Output from fuelr1.sas	Source 0 Graphs

                        Fuel Consumption across the US                       1

                             Correlation Analysis

    6 'VAR' Variables:  TAX      INC      DRIVERS  ROAD     POP      FUEL

   Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0 / N = 48

                                           TAX             INC         DRIVERS

TAX                                    1.00000         0.01267        -0.28804
Motor fuel tax (cents/gal.)             0.0             0.9319          0.0471

INC                                    0.01267         1.00000         0.15707
Per Capita Personal income ($)          0.9319          0.0             0.2863

DRIVERS                               -0.28804         0.15707         1.00000
Proportion licensed drivers             0.0471          0.2863          0.0

ROAD                                  -0.52213         0.05016        -0.06413
Length Federal Highways (mi.)           0.0001          0.7349          0.6650

POP                                   -0.14665         0.40999        -0.36544
Population (1000s)                      0.3199          0.0038          0.0106

FUEL                                  -0.45128        -0.24486         0.69897
Fuel consumption (/person)              0.0013          0.0935          0.0001

                                          ROAD             POP            FUEL

TAX                                   -0.52213        -0.14665        -0.45128
Motor fuel tax (cents/gal.)             0.0001          0.3199          0.0013

INC                                    0.05016         0.40999        -0.24486
Per Capita Personal income ($)          0.7349          0.0038          0.0935

DRIVERS                               -0.06413        -0.36544         0.69897
Proportion licensed drivers             0.6650          0.0106          0.0001

ROAD                                   1.00000         0.64633         0.01904
Length Federal Highways (mi.)           0.0             0.0001          0.8978

POP                                    0.64633         1.00000        -0.46276
Population (1000s)                      0.0001          0.0             0.0009

FUEL                                   0.01904        -0.46276         1.00000
Fuel consumption (/person)              0.8978          0.0009          0.0

                        Fuel Consumption across the US                       2

      Plot of FUEL*TAX=STATE.                  Plot of FUEL*INC=STATE.

1000 +                                   1000 +
     |               W                        |             W
     |                                        |
     |               S                        |                 S
 800 +          N                         800 +                      N
     |                                        |
FUEL |               M                   FUEL |       N M
     |     T       O A  A    I                |    A I G T  A  K
 600 +               C    I               600 + M  S  U    MOC
     |               A    D    K              |   A  KN V  FM    M D
     |               C    L    N              |     L     NW  O    C
     |                  I N  W M    C         |              P W  M I C
 400 +                  M R               400 +              R    M
     |                    N                   |                       N
     |                                        |
     |                                        |
 200 +                                    200 +
     -+---------+---------+---------+         -+---------+---------+---------+
     4.0       6.0       8.0     10.0        3000      4000      5000     6000

        Motor fuel tax (cents/gal.)            Per Capita Personal income ($)

NOTE: 23 obs hidden.                     NOTE: 10 obs hidden.


    Plot of FUEL*DRIVERS=STATE.                Plot of FUEL*ROAD=STATE.

1000 +                                   1000 +
     |                    W                   |      W
     |                                        |
     |                        S               |         S
 800 +                    N               800 +   N
     |                                        |
FUEL |           NN M                    FUEL |      NN  M
     |           A TGA O IN                   |     AA  N  K G I          T
 600 +         UIS M   C                  600 +    U OCSIM  M
     |        KAMNFMVDM                       | DVM   K FA M
     |       L   WON C                        |  N  LW   W  O C
     |         MI NC                          |  CNM        P       I
 400 +          MR                        400 + R  M
     |     N                                  |                  N
     |                                        |
     |                                        |
 200 +                                    200 +
     --+------+------+------+------+-         -+--------------+--------------+
     .400   .500   .600   .700   .800          0            10000        20000

        Proportion licensed drivers             Length Federal Highways (mi.)

NOTE: 9 obs hidden.                      NOTE: 7 obs hidden.

