I've done nearly everything but at the end when I need to $\alpha$ it doesn't work and I'm not sure what's wrong. This is the function:
$y = \alpha\beta^x$
I transformed it into a linear equation and I get this:
$ln(y) = ln(\alpha)+xln(\beta)$
After all that stuff, I changed my data points, which are these:
\begin{array}{c|c|c|} X &-4 &-2 &3 &5 &7\\ \hline Y &ln(50)&ln(30)&ln(10)&ln(6)&ln(2) \end{array}
After doing a bunch of calculations this is what I got for everything:
$\sum x = 9$
$\sum y = 12.1$
$\sum xy = -1.732$
$\sum x^2 = 103$
$\sum y^2 = 35.865$
So I do all that and find that
$\beta = e^{-0.2709} = 0.7627$
Then I try to use this formula
$\alpha = \hat{y} -\beta\hat{x} $
But I get the wrong answer, can anyone help me out, I've no clue as to why I can't get $\alpha$. It is supposed to be $18.3154$. Any help is appreciated.