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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