                        Fuel Consumption across the US                       3
                               RSquare analysis

   N = 48     Regression Models for Dependent Variable: FUEL

 Number in     R-square         C(p)          MSE   Variables in Model
   Model

       1     0.48855266     27.26583     6541.706   DRIVERS
       1     0.21414550     65.50214    10051.531   POP
       1     0.20365389     66.96405    10185.725   TAX
       1     0.05995744     86.98693    12023.686   INC
       1     0.00036260     95.29097    12785.938   ROAD
  ------------------------------------------------------
       2     0.61750981     11.29675     5000.987   DRIVERS INC
       2     0.55668109     19.77272     5796.311   TAX DRIVERS
       2     0.53816217     22.35317     6038.442   DRIVERS POP
       2     0.49264840     28.69513     6633.526   DRIVERS ROAD
       2     0.48957868     29.12287     6673.662   TAX POP
       2     0.38797374     43.28065     8002.128   ROAD POP
       2     0.26814438     59.97785     9568.874   TAX ROAD
       2     0.26085413     60.99369     9664.192   TAX INC
       2     0.21779981     66.99294    10227.119   INC POP
       2     0.06094116     88.84986    12278.017   ROAD INC
  ----------------------------------------------------------
       3     0.67485834      5.30572     4347.783   TAX DRIVERS INC
       3     0.65222138      8.45999     4650.484   TAX DRIVERS POP
       3     0.62492422     12.26362     5015.500   DRIVERS ROAD INC
       3     0.62087362     12.82803     5069.665   DRIVERS ROAD POP
       3     0.61968405     12.99379     5085.572   DRIVERS INC POP
       3     0.56697273     20.33867     5790.426   TAX DRIVERS ROAD
       3     0.51069901     28.17993     6542.916   TAX ROAD POP
       3     0.48990880     31.07687     6820.922   TAX INC POP
       3     0.39312108     44.56341     8115.164   ROAD INC POP
       3     0.31776329     55.06388     9122.846   TAX ROAD INC
  --------------------------------------------------------------
       4     0.69558820      4.41719     4165.249   TAX DRIVERS INC POP
       4     0.67868671      6.77227     4396.511   TAX DRIVERS ROAD INC
       4     0.66872863      8.15985     4532.767   TAX DRIVERS ROAD POP
       4     0.65237216     10.43898     4756.571   DRIVERS ROAD INC POP
       4     0.51159447     30.05515     6682.824   TAX ROAD INC POP
  ------------------------------------------------------------------
       5     0.69858224      6.00000     4222.479   TAX DRIVERS ROAD INC POP
  --------------------------------------------------------------------------

                        Fuel Consumption across the US                       4
                              Stepwise analysis

              Stepwise Procedure for Dependent Variable FUEL

Step 1   Variable DRIVERS Entered   R-square = 0.48855266   C(p) = 27.26583471

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       1        287448.00860513  287448.00860513      43.94   0.0001
Error           46        300918.47056154    6541.70588177
Total           47        588366.47916667

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP    -227.30911749    121.86166772   22760.95558420       3.48   0.0685
DRIVERS     1409.84211133    212.68474141  287448.00860513      43.94   0.0001

Bounds on condition number:            1,            1
------------------------------------------------------------------------------

Step 2   Variable INC Entered       R-square = 0.61750981   C(p) = 11.29675275

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       2        363322.07482624  181661.03741312      36.33   0.0001
Error           45        225044.40434043    5000.98676312
Total           47        588366.47916667

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP       7.83709199    122.46304265      20.48120493       0.00   0.9493
DRIVERS     1525.04288666    188.29687497  328045.12944542      65.60   0.0001
INC           -0.07092430      0.01820859   75874.06622111      15.17   0.0003

Bounds on condition number:     1.025295,      4.10118
------------------------------------------------------------------------------

Step 3   Variable TAX Entered       R-square = 0.67485834   C(p) =  5.30572374

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3        397064.02474754  132354.67491585      30.44   0.0001
Error           44        191302.45441912    4347.78305498
Total           47        588366.47916667

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP     307.32789650    156.83066992   16695.90009275       3.84   0.0564
TAX          -29.48380857     10.58357587   33741.94992131       7.76   0.0078
DRIVERS     1374.76841106    183.66953983  243586.19913781      56.03   0.0001
INC           -0.06802286      0.01700975   69531.52990819      15.99   0.0002

                        Fuel Consumption across the US                       5
                              Stepwise analysis

