Question

The following data give the stopping distance d as a function of initial speed υ, for a certain car model. Find a quadratic polynomial that fits the data. Determine the quality of the curve t by computing J, S, and r².

Answer 1

 

Determine the quality of the curve fit by computing J, S, and r².

The following data gives the stopping distance d as a function of initial speed v

 

 

 

 

To plot the above data set and to curve fit in MATLAB type the below code in script:

%enter the values of v

v = 20:10:70;

%enter the values of d

d = [45,80,130,185,250,330];

%give step increment for v

vf = 20:0.1:70;

%use ployfit command

p = polyfit(v,d,2);

df = polyval(p,vf);

J = sum((polyval(polyfit(v,d,2),v)-d).^2);

%use plot command

plot(vf,df,v,d,'*')

%give axis start values

axis([20 70 0 350])

%give y axis label

ylabel('d(ft)')

%give x axis label

xlabel('v(mi/hr)')

m = mean(d);

S = sum((d-m).^2);

r2 = 1-J/S;

J

S

r²

 

Now, RUN the code,

The plot display as follows:

 

 

And in command window results will prompt

 

 

 

 

The results are J = 10.1786 for the first through fourth-order polynomials. In addition, S = 57550 and r² = 0.9998.

 

 

The results are J = 10.1786 for the first through fourth-order polynomials. In addition, S = 57550 and r² = 0.9998.