# Standardized beta on standardized variables

I am having trouble understanding why the standardized beta option in regress in Stata gives me different results when I manually standardize all variables. Say x1 x2 x3 x4 x5 y are the original data, X1 X2 X3 X4 X5 Y are standardized variables with 0 mean and 1 standard deviation. I have missing data on the x4 and y .

sum x1 x2 x3 x4 x5 y

Variable Obs    Mean    Std. Dev.   Min   Max

x1      146 .0584795    .0801943     0      .401
x2      146 .1780685    .1500611    .026    1
x3      146 .8747945    .1389587    .309    1
x4      123 14.24472    2.007943    11.1    22.2
x5      146 .5480685    .3825432    .005    1
y       140 2.991429    .8211665    1.3     4.9


sum X1 X2 X3 X4 X5 Y

Variable Obs     Mean   Std. Dev.  Min       Max

X1      146    1.99e-08     1   -.7292224   4.271135
X2      146    2.50e-08     1   -1.013377   5.477312
X3      146   -1.70e-07     1   -4.071673   .9010261
X4      123   -1.22e-07     1   -1.566137   3.961907
X5      146    7.00e-08     1   -1.419626   1.181387
Y       140   -4.35e-08     1   -2.059788   2.32422


I thought regression (2) will give me same results as regression (3) since Stata manual says:

The beta coefficients are the regression coefficients obtained by first standardizing all variables to have a mean of 0 and a standard deviation of 1.

reg y x1 x2 x3 (1) reg y x1 x2 x3, beta (2) reg Y X1 X2 X3 (3) reg Y X1 X2 X3, beta (4)

The results are as follows:

             (2)          (3)         (4)
x1       -0.1964757   -0.2524519  -0.1964757
x2       -0.1864261   -0.4689916  -0.1864261
x3        0.0219722    0.020811    0.0219722
x4        0.5246134    0.5251326   0.5246134
x5       -0.3346567   -0.3290855  -0.3346567


And it turns out the regression (4) gives same results to (2), but all the variables in regression 4 are already standardized. My guess is that since the variables are all proportions, they are not normally distributed and vary in range. For instance x1 is between 0-0.4 while x2 is binomial distribution between 0-0.99. Would that be a problem? Should I choose (2) over (3) and why?

• Please tell us how the results differ between (2) and (3). It would also help to describe how you standardized the variables. One possible source of slight discrepancies in estimates would be the presence of missing data, so in your testing have you made sure there are no missing data? – whuber Aug 7 '15 at 13:36
• @whuber Thanks! I have included the results in the original post. I tested the missing data by using ovtest and it showed that Prob > F = 0.1511. I tried the linktest but I am not sure how to interpret the results. – whyq Aug 7 '15 at 16:25
• @whyq did you do anything with your outcome (the Y)? – Repmat Aug 7 '15 at 17:08
• It would help to see fuller output, including standard errors. You might also consider reporting some summary statistics for each of the variables--especially including their means, standard deviations, and counts, to confirm they have been correctly standardized. I do not understand what you are doing with ovtest: the issue with missing data is that if even a single value is missing in the dataset, then standardizing the original data and standardizing the data actually used in the regression could be quite different. – whuber Aug 7 '15 at 18:42
• @whuber After dropping the observations with missing data (2) and (3) give same results. Thanks!! – whyq Aug 11 '15 at 16:32