Used when data are ordinal. Interpreted like a Pearson correlation.

use http://www.philender.com/courses/data/hsb2, clear

corr write ses prog

         |    write      ses     prog
---------+---------------------------
   write |   1.0000
     ses |   0.2075   1.0000
    prog |  -0.1811   0.0173   1.0000

Do these correlations make sense? What kind of variable
is ses?  prog?

tab1 ses prog

-> tabulation of ses  

        ses |      Freq.     Percent        Cum.
------------+-----------------------------------
        low |         47       23.50       23.50
     middle |         95       47.50       71.00
       high |         58       29.00      100.00
------------+-----------------------------------
      Total |        200      100.00

-> tabulation of prog  

    type of |
    program |      Freq.     Percent        Cum.
------------+-----------------------------------
    general |         45       22.50       22.50
   academic |        105       52.50       75.00
   vocation |         50       25.00      100.00
------------+-----------------------------------
      Total |        200      100.00 
    
spearman write ses

 Number of obs =     200
Spearman's rho =       0.2224

Test of Ho: write and ses independent
      Pr > |t| =       0.0016

Indicates the degree of relationship between two variables even if the relationships is nonlinear.

Indicates how well one variable can be predicted from another even with nonlinear relationships. Interpreted in a manner similar to r².

For use when one variable is continuous (interval) and the other is a dichotomous variable that reflects an underlying normal distribution.

For use when one variable is continuous (interval) and the other is a 'true' dichotomous variable.

For use with two 'true' dichotomous variables.

For use with two dichotomous variables with underlying normal distributions.

The correlation between a and the set of variables b, c, and d.

The squared correlation between a and the set of variables b, c, and d. It represents the proportion of variability of a that is accounted for by the combination of b, c, and d.

regress write read

  Source |       SS       df       MS                  Number of obs =     200
---------+------------------------------               F(  1,   198) =  109.52
   Model |  6367.42127     1  6367.42127               Prob > F      =  0.0000
Residual |  11511.4537   198  58.1386552               R-squared     =  0.3561
---------+------------------------------               Adj R-squared =  0.3529
   Total |   17878.875   199   89.843593               Root MSE      =  7.6249

------------------------------------------------------------------------------
   write |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
    read |   .5517051   .0527178     10.465   0.000       .4477446    .6556656
   _cons |   23.95944   2.805744      8.539   0.000       18.42647    29.49242
------------------------------------------------------------------------------

regress write read female

  Source |       SS       df       MS                  Number of obs =     200
---------+------------------------------               F(  2,   197) =   77.21
   Model |  7856.32118     2  3928.16059               Prob > F      =  0.0000
Residual |  10022.5538   197  50.8759077               R-squared     =  0.4394
---------+------------------------------               Adj R-squared =  0.4337
   Total |   17878.875   199   89.843593               Root MSE      =  7.1327

------------------------------------------------------------------------------
   write |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
    read |   .5658869   .0493849     11.459   0.000        .468496    .6632778
  female |   5.486894   1.014261      5.410   0.000        3.48669    7.487098
   _cons |   20.22837   2.713756      7.454   0.000       14.87663    25.58011
------------------------------------------------------------------------------

The correlation between a and b with variable c partialed out.

corr write female read
(obs=200)

         |    write   female     read
---------+---------------------------
   write |   1.0000
  female |   0.2565   1.0000
    read |   0.5968  -0.0531   1.0000


pcorr write female read
(obs=200)

Partial correlation of write with
Variable |    Corr.     Sig.
---------+------------------
  female |   0.3596    0.000
    read |   0.6324    0.000

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