What's the optimal parameter for vector B given x and y

Question

I need to brush up my Maths, for sure, but, meanwhile I hope you could help me with this.

This is a Linear Regression problem.

Question: given X and Y compute the optimale B (from what I understand, B is the constant and the slope )

I've this 2 variables x and y : X=(-0.78, -1.51, 0.74, -0.62) Y=(-34.5, -30.79, 19.31, -19.44)

The result choices are : 52, 13, 26, 32

I've check the formula y=mx+b, and of course f(x)=b0+b1x1+b2x2+...+bnxn but I'm a little bit lost.

So, if you could help me with this, that would be great.

Thank you

Answer 1

The optional parameter $t$ is obtained by minimizing

$$(t\vec{X} - \vec{Y})^2$$

which is also a linear regression problem. The optimal solution is

$$t=\frac {\vec{X}\cdot\vec{Y}}{X^2}=\frac{99.9}{3.82}=26.1$$