## Output from imlregr.sas

Source
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```                          Regression using the SWEEP operator in IML                          1
Water use data
```
```                                General Linear Models Procedure
```
```                            Number of observations in data set = 17
```

```                          Regression using the SWEEP operator in IML                          2
Water use data
```
```                                General Linear Models Procedure

Dependent Variable: Y   MONTHLY WATER USAGE (GALLONS)

Source                  DF           Sum of Squares             Mean Square  F Value    Pr > F
```
```Model                    4         2448834.00990638         612208.50247659     9.88    0.0009

Error                   12          743797.51950539          61983.12662545

Corrected Total         16         3192631.52941177```
```
R-Square                     C.V.                Root MSE             Y Mean
```
```                  0.767027                 7.535904            248.96410710      3303.70588235
```
```
Source                  DF                Type I SS             Mean Square  F Value    Pr > F
```
```X1                       1          260701.93234021         260701.93234021     4.21    0.0628
X2                       1         1298823.50094793        1298823.50094793    20.95    0.0006
X3                       1          333276.22800977         333276.22800977     5.38    0.0389
X4                       1          556032.34860847         556032.34860847     8.97    0.0112```
```
Source                  DF              Type III SS             Mean Square  F Value    Pr > F
```
```X1                       1          447803.01331977         447803.01331977     7.22    0.0197
X2                       1         1339312.03993511        1339312.03993511    21.61    0.0006
X3                       1          431393.89321534         431393.89321534     6.96    0.0216
X4                       1          556032.34860847         556032.34860847     8.97    0.0112
```
```
T for H0:        Pr > |T|       Std Error of
Parameter                      Estimate        Parameter=0                        Estimate
```
```INTERCEPT                   6360.337333               4.84         0.0004        1314.391613
X1                            13.868864               2.69         0.0197           5.159815
X2                             0.211703               4.65         0.0006           0.045543
X3                          -126.690357              -2.64         0.0216          48.022338
X4                           -21.817964              -3.00         0.0112           7.284520

```

```                          Regression using the SWEEP operator in IML                          3
Water use data
```
```                                   Raw Cross Product Matrix

XPX        INTCEPT        X1        X2        X3        X4         Y

INTCEPT         17    1102.5    219308       365      3091     56163
X1          1102.5  74420.73  14204390   23809.7  200070.3 3669928.2
X2          219308  14204390 3.02819E9   4717399  41015322 740428154
X3             365   23809.7   4717399      7871     66382   1204924
X4            3091  200070.3  41015322     66382    569757  10276718
Y            56163 3669928.2 740428154   1204924  10276718 188738665

MEANS   INTCEPT        X1        X2        X3        X4         Y

1 64.852941 12900.471 21.470588 181.82353 3303.7059

Sweeping the X variables

XPX          SWEPT        X1        X2        X3        X4         Y

SWEPT    0.0588235 64.852941 12900.471 21.470588 181.82353 3303.7059
X1       -64.85294 2920.3624 -18378.42 138.37647 -390.1412 27592.465
X2       -12900.47 -18378.42 199011580 8727.2353 1139967.4  15899024
X3       -21.47059 138.37647 8727.2353 34.235294 16.411765 -928.6471
X4       -181.8235 -390.1412 1139967.4 16.411765 7740.4706 64963.118
Y        -3303.706 27592.465  15899024 -928.6471 64963.118 3192631.5

XPX          SWEPT     SWEPT        X2        X3        X4         Y

SWEPT    1.4990229 -0.022207 13308.603  18.39764 190.48746 2690.9557
SWEPT    -0.022207 0.0003424   -6.2932 0.0473833 -0.133593 9.4483017
X2        -13308.6 6.2931997 198895921 9598.0661 1137512.2  16072669
X3       -18.39764 -0.047383 9598.0661 27.678557  34.89795  -2236.07
X4       -190.4875 0.1335934 1137512.2  34.89795 7688.3503 68649.289
Y        -2690.956 -9.448302  16072669  -2236.07 68649.289 2931929.6

XPX          SWEPT     SWEPT     SWEPT        X3        X4         Y

SWEPT    2.3895334 -0.022628 -0.000067 17.755411 114.37379 1615.4949
SWEPT    -0.022628 0.0003426 3.1641E-8  0.047687 -0.097602 9.9568517
SWEPT    -0.000067 3.1641E-8 5.0278E-9 0.0000483 0.0057191 0.0808094
X3       -17.75541 -0.047687 -0.000048 27.215386 -19.99466 -3011.684
X4       -114.3738 0.0976018 -0.005719 -19.99466 1182.7672 -23272.44```

```                          Regression using the SWEEP operator in IML                          4
Water use data
```
```             Y        -1615.495 -9.956852 -0.080809 -3011.684 -23272.44 1633106.1

XPX          SWEPT     SWEPT     SWEPT     SWEPT        X4         Y

SWEPT    13.973224 0.0084829 -0.000035 -0.652403 127.41837 3580.3279
SWEPT    0.0084829 0.0004262  1.162E-7 -0.001752 -0.062567 15.233948
SWEPT    -0.000035  1.162E-7 5.1133E-9 -1.773E-6 0.0057546 0.0861496
SWEPT    -0.652403 -0.001752 -1.773E-6 0.0367439 -0.734682 -110.6611
X4       -127.4184  0.062567 -0.005755 0.7346824 1168.0774 -25485.07
Y        -3580.328 -15.23395  -0.08615 110.66108 -25485.07 1299829.9

XPX          SWEPT     SWEPT     SWEPT     SWEPT     SWEPT         Y

SWEPT     27.87251 0.0016579 0.0005923 -0.732545 -0.109084 6360.3373
SWEPT    0.0016579 0.0004295  -1.92E-7 -0.001713 0.0000536 13.868864
SWEPT    0.0005923  -1.92E-7 3.3464E-8 -5.393E-6 -4.927E-6 0.2117029
SWEPT    -0.732545 -0.001713 -5.393E-6  0.037206  0.000629 -126.6904
SWEPT    -0.109084 0.0000536 -4.927E-6  0.000629 0.0008561 -21.81796
Y        -6360.337 -13.86886 -0.211703 126.69036 21.817964 743797.52

Parameter Estimates

A             Beta    StdDev   T Ratio    Prob>T    Seq SS   Part SS

INTCEPT  6360.3373 1314.3916 4.8389972 0.0004057 185546033 1451390.3
X1       13.868864 5.1598151 2.6878608 0.0197478 260701.93 447803.01
X2       0.2117029 0.0455431  4.648407  0.000562 1298823.5   1339312
X3       -126.6904 48.022338 -2.638155 0.0216474 333276.23 431393.89
X4       -21.81796 7.2845197 -2.995114 0.0111676 556032.35 556032.35

Correlation Matrix of the Estimates
```