Linear Regression with PROC REG

Linear regression models a numeric outcome as a straight-line function of one or more predictors. Can a student's height predict their weight?

proc reg data=sashelp.class;
   model weight = height;
run;
quit;

Output (abridged):

                      The REG Procedure
                        Model: MODEL1
                   Dependent Variable: Weight

                        Analysis of Variance

                             Sum of          Mean
Source             DF       Squares        Square    F Value    Pr > F

Model               1    7193.24912    7193.24912      57.08    <.0001
Error              17    2142.48772     126.02869
Corrected Total    18    9335.73684

Root MSE             11.22625    R-Square     0.7705
Dependent Mean      100.02632    Adj R-Sq     0.7570
Coeff Var            11.22330

                        Parameter Estimates

                    Parameter       Standard
Variable     DF      Estimate          Error    t Value    Pr > |t|

Intercept     1    -143.02692       32.27459      -4.43      0.0004
Height        1       3.89903        0.51609       7.55      <.0001

How to read it:

• The fitted line: weight = -143.03 + 3.899 × height. Each extra inch of height goes with about 3.9 more pounds.
• Pr > |t| for Height is below 0.0001: the slope is clearly not zero.
• R-Square 0.7705: height explains about 77% of the variation in weight.
• Root MSE 11.2: the typical prediction error, in pounds.
• The intercept (a student of height 0) has no real-world meaning here — it just positions the line.

PROC REG is interactive: it keeps running so you can add more MODEL statements, which is why it ends with QUIT;.

Predictions and residuals

proc reg data=sashelp.class noprint;
   model weight = height;
   output out=fitted p=predicted r=residual;
run;
quit;

proc print data=fitted(obs=3) noobs;
   var name height weight predicted residual;
   format predicted residual 8.2;
run;

Name       Height    Weight    predicted    residual

Alfred      69.0      112.5       126.01      -13.51
Alice       56.5       84.0        77.27        6.73
Barbara     65.3       98.0       111.58      -13.58

More than one predictor

proc reg data=sashelp.class;
   model weight = height age / vif;
run;
quit;

• Each estimate is now the effect of that predictor holding the others constant.
• / vif reports variance inflation factors — large values warn that predictors are strongly correlated with each other.
• / selection=stepwise and similar options do variable selection; use them with care.

Checking the assumptions

With ODS Graphics on, PROC REG draws a diagnostics panel: residuals versus predicted values (look for no pattern), a Q-Q plot of residuals (look for a straight line), and influence measures such as Cook's D. Always look at it before trusting the p-values.

For categorical predictors, use PROC GLM (next lesson), which has a CLASS statement; PROC REG needs numeric predictors only.