Error on slope using LSQ method

[Matt21]

Homework Statement

Three points are given with errors on y coordinates.
(2.00,4.70±0.36); (4.00,6.8&±0.45); (5.00, 9.10±0.50)
Using LSQ method, find the error on slope.

Homework Equations

σm = σy√(n/Δ), where σy = √(1/n-2(Σ(yk - y(xk))^2)) and Δ = nΣxk^2 - (Σxk)^2

The Attempt at a Solution

I do not know if this is the correct equation or if I made an error in my calculations but what I got was:
σy = 1/3-2((4.7-4.7(2))^2+(6.8-6.8(4))^2+(9.1-9.1(5))^2) = 42 and
Δ = (2^2+4^2+5^2)-(2+4+5)^2 = -76
n = 3
Obviously I can't use Δ since you can't get a root of a negative number. Can anyone see what I'm doing wrong? Any help would be much appreciated.

 

[haruspex]

1/n-2(Σ(yk - y(xk))^2))

That's a very strange looking expression. Are you sure about the minus sign after 1/n?

 

[Matt21]

Yes I'm positive. The formula given in my notes was √((1/n-2)(Σ(yk - y(xk))^2)

 

[haruspex]

Yes I'm positive. The formula given in my notes was √((1/n-2)(Σ(yk - y(xk))^2)

Ah, you mean √(1/(n-2)(Σ(yk - y(xk))^2)), i.e. $\sqrt{\frac 1{n-2}\Sigma( y_k-y(x_k))^2}$? That would make more sense. Originally you had √((1/n)-2Σ(yk - y(xk))^2)), i.e. $\sqrt{\frac 1n-2\Sigma(y_k-y(x_k))^2}$.
By the way, please clarify what you mean by y(x_k).

 

[Matt21]

Yes that was the equation was trying to convey. In regards to y(xk) I would assume that means y*(xk) where xk = x1, x2, x3...xk

 

[ifly22hi]

Δ = (3*(2^2+4^2+5^2))-(2+4+5)^2 = 14