How to know which plot is more linear then the other?

Dear all,

I have two datasets arrays:

A = [0
0.423891532
0.819380304
1.289479809
1.739548357
2.288748183
2.8990623
3.618974647
4.402757506
5.268816221
6.240886445
7.278958674
8.321358342
9.369407383
10.37825178
11.17417756
12.02774088
12.69808163
13.49653247
14.36958724
15.50198578
16.68295148
20.09421834]
%%
B = [0
0.406558949
0.771247013
1.123943155
1.487752056
1.915016538
2.365427777
2.852526752
3.419995212
3.933726314
4.436914792
4.958793052
5.510476759
5.961517074
6.415268974
6.843890692
7.102927349
7.118216122
7.677116245
8.751585797
9.636923065
10.32502819
12.9488068]
%%
plot(A, 'green')
hold on
plot(B, 'blue')
hold off
%%

Both A and B are nonlinear curves, but B seems to be more linear (less curvature) than A.

How can I show such information numerically?

Any sugguestion will be appreciated.

Best,

Meshoo

Answer 1

[Ameer Hamza]

You can see the residual error with linear fit to see which dataset is more linear

[~, eA] = polyfit(1:numel(A), A, 1)
[~, eB] = polyfit(1:numel(B), B, 1)

Result

>> eA.normr
ans =
    4.0713
>> eB.normr
ans =
    2.8868

Vector 'B' is more linear as compared to A.

[Mustafa Sami]

Thank you very much Ameer.

Is there any range (maximum and minimum) for eA.normr?

[Meshooo]

Thank you Ameer.

Answer 2

[KSSV]

How about finding the area bounded by the curves..which ever has least area is straight.

A = [0
0.423891532
0.819380304
1.289479809
1.739548357
2.288748183
2.8990623
3.618974647
4.402757506
5.268816221
6.240886445
7.278958674
8.321358342
9.369407383
10.37825178
11.17417756
12.02774088
12.69808163
13.49653247
14.36958724
15.50198578
16.68295148
20.09421834]
%%
B = [0
0.406558949
0.771247013
1.123943155
1.487752056
1.915016538
2.365427777
2.852526752
3.419995212
3.933726314
4.436914792
4.958793052
5.510476759
5.961517074
6.415268974
6.843890692
7.102927349
7.118216122
7.677116245
8.751585797
9.636923065
10.32502819
12.9488068]
%%
plot(1:length(A),A, 'g')
hold on
plot(1:length(B),B, 'b')

%%
x = [1:length(A)]' ;

L1 = [[x ; x(1)] [A ;A(1)]] ;
L2 = [[x ;x(1)] [B;B(1)]] ; 

patch(L1(:,1),L1(:,2),'r')
hold on
patch(L2(:,1),L2(:,2),'b')

A1 = polyarea(L1(:,1),L1(:,2)) ; 
A2 = polyarea(L2(:,1),L2(:,2)) ;