What the two columns represnt when i generate a multivarite normal random numbers

I run the following command to genrate two variables joint normally distributed with mean Mu and covariance matrix Sigma, which are defined below

MU=zeros(2,1)

sigma=[1 0.7;0.7 1]

M=mvnrnd(MU,sigma,N)

Then it genartes N,2 vector. But I want to know what the two columns represent.

Thank you!

Answer 1

[Jeff Miller]

The two columns represent the two variables measured for each case, and the N rows represent the N randomly selected cases from this bivariate normal distribution. For example, the cases/rows might be analogous to people, and the variables/columns analogous to their heights and weights.

[Fissha Marye]

Thank you Jeff, but to be more precise I want to generate two vectors x and y, which are jointly normally distributed with mean MU=zeros(2,1) sigma=[1 2;2 1], Can I take the two clumns that I get by using the command M=mvnrnd(MU,sigma,N) as x and y respectively. i.e, Taking the first column as x and the second column as y in M based on their order.

And then i used the following code to extract x and y as a separte variable from M, so that i can use them in a regression.

X= M(:,1)

Y= M(:,2)

Is it correct?

Thanks!

[Jeff Miller]

Yes, that's correct. You might have a look at the scattergram to make sure that the variables look like what you expect:

plot(X,Y,'*');
xlabel('X');
ylabel('Y');

[Fissha Marye]

Many thanks Jeff,

Could you explain about error: horizontal dimensions mismatch (1000x1 vs 499x1).

I am running the following code

X=2+5*w+e

Y=10+3*X+i

Now I want to use x and y to run an OLS and I save as a dtagrid using dataGrid = [Y X(:,1)]

data = importdata(filename,delimiterIn,headerlinesIn);

Y= data.data(:,1)

y_lab = data.colheaders{1}

x = [ones(N,1),data.data(:,2)]

x_lab = data.colheaders{2}

But I got the error message

horizontal dimensions mismatch (1000x1 vs 499x1). In my case I want to use N=1000

[Jeff Miller]

Sorry, I don't see what's going on with that.

You'd better open a new question.