generate random sample for linear regression

Hi guys

can anyone help me how to generate random sample for y, x1 and x2 in the following model (multiple linear regression):

yi= a + bx1 + cx2 + e

where a, b and c are parameters and e is random error.

Answer 1

[Jeff Miller]

% First you have to define the characteristics of x1, x2, and e.
% These can be any values you want, such as:

mu1 = 0;   % Mean of x1
sd1 = 1;   % Standard deviation of x1
mu2 = 100;
sd2 = 10;

rhoxy = 0.3;  % the true correlation of x1 and x2

mue = 0;   % Mean of e, usually assumed to be zero
sde = 5;   % Standard deviation of e

a = 4;  % Known parameters of your regression model
b = 3;
c = 2;

nPoints = 100;  % the number of data rows you want to generate

% The rest just uses those values:

mu = [mu1, mu2];
sigma = [sd1^2 sd1*sd2*rhoxy; sd1*sd2*rhoxy sd2^2];
x = mvnrnd(mu,sigma,nPoints);

e = mue + sde*randn(nPoints,1);

y = a + b*x(:,1) + c*x(:,2) + e;

[Abas Arkawazi]

Thank u very much

Answer 2

[Abhishek Gangwar]

You can generate random values for x1, x2 using "randperm()" function and then find out corresponding 'y' values,

x1 = randperm(100);

x2 = randperm(100);

and put these values into your equation to find out corresponding 'y' values.

Note: 'randperm()' function gives you the random permutation of number from 1....n.

other functions, for example 'rand()', 'randn()' generates decimal numbers.

[Abas Arkawazi]

Thank u very much