them.
Hadi Data
2019-10-7
Star Strider
2019-10-7
As always, my pleasure.
I do not have the Curve Fitting Toolbox, so I cannot help you with anything regarding it.
Doing the same thing with polyfit and polyval:
B = polyfit(volume_flow_rate1(:), influence(:), 2); % Estimate PArameters
infl_fit = polyval(B, volume_flow_rate1(:)); % Evaluate At Independent Variable Values
resid = influence(:) - infl_fit(:); % Calculate Residuals
You can then do statistics on the residuals.
Hadi Data
2019-10-15
Star Strider
2019-10-15
As always, my pleasure.
You will have problems with that, since:
volume_flow_rate1(1) = 0
However if you are using different data, I would calculate it as:
B = [1./x(:) ones(size(x(:)))] \ y(:) % Estimate Parameters
y_fit = [1./x(:) ones(size(x(:)))] * B % Fit To Data
This uses 
which is more efficient than 
.
which is more efficient than .
Hadi Data
2019-10-15
Star Strider
2019-10-15
As always, my pleasure!
That is actually what Answers is for!
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