calculate empirical distribution function and interpolation

I have a data of

column 1 = temperature at 55F, 57F, 60F,...

column 2 = sales of sunglasses at these temperatures

I want to calculate the empirical distribution of sales of sunglasses over time and then use this empirical distribution to estimate the sales of sunglasses when the temperature is 56.6F, etc.

I tried to use polyfit but told that polynomial is badly conditioned.

Answer 1

[Jeff Miller]

You want to use the regress function, something like this:

X = [ones(size(temp) temp)];  % temp is a column vector of temperatures
b = regress(sales,X);  % sales is a column vector of sales
SalesAt56pt6 = b(1) + b(2)*56.6;

empirical distribution functions and polyfit are both used in different types of situations than you are describing.

hth

[alpedhuez]

I wanted to improve over a linear regression.

[Jeff Miller]

You can add some nonlinear terms like this:

X = [ones(size(temp)) temp temp.^2 temp.^3];  % temp is a column vector of temperatures
b = regress(sales,X);  % sales is a column vector of sales
SalesAt56pt6 = b(1) + b(2)*56.6 + b(3)*56.6^2 + b(4)*56.6^3;

This technique will fit a polynomial of any order you want

[alpedhuez]

Thank you. How does it differ from polyfit?