Applied Regression Analysis by John Fox Chapter 5: Linear Least Squares Regression | SAS Textbook Examples

Figure 5.1, using data file davis. We create a dataset containing observations just on women. Then use proc gplot to create the graph. We also fix the error on case 12 in the data file. The measured weight (measwt) and measured height (measht) were switched.

data davis_co;
  set davis;
  if _n_=12 then do
  temp=measht;
  measht=measwt;
  measwt=temp;
  end;
  drop temp male;
  if male =0;
run;
proc reg data=davis_co noprint;
  model measwt = reptwt;
  output out=dvs_reg p=p;
  proc sort data=dvs_reg;
  by reptwt;
proc sort data=davis_co;
  by reptwt;
data dvs_all;
  merge davis_co dvs_reg;
  by reptwt;
run;
symbol1 color=black i=none v=star height=0.5;
symbol2 color=blue i=join v=none height=1;
symbol3 color=black i=join v=none height=1;
axis1 order=(40 to 80 by 20);
axis2 order=(40 to 80 by 20) label=(r=0 a=90);
filename outfiles 'https://stats.idre.ucla.edu/wp-content/uploads/2016/02/chap5ex1.gif';
goptions gsfname=outfiles dev=gif373;
proc gplot data=dvs_all;
  plot measwt*reptwt=1 p*reptwt=2 reptwt*reptwt=3
  /overlay haxis=axis1 vaxis=axis2 hminor=0 vminor=0;
run;
quit;

The following shows how to get the regression equation shown on page 89 using proc reg that has been used in last example to get the least-square fit. This still uses the davis data file we previously used and fixed.

proc reg data=davis_co usscp;
  model measwt=reptwt;
run;
quit;

The REG Procedure
         Uncorrected Sums of Squares and Crossproducts
Variable          Intercept            reptwt            measwt
Intercept               101              5731              5780
reptwt                 5731            329731            332408
measwt                 5780            332408            335530
The REG Procedure
Model: MODEL1
Dependent Variable: measwt
                             Analysis of Variance
                                    Sum of           Mean
Source                   DF        Squares         Square    F Value    Pr > F
Model                     1     4334.88935     4334.88935    1024.54    <.0001
Error                    99      418.87303        4.23104
Corrected Total         100     4753.76238
Root MSE              2.05695    R-Square     0.9119
Dependent Mean       57.22772    Adj R-Sq     0.9110
Coeff Var             3.59432
                        Parameter Estimates
                     Parameter       Standard
Variable     DF       Estimate          Error    t Value    Pr > |t|
Intercept     1        1.77750        1.74441       1.02      0.3107
reptwt        1        0.97722        0.03053      32.01      <.0001

In the output above, Root MSE is the standard error of regression and it also show TSS, RSS, Regss and R-Square on page 94.

The following example is based on data file prestige for the result on page 102 and 103. The option outsscp is used to produce Table 5.2

proc reg data=prestige outsscp=temp;
  model prestige=educat income percwomn;
run;
quit;
proc print data=temp;
run;

The REG Procedure
Model: MODEL1
Dependent Variable: prestige
                             Analysis of Variance
                                    Sum of           Mean
Source                   DF        Squares         Square    F Value    Pr > F
Model                     3          23862     7953.95216     129.19    <.0001
Error                    98     6033.57019       61.56704
Corrected Total         101          29895
Root MSE              7.84647    R-Square     0.7982
Dependent Mean       46.83333    Adj R-Sq     0.7920
Coeff Var            16.75402
                        Parameter Estimates
                     Parameter       Standard
Variable     DF       Estimate          Error    t Value    Pr > |t|
Intercept     1       -6.79433        3.23909      -2.10      0.0385
educat        1        4.18664        0.38870      10.77      <.0001
income        1        0.00131     0.00027778       4.73      <.0001
percwomn      1       -0.00891        0.03041      -0.29      0.7702
 

Obs   _TYPE_   _NAME_      Intercept       educat          income      percwomn      prestige

 1     SSCP    Intercept      102.00      1095.28       693386.00       2955.86       4777.00  2     SSCP    educat        1095.28     12513.04      8121410.14      32280.89      55326.38  3     SSCP    income      693386.00   8121410.14   6534383460.00   14093096.74   37748108.50  4     SSCP    percwomn      2955.86     32280.89     14093096.74     187311.52     131909.38  5     SSCP    prestige      4777.00     55326.38     37748108.50     131909.38     253618.26  6     N                      102.00       102.00          102.00        102.00        102.00

Results on page 108 for standardized partial regression coefficient using option stb in model statement.

proc reg data=prestige;
model prestige = educat income percwomn /stb;
run;
quit;

The REG Procedure
Model: MODEL1
Dependent Variable: prestige
                             Analysis of Variance
                                    Sum of           Mean
Source                   DF        Squares         Square    F Value    Pr > F
Model                     3          23862     7953.95216     129.19    <.0001
Error                    98     6033.57019       61.56704
Corrected Total         101          29895
Root MSE              7.84647    R-Square     0.7982
Dependent Mean       46.83333    Adj R-Sq     0.7920
Coeff Var            16.75402
                                Parameter Estimates
                     Parameter       Standard                           Standardized
Variable     DF       Estimate          Error    t Value    Pr > |t|        Estimate
Intercept     1       -6.79433        3.23909      -2.10      0.0385               0
educat        1        4.18664        0.38870      10.77      <.0001         0.66396
income        1        0.00131     0.00027778       4.73      <.0001         0.32418
percwomn      1       -0.00891        0.03041      -0.29      0.7702        -0.01642