Example 74.3 Predicting Weight by Height and Age

In this example, the weights of schoolchildren are modeled as a function of their heights and ages. The example shows the use of a BY statement with PROC REG, multiple MODEL statements, and the OUTEST= and OUTSSCP= options, which create data sets. Here are the data:

*------------Data on Age, Weight, and Height of Children-------*
| Age (months), height (inches), and weight (pounds) were      |
| recorded for a group of school children.                     |
| From Lewis and Taylor (1967).                                |
*--------------------------------------------------------------*;

data htwt;
   input sex $ age :3.1 height weight @@;
   datalines;
f 143 56.3  85.0 f 155 62.3 105.0 f 153 63.3 108.0 f 161 59.0  92.0
f 191 62.5 112.5 f 171 62.5 112.0 f 185 59.0 104.0 f 142 56.5  69.0
f 160 62.0  94.5 f 140 53.8  68.5 f 139 61.5 104.0 f 178 61.5 103.5
f 157 64.5 123.5 f 149 58.3  93.0 f 143 51.3  50.5 f 145 58.8  89.0

   ... more lines ...   

m 164 66.5 112.0 m 189 65.0 114.0 m 164 61.5 140.0 m 167 62.0 107.5
m 151 59.3  87.0
;

Modeling is performed separately for boys and girls. Since the BY statement is used, interactive processing is not possible in this example; no statements can appear after the first RUN statement.

The following statements produce Output 74.3.1 through Output 74.3.4:

proc reg outest=est1 outsscp=sscp1 rsquare;
   by sex;
   eq1: model  weight=height;
   eq2: model  weight=height age;

proc print data=sscp1;
   title2 'SSCP type data set';

proc print data=est1;
   title2 'EST type data set';
run;

For both female and male children, the overall statistics for both models are significant, indicating that the model explains a significant portion of the variation in the data. For females, the full model is

and for males, the full model is

The OUTSSCP= data set is shown in Output 74.3.5. Note how the BY groups are separated. Observations with _TYPE_=‘N’ contain the number of observations in the associated BY group. Observations with _TYPE_=‘SSCP’ contain the rows of the uncorrected sums of squares and crossproducts matrix. The observations with _NAME_=‘Intercept’ contain crossproducts for the intercept.

The OUTEST= data set is displayed in Output 74.3.6; again, the BY groups are separated. The _MODEL_ column contains the labels for models from the MODEL statements. If no labels are specified, the defaults MODEL1 and MODEL2 would appear as values for _MODEL_. Note that _TYPE_=‘PARMS’ for all observations, indicating that all observations contain parameter estimates. The _DEPVAR_ column displays the dependent variable, and the _RMSE_ column gives the root mean square error for the associated model. The Intercept column gives the estimate for the intercept for the associated model, and variables with the same name as variables in the original data set (height, age) give parameter estimates for those variables. The dependent variable, weight, is shown with a value of . The _IN_ column contains the number of regressors in the model not including the intercept; _P_ contains the number of parameters in the model; _EDF_ contains the error degrees of freedom; and _RSQ_ contains the statistic. Finally, note that the _IN_, _P_, _EDF_, and _RSQ_ columns appear in the OUTEST= data set since the RSQUARE option is specified in the PROC REG statement.