2. Linear Regression

a) Find the best straight line for the following data:

x	f(x)
-10.000	122.7106
-8.0000	96.9288
-6.0000	80.9006
-4.0000	62.2326
-2.0000	35.1397
0.0000	19.6305
2.0000	5.9876
4.0000	-17.7030
6.0000	-20.4644
8.0000	-54.1783
10.0000	-71.2149

slope =

-9.3962

y-intercept =

23.6336

b) Find the sum of squares error (ss) and the sum of squares error per data point (ssdp).

ss =

274.5485

ssdp =

24.9590

c) Produce a plot showing the raw data and the fitted line.

%Program to Solve Problem 2 for Linear Curve Fitting Homework

%version 2007-10-10 D.W. Donovan

clear all;

x=[-10.0000; -8.0000; -6.0000; -4.0000; -2.0000; 0.00;

2.0000; 4.0000; 6.0000; 8.0000; 10.0000];

fx=[122.7106; 96.9288; 80.9006; 62.2326; 35.1397; 19.6305;

5.9876; -17.7030; -20.4644; -54.1783; -71.2149];

A(:,2)=x;

A(:,1)=ones(size(x));

c=A\fx;

m=c(2);

b=c(1);

ffx=m*x+b;

ss=(fx-ffx)'*(fx-ffx);

ssdp=ss/size(fx,1);

xc=[min(x):(max(x)-min(x))/100:max(x)]';

fxc=m*xc+b;

lm=['slope = ',num2str(m)];

lb=['y-intercept = ',num2str(b)];

lss=['sum of squares error = ',num2str(ss)];

lssdp=['sum of squares per data point = ',num2str(ssdp)];

figure

hold on;

name='D. W. Donovan - ';

t1='Linear Curve Fitting Homework Problem #2';

t2='Data Fitted to F(x) = mx + b';

t=[t1,'\newline',t2,'\newline',name,date];

title(t)

xlabel('x in unitless numbers')

ylabel('f(x) in unitless numbers')

plot(x,fx,'r*')

plot(xc,fxc,'b')

plot(min(xc),max(fxc),'w')

plot(min(xc),max(fxc),'w')

plot(min(xc),max(fxc),'w')

plot(min(xc),max(fxc),'w')

legend('raw data','fitted curve',lm,lb,lss,lssdp,3);

legend('boxoff')

%{

m = -9.3962

b = 23.6336

ss = 274.5485

ssdp = 24.9590

%}

Back To Dr. Donovan's Courses Page

Back To Dr. Donovan's Homepage

Physics Dept. Homepage

NMU Homepage

Please send any comments or questions about this page to ddonovan@nmu.edu

This page last updated on October 9, 2015