Question

Given 16 pairs of prices (as dependent variable) and corresponding demands (as independent variable), use the curve fitting tool to estimate the best fitting linear, exponential, logarithmic, and power curves.

Price Demand

127 3420

134 3400

136 3250

139 3410

140 3190

141 3250

148 2860

149 2830

151 3160

154 2820

155 2780

157 2900

159 2810

167 2580

168 2520

171 2430

Answer 1

I have implemented the code in MATLAB, and provided the code and the screenshot with output.

Code:

clc
x = [127, 134, 136, 139, 140, 141,...
148, 149, 151, 154, 155, 157, 159, 167, 168, 171]';
y = [3420, 3400, 3250, 3410, 3190, 3250, 2860,...
2830, 3160, 2820, 2780, 2900, 2810, 2580, 2520, 2430]';

figure()
p = polyfit(x,y,1)
f0 = polyval(p,x);
plot(x,y,'o',x,f0,'-')
title('linear')

figure()
f1 = fit(x,y,'exp1')
plot(f1,x,y);
title('Exponential')

figure()
f2 = fit(x,y,'power1')
plot(f2,x,y);
title('Power')

figure()
myfit = fittype('a + b*log(x)','dependent',...
{'y'},'independent',{'x'},'coefficients',{'a','b'});
f3 = fit(x,y,myfit)
plot(f3,x,y);
title('Logarithmic')

Screenshot: