How to find the intersection of linear regression model and yline

Say I have a table with the following values:

T(:,1) = [0 1 2 3 4 5]

T(:,2) = [0 1 2 3 4 5]

I want to be able to predict values so I fit a simple linear regression model to it. I also want to extract the X value for when the lin reg model intersects a value Y = 4.3. Is there a way to find the coordinates of this intersection?

Answer 1

[Star Strider]

Use the interp1 function for this —

T(:,1) = [0 1 2 3 4 5].';
T(:,2) = [0 1 2 3 4 5].';
x = T(:,1);
y = T(:,2);
p = polyfit(x, y, 1)

p = 1x2

1.0000 0.0000

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f = polyval(p, x);

ylv = 4.3;

xv = interp1(f, x, ylv)

xv = 4.3000

figure
plot(x, y, '.', 'DisplayName','Data')
hold on
plot(x, f, '-r', 'DisplayName','Regression')
plot(xv, ylv, 'ms', 'DisplayName','Intersection Of ‘yline’')
hold off
yline(ylv, '--k', 'DisplayName','yline')
xlabel('x')
ylabel('y')
legend('Location','best')

.

Answer 2

[John D'Errico]

Pretty boring data.

T(:,1) = [0 1 2 3 4 5];
T(:,2) = [0 1 2 3 4 5];

P = polyfit(T(:,1),T(:,2),1)

P = 1x2

1.0000 0.0000

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a = P(1)

a = 1.0000

b = P(2)

b = 3.1322e-16

They are the coefficients of the linear polynomial model. The model is of the form:

Y = a*X + b

So if you want to solve for x, given y, just use algebra.

Y0 = 4.3

Y0 = 4.3000

X0 = (Y0 - b)/a

X0 = 4.3000

Since your data was so simple, the line is just the 45 degree line, with X == Y here.