Question

of motor vehicles 2. The table displays the mass M and average fuel consumption manufactured by Ford and Honda. Using the least square fit for linear regression, do the following: a) Fit a straight line p a +bMto the data b) Compute the standard deviation c) Plot the mass vs fuel consumption, and overlay the data with the linear regression function. Use matlab for plotting the data M(kg)(km/liter) Model Contour 1310 10.2 Crown Victoria 1810 8.1 Escort 1175 11.9 Expedition Explorer 2360 5.5 6.8 1960 F-150 2020 6.8 Ranger 1755 7.7 Taurus 1595 8.9 Аccord 1470 9.8 10.2 CR-V 1430 Civic 1110 13.2 Passport 1785 7.7

USE MATLAB FOR ALL ANSWERS

Answer 1

Using the least square fit for linear regression, the required straight line fit for the given data is obtained using MATLAB. The required mass vs fuel consumption graph is also plotted and the standard deviation is computed as well. All the results are attached below: (MATLAB codes are also attached)
Command Wind ow >>M-[1310 1810 1175 2360 1960 2020 1755 1595 1470 1430 1110 1785]; >>phi = [10.2 8.1 11.9 5.5 6.8 6.8 7.7 8.9 9.8 10.2 13.2 7.7]; >> linear fit (phi,M) Required straight line fit is: phi = (18.6191) + (-0 . 00589633) M Required standard deviation of the fit is: 0.510897 Mass Fuel_consumption_from_regression_line 1310 10.895 7.9468 1810 1175 11.691 2360 4.7038 1960 7.0623 2020 6.7085 1755 8.2711 1595 9.2145 1470 9.9515 10.187 1430 12.074 1110 1785 8.0942

Mass vs Fuel consumption Regression line Data using regression line Actual data 13 12 11 7 6 5 4 2000 2500 1000 1500 Mass(kg) Fuel consumption(km/litre) 14

MATLAB code:

function linear_fit(phi,M)

M1=sum(M);
M2=sum(M.^2);
phi1=sum(phi);
phi1M1=sum(phi.*M);
n=numel(M);
A=[n M1;M1 M2];
b=[phi1;phi1M1];
ab=A\b;
fprintf('\nRequired straight line fit is: phi=(%g)+(%g) M\n\n',ab(1),ab(2));
  
f=@(ab,M) ab(1)+ab(2)*M;
x=min(M)-100:1:max(M)+100;
y=f(ab,x);
y1=f(ab,M);
y2=(y1-phi).^2;
SD=sqrt(sum(y2)/n);
fprintf('\nRequired standard deviation of the fit is: %g\n\n',SD);
plot(x,y,M,y1,'o',M,phi,'*');
xlabel('Mass(kg)')
ylabel('Fuel consumption(km/litre)')
legend('Regression line','Data using regression line','Actual data')
title('Mass vs Fuel consumption')
AA=[M' y1'];
VarNames = {'Mass','Fuel_consumption_from_regression_line'};
TT=table(AA(:,1),AA(:,2), 'VariableNames',VarNames);
disp(TT);
end