Bounds on condition number:     1.122082,     9.737433
------------------------------------------------------------------------------

Step 4   Variable POP Entered       R-square = 0.69558820   C(p) =  4.41719337

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       4        409260.78279972  102315.19569993      24.56   0.0001
Error           43        179105.69636694    4165.24875272
Total           47        588366.47916667

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP     420.13369489    167.05968984   26343.44866428       6.32   0.0157
TAX          -36.43401312     11.12681162   44659.46259276      10.72   0.0021
DRIVERS     1167.83292976    216.66154123  121014.86500663      29.05   0.0001
INC           -0.04930472      0.01992077   25515.58798203       6.13   0.0173
POP           -0.00486078      0.00284056   12196.75805218       2.93   0.0942

Bounds on condition number:     1.795759,     24.64734
------------------------------------------------------------------------------

All variables left in the model are significant at the 0.1500 level.
No other variable met the 0.1500 significance level for entry into the model.

        Summary of Stepwise Procedure for Dependent Variable FUEL

       Variable        Number   Partial    Model
Step   Entered Removed     In      R**2     R**2      C(p)          F   Prob>F
       Label

   1   DRIVERS              1    0.4886   0.4886   27.2658    43.9408   0.0001
       Proportion licensed drivers
   2   INC                  2    0.1290   0.6175   11.2968    15.1718   0.0003
       Per Capita Personal income ($)
   3   TAX                  3    0.0573   0.6749    5.3057     7.7607   0.0078
       Motor fuel tax (cents/gal.)
   4   POP                  4    0.0207   0.6956    4.4172     2.9282   0.0942
       Population (1000s)

                        Fuel Consumption across the US                       6
                     A closer look at the stepwise model

Model: MODEL1
Dependent Variable: FUEL       Fuel consumption (/person)

                             Analysis of Variance

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

       Model            4 409260.78280 102315.19570       24.564       0.0001
       Error           43 179105.69637   4165.24875
       C Total         47 588366.47917

           Root MSE      64.53874     R-square       0.6956
           Dep Mean     576.77083     Adj R-sq       0.6673
           C.V.          11.18967

                             Parameter Estimates

                      Parameter      Standard    T for H0:
     Variable  DF      Estimate         Error   Parameter=0    Prob > |T|

     INTERCEP   1    420.133695  167.05968984         2.515        0.0157
     TAX        1    -36.434013   11.12681162        -3.274        0.0021
     DRIVERS    1   1167.832930  216.66154123         5.390        0.0001
     INC        1     -0.049305    0.01992077        -2.475        0.0173
     POP        1     -0.004861    0.00284056        -1.711        0.0942

     Variable  DF     Type I SS    Type II SS

     INTERCEP   1      15967901         26343
     TAX        1        119823         44659
     DRIVERS    1        207709        121015
     INC        1         69532         25516
     POP        1         12197         12197

                   Variable
     Variable  DF     Label

     INTERCEP   1  Intercept
     TAX        1  Motor fuel tax (cents/gal.)
     DRIVERS    1  Proportion licensed drivers
     INC        1  Per Capita Personal income ($)
     POP        1  Population (1000s)

                        Fuel Consumption across the US                       7
                     A closer look at the stepwise model

                   Dep Var   Predict   Std Err             Std Err   Student
   Obs   STATE      FUEL       Value   Predict  Residual  Residual  Residual

