Question

Data for the mean mass of various animal species and their corresponding metabolic rate is provided below. It is believed that the data follows the power model. i.e. ?????????? = ? (????)? where α and β are the regression coefficients.

Animal	Mass (kg)	Metabolism (watts)
Cow	400	270
Human	70	82
Sheep	45	50
Hen	2	4.8
Rat	0.3	1.45
Dove	0.16	0.97

Show by hand with pen and paper the linearisation of this nonlinear model.

Answer 1

answer:

matlab code:

 x = [400 70 45 2 .3 .16]; % x data for mass
y = [270 82 50 4.8 1.55 0.95]; % given y data for metabolism
p = polyfit(x,y,2); % fitting the data using polyfit function
Y = polyval(p,x); % metabolism evaluated using
Rsqu = 1-(sum((y-Y).^2)/sum((y-mean(y)).^2)); % Computing the r^2
fprintf('metabolism = %f mass^2+ %f mass + %f\n',p); % Printing the nonlinear equation
fprintf('r^2 = %f\n',Rsqu); % Printing r^2
% Part B
plot(x,y,'rd',0:500,polyval(p,0:500),'b'); % Plotting the data and interpolate function
Mass_Tiger = 200; % Tiger mass
Meta_Tiger = polyval(p,Mass_Tiger); % evaluating tiger metabolism
hold on;
plot(Mass_Tiger,Meta_Tiger,'dk'); % plotting the tiger details in graph
Title = sprintf('metabolism = %f mass^2+ %f mass + %f',p); % using sprintf
title(Title); % Adding title
xlabel('Mass');ylabel('Metabolism'); % adding axes labels
metabolism = -0.001371 mass^2+ 1.220664 mass + 1.078511
r^2 = 0.999686

matlab output: