Use a least squares approximation to find the best linear fit (i. e., the best line) ()=+,L(t)=C+Dt, which is closest, in the sense of least squares, to passing through the through the following data points:

(t1, b1) = (-2, 12)
(t2, b2) = (0,9).
(t3, b3) = (2, 0)
(t4, b4) = (4, -5)

What are the y-intercept and the slope D of this line?

The y-intercept is C=7 and the slope is D=-3

Step-by-step explanation:

Let   be the best linear fit.

This is the best straight line that passes through

The resulting linear system is  

The corresponding matrices form , has  and

The components of the normal equations are:

and

We now obtain, the normal equations:

We use row operation to obtain

This implies C=7, and D=-3

Therefore the best fit line is

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step-by-step explanation: