Predict y values from x values
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If x=[0 1 2 3 4 5]; and y=[0 20 60 68 77 110]; To get a linear equation I can use coefficients=polyfit(x,y,1) which gives me coefficients 20.8286 3.7619 so my linear equation is y = 20.8286 x + 3.7619 If I want to find an unknown y value from a known x value e.g. 1.5 I can use y=polyval(coefficients, 1.5) and I get y = 35.0048. In other words, using polyval, and using the equation derived from polyfit, when x = 1.5, y = 35.0048.
However, if I want to find an unknown x value from a known y value, what do I do?
Kind regards, Wendy
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Accepted Answer
Stephan
on 29 Aug 2018
Edited: Stephan
on 29 Aug 2018
Hi,
many options to do this - here you have 3 of them. All options start with your known code and want to know the x-value for y = 35.0048:
x=[0 1 2 3 4 5];
y=[0 20 60 68 77 110];
coeffs = polyfit(x,y,1);
y_val = 35.0048;
coeffs_new = coeffs;
coeffs_new(2) = coeffs_new(2) - y_val;
result1 = roots(coeffs_new);
leads to:
result1 =
1.5000
syms f(x) f(y)
f(x) = coeffs(1) * x + coeffs(2)
f(y) = finverse(f)
which gives:
f(x) =
(729*x)/35 + 79/21
f(y) =
(35*x)/729 - 395/2187
To calculate values with this you will need a function handle:
f_y = matlabFunction(f(y))
which is:
f_y =
function_handle with value:
@(x)x.*(3.5e1./7.29e2)-1.80612711476909e-1
Then you can calculate the x-value belonging to 35.0048:
>> result2 = f_y(y_val)
result2 =
1.5000
result3 = fsolve(@(x)coeffs(1)*x+coeffs(2)-y_val,0)
which results in:
Equation solved.
fsolve completed because the vector of function values is near zero
as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
<stopping criteria details>
result3 =
1.5000
Best regards
Stephan
2 Comments
Henning Eimstad
on 3 Apr 2020
How would this be if I know the x value instead, such that I want to find the corresponding y value? I have used the same method with polyfit and want to find a lot of different y values for different x values along the fitted line.
Thanks in advance!
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