How to standardize unstandardized beta coefficients

Hi, I read once that unstandardized beta coefficients (from regress function) can be standardized by just dividing them by the std of the respective variable. However, some simulations in Matlab tell me this is wrong. The only way I know of getting standardized betas is just to use zscored variables in the regress function, but I was wondering if there is another was to turn unstandardized betas into standardized ones. Thank you.

[John D'Errico]

It depends on what you mean by standardization, and why you think that solution was wrong. That is an entirely reasonable way to standardize your variables. So if you are unhappy with it, you need to explain your reasoning as to why you think it is wrong. Then we can either convince you that you are incorrect in your reasoning, or offer a different scheme that will satisfy you.

[Nuchto]

It is wrong because when I zscore (standardize) the variables the resulting standardized beta is not the same as the beta I get by not zscoring the variables and dividing it by the std of the respective variable.

[Nuchto]

This is what I mean:

% create IVs x1 and x2 and DV y as unstandardized variables 
x1=rand(100,1)*30;
x2=rand(100,1)*2;
y=rand(100,1)*10;

% create column of ones
X=[ones(size(x1)) x1 x2];

% perform regression on these
beta1=regress(y,X)

% standardize variables and perform regression again
X=[ones(size(x1)) zscore(x1) zscore(x2)]; % attach ones
beta2=regress(zscore(y),X)

% beta2 should be equal to beta1(2)/std(x1) but it isn't
beta1(2)/std(x1)
beta2(2)

[Nuchto]

Anyone help?

Answer 1

[David Goodmanson]

Hi Nuchto

You forgot that you need to regress against the same y, otherwise it's apples and oranges. So the second regression should be

beta2=regress(y,X)

and in addition the comparison is

beta1(2)*std(x1)
beta2(2)

which does seem counterintuitive at first.

[Nuchto]

Mmm, thanks! Why does it seem counterintuitive? Thanks!

Answer 2

[muqdad aljuboori]

% create IVs x1 and x2 and DV y as unstandardized variables

x1=rand(100,1)*30;

x2=rand(100,1)*2;

y=rand(100,1)*10;

% create column of ones X=[ones(size(x1)) x1 x2];

% perform regression on these

beta1=regress(y,X)

% standardize variables and perform regression again

Z=[ones(size(x1)) zscore(x1) zscore(x2)]; % attach ones

beta2=regress(y,Z)

% beta2 should be equal to beta1(2)/std(x1) but it isn't

beta1(2)*std(x1)

beta2(2)

beta1(3)*std(x2)

beta2(3)

it is working now

Answer 3

[muqdad aljuboori]

% create IVs x1 and x2 and DV y as unstandardized variables x1=rand(100,1)*30;

x2=rand(100,1)*100;

x3=rand(100,1)*521;

x4=rand(100,1)*7;

y=rand(100,1)*10; % create column of ones

X=[ones(size(x1)) x1 x2 x3 x4];

% perform regression on these

beta1=regress(y,X)

% standardize variables and perform regression again

Z=[ones(size(x1)) zscore(x1) zscore(x2) zscore(x3) zscore(x4)]; % attach ones

beta2=regress(zscore(y),Z)

% beta2 should be equal to beta1(2)/std(x1) but it isn't

beta1(2)*std(x1)/std(y)

beta2(2)

beta1(3)*std(x2)/std(y)

beta2(3)

beta1(4)*std(x3)/std(y)

beta2(4)

beta1(5)*std(x4)/std(y)

beta2(5)

this for zscore(y)