Chapter 11.2, Problem 31Q

The following table shows a portion of the results from a clinical trial investigating the effectiveness of a monoamine oxidase inhibitor as a treatment for depression $\left(219\right)$. The relationship between $y$, the percentage of subjects showing improvement, and $x$, the patient’s age, appears to be S-shaped. Graph the data and superimpose a graph of the least squares curve $y=\frac{L}{1+e^{a+bx}}$. Take $L$ to be 60.

Age Group	Age Mid-Point, $x$	% Improved, $y$	$\ln \left(\frac{60-y}{y}\right)$
$\left[28,32\right)$	30	11	1.49393
$\left[32,36\right)$	34	14	1.18958
$\left[36,40\right)$	38	19	0.76913
$\left[40,44\right)$	42	32	–0.13353
$\left[44,48\right)$	46	42	–0.84730
$\left[48,52\right)$	50	48	–1.38629
$\left[52,56\right)$	54	50	–1.60944
$\left[56,60\right)$	58	52	–1.87180