Question

The power regression function on the calculator returns these values:

y = axb

a = 72.53

b = 0.49

Which is the power regression function expressed as a square root function?

Answer 1

The given model is y = 72.53 x^{0.49}. Writing that exactly in terms of a square root (x^{1/2}) gives

y = 72.53 (sqrt(x))^{0.98},

because x^{0.49} = (x^{1/2})^{0.98}.

If you want the simpler square-root form y = K sqrt(x), note 0.49 ≈ 0.5, so as an approximation you can use

y ≈ 72.53 sqrt(x),

but that is only an approximation (the exponent was 0.49, not exactly 0.5).