# Predict y values from x values

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Wendy Cameron on 29 Aug 2018
Commented: Henning Eimstad on 3 Apr 2020
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

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;
#1 - Using the elementary Matlab function roots
coeffs_new = coeffs;
coeffs_new(2) = coeffs_new(2) - y_val;
result1 = roots(coeffs_new);
result1 =
1.5000
#2 - If you have Symbolic Math Toolbox you can use the finverse function:
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
*#3 - Use fsolve* (from Optimization Toolbox) to solve the problem:
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 CommentsShowHide 1 older comment
Henning Eimstad on 3 Apr 2020
For ur first example (#1 - Using the elementary Matlab function roots),
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.

Stephen23 on 29 Aug 2018
Edited: Stephen23 on 29 Aug 2018
"Predict y values from x values"
If you want a better fit to the actual data than fitting a curve, then just use interp1:
>> x = [0,1,2,3,4,5];
>> y = [0,20,60,68,77,110];
>> ynew = 35;
>> xnew = interp1(y,x,ynew)
xnew = 1.3750
You can see how this value actually fits into your data:
>> plot(x,y,'-',xnew,ynew,'*') Wendy Cameron on 30 Aug 2018
Thanks Stephen, this makes sense and will be useful in future but in this instance I accepted the previous answer which utilized the regression line derived from polyfit. Thanks again for your input.