Before you turn this problem in, make sure everything runs as expected. First, restart the kernel (in the menubar, select Kernel\(\rightarrow\)Restart) and then run all cells (in the menubar, select Cell\(\rightarrow\)Run All).

Make sure you fill in any place that says YOUR CODE HERE or “YOUR ANSWER HERE”, as well as your name and collaborators below:

NAME = ""
COLLABORATORS = ""

Nonlinear regression for drug response

The following data is given for dose/response of a new drug.

Dose	Response
0	0.1
1.3	0.5
2.8	0.9
5	2.6
10.2	7.1
16.5	12.3
21.3	15.3
31.8	20.4
52.2	24.2

A typical model for this data is

\(F(x) = d + \frac{a - d}{1 + \left(\frac{x}{c}\right)^b}\)

where

• a: Minimum asymptote. In a bioassay where you have a standard curve, this can be thought of as the response value at 0 standard concentration.

• b: Hill’s slope. The Hill’s slope refers to the steepness of the curve (can be positive or negative) at the inflection point.

• c: Inflection point. The inflection point is defined as the point on the curve where the curvature changes direction or signs. \(c\) is the dose where \(y=(d-a)/2\).

• d: Maximum asymptote. In a bioassay where you have a standard curve, this can be thought of as the response value for infinite standard concentration.

Use this data to find values for \(a, b, c, d\) and the confidence interval for each parameter. Provide an interpretation of the confidence intervals.

Use pycse.nlinfit for the fit.

Show your fit in a plot and comment on whether it looks good or not.

When you are done, download a PDF and turn it in on Canvas. Make sure to save your notebook, then run this cell and click on the download link.

%run ~/f23-06623/f23.py
%pdf