Tutorial: A Module for Linear Regression

Plotting Regression Results

You can create some simple plots by using the PGRAF subroutine. The PGRAF subroutine produces scatter plots suitable for printing on a line printer. If you want to produce better-quality graphics that include color, you can use the graphics capabilities of IML (see Chapter 12 for more information).

Here is how you can plot the residuals against . First, create a matrix containing the pairs of points by concatenating X1 with RESID, using the horizontal concatenation operator ( $\vert$ ):

  
     > xy=x1||resid; 
  
                XY            5 rows      2 cols    (numeric) 
  
                                      1      -0.2 
                                      2         1 
                                      3      -1.8 
                                      4       1.4 
                                      5      -0.4

Next, use a CALL statement to call the PGRAF subroutine to produce the desired plot. The arguments to PGRAF are as follows, in the order shown:

the matrix containing the pairs of points
a plotting symbol
a label for the X axis
a label for the Y axis
a title for the plot

  
     > call pgraf(xy,'r','x','Residuals','Plot of Residuals'); 
  
                              Plot of Residuals 
    2 + 
      | 
      |                                                 r 
 R    | 
 e    |                     r 
 s    | 
 i    | 
 d  0 + 
 u    |       r                                                       r 
 a    | 
 l    | 
 s    | 
      | 
      |                                   r 
   -2 + 
      --------+------+------+------+------+------+------+------+------+-------- 
             1.0    1.5    2.0    2.5    3.0    3.5    4.0    4.5    5.0 
                                          x

You can also plot the predicted values ${\hat{y}}$ against . You must first create a matrix - say, XYH - containing the points. Do this by concatenating X1 with YHAT. Next, call the PGRAF subroutine to plot the points. You can perform these operations by using the following statements:

  
    > xyh=x1||yhat; 
  
                XYH           5 rows      2 cols    (numeric) 
  
                                      1       1.2 
                                      2         4 
                                      3      10.8 
                                      4      21.6 
                                      5      36.4 
  
  
    > call pgraf(xyh,'*','x','Predicted','Plot of Predicted Values');

  
  
                           Plot of Predicted Values 
   40 + 
      |                                                               * 
      | 
 P    | 
 r    | 
 e    | 
 d    |                                                 * 
 i 20 + 
 c    | 
 t    | 
 e    |                                   * 
 d    | 
      | 
      |                     * 
    0 +       * 
      --------+------+------+------+------+------+------+------+------+-------- 
             1.0    1.5    2.0    2.5    3.0    3.5    4.0    4.5    5.0 
                                          x

You can get a more detailed plot, denoting the observed values with a "y" and the predicted values with a "p" by using the following statements. Create a matrix NEWXY containing the pairs of points to overlay. You need to use both the horizontal concatenation operator ( $\vert$ ) and the vertical concatenation operator (//). The NROW function returns the number of observations - that is, the number of rows of X1. The matrix LABEL contains the character label for each point, plotting a "y" for each observed point and a "p" for each predicted point.

  
    > newxy=(x1//x1)||(y//yhat); 
  
                NEWXY        10 rows      2 cols    (numeric) 
  
                                      1         1 
                                      2         5 
                                      3         9 
                                      4        23 
                                      5        36 
                                      1       1.2 
                                      2         4 
                                      3      10.8 
                                      4      21.6 
                                      5      36.4 
  
    > n=nrow(x1); 
  
  
                N             1 row       1 col     (numeric) 
  
                                           5 
  
  
    > label=repeat('y',n,1)//repeat('p',n,1); 
  
  
                LABEL        10 rows      1 col     (character, size 1) 
  
                                          y 
                                          y 
                                          y 
                                          y 
                                          y 
                                          p 
                                          p 
                                          p 
                                          p 
                                          p 
  
  
    > call pgraf(newxy,label,'x','y','Scatter Plot with Regression Line' ); 
  
  
                      Scatter Plot with Regression Line 
 y 40 + 
      |                                                               y 
      | 
      | 
      | 
      | 
      |                                                 y 
   20 + 
      | 
      | 
      |                                   p 
      |                                   y 
      |                     y 
      |                     p 
    0 +       y 
      --------+------+------+------+------+------+------+------+------+---- 
             1.0    1.5    2.0    2.5    3.0    3.5    4.0    4.5    5.0 
                                          x

As you can see, the observed and predicted values are too close together to be distinguishable at all values of .

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