     1  AL           554.0     582.8    21.222  -28.7999    60.950    -0.473
     2  AR           628.0     610.6    17.464   17.4473    62.131     0.281
     3  AZ           632.0     647.8    13.496  -15.8344    63.112    -0.251
     4  CA           524.0     511.5    41.299   12.4921    49.595     0.252
     5  CO           587.0     665.3    14.544  -78.3455    62.879    -1.246
     6  CT           457.0     444.3    31.428   12.7405    56.370     0.226
     7  DE           540.0     583.3    21.191  -43.2653    60.960    -0.710
     8  FL           574.0     544.4    13.711   29.6210    63.065     0.470
     9  GA           631.0     610.5    13.072   20.5150    63.201     0.325
    10  IA           635.0     622.5    12.838   12.4657    63.249     0.197
    11  ID           648.0     701.8    28.578  -53.8204    57.867    -0.930
    12  IL           471.0     452.6    20.977   18.4337    61.035     0.302
    13  IN           580.0     505.4    12.376   74.6023    63.341     1.178
    14  KS           649.0     701.9    18.768  -52.9366    61.750    -0.857
    15  KY           534.0     474.4    20.972   59.6128    61.036     0.977
    16  LA           487.0     505.4    19.642  -18.3671    61.477    -0.299
    17  MA           414.0     496.4    18.962  -82.4189    61.690    -1.336
    18  MD           464.0     427.8    23.163   36.1703    60.239     0.600
    19  ME           541.0     524.3    19.864   16.7290    61.406     0.272
    20  MI           525.0     553.8    15.983  -28.7853    62.528    -0.460
    21  MN           566.0     642.6    12.378  -76.6124    63.341    -1.210
    22  MO           603.0     602.6    11.583    0.3829    63.491     0.006
    23  MS           577.0     641.6    24.372  -64.6487    59.760    -1.082
    24  MT           704.0     653.8    14.721   50.1897    62.837     0.799
    25  NC           566.0     518.7    21.166   47.2783    60.969     0.775
    26  ND           714.0     609.3    19.019     104.7    61.673     1.697
    27  NE           640.0     679.6    25.878  -39.6230    59.123    -0.670
    28  NH           524.0     554.7    17.261  -30.7255    62.188    -0.494
    29  NJ           467.0     485.9    18.187  -18.9279    61.923    -0.306
    30  NM           699.0     637.2    16.278   61.8492    62.452     0.990
    31  NV           782.0     726.6    31.339   55.3724    56.419     0.981
    32  NY           344.0     303.8    34.448   40.1706    54.576     0.736
    33  OH           498.0     534.9    17.292  -36.8627    62.179    -0.593
    34  OK           644.0     714.7    18.230  -70.7050    61.911    -1.142
    35  OR           610.0     670.2    13.901  -60.2362    63.024    -0.956
    36  PA           464.0     469.2    20.160   -5.2175    61.309    -0.085
    37  RI           410.0     542.4    17.049    -132.4    62.246    -2.126
    38  SC           577.0     585.7    16.622   -8.6774    62.362    -0.139
    39  SD           865.0     775.3    27.952   89.7288    58.171     1.542
    40  TN           571.0     571.0    18.223    0.0299    61.913     0.000
    41  TX           640.0     642.9    31.610   -2.8963    56.268    -0.051
    42  UT           591.0     568.2    22.962   22.7647    60.316     0.377
    43  VA           547.0     462.9    17.082   84.0990    62.237     1.351
    44  VT           561.0     576.8    18.650  -15.7623    61.785    -0.255
    45  WA           510.0     521.6    16.934  -11.6366    62.277    -0.187
    46  WI           508.0     572.2    13.986  -64.1689    63.005    -1.018
    47  WV           460.0     519.7    16.780  -59.7437    62.319    -0.959
    48  WY           968.0     734.0    19.900     234.0    61.394     3.812

                        Fuel Consumption across the US                       8
                     A closer look at the stepwise model

                                     Cook's            Hat Diag       Cov
   Obs   STATE      -2-1-0 1 2            D  Rstudent         H     Ratio

     1  AL        |      |      |     0.005   -0.4682    0.1081    1.2288
     2  AR        |      |      |     0.001    0.2778    0.0732    1.2026
     3  AZ        |      |      |     0.001   -0.2481    0.0437    1.1677
     4  CA        |      |      |     0.009    0.2491    0.4095    1.8908
     5  CO        |    **|      |     0.017   -1.2543    0.0508    0.9860
     6  CT        |      |      |     0.003    0.2235    0.2371    1.4658
     7  DE        |     *|      |     0.012   -0.7056    0.1078    1.1886
     8  FL        |      |      |     0.002    0.4654    0.0451    1.1481
     9  GA        |      |      |     0.001    0.3212    0.0410    1.1587
    10  IA        |      |      |     0.000    0.1949    0.0396    1.1659
    11  ID        |     *|      |     0.042   -0.9286    0.1961    1.2640
    12  IL        |      |      |     0.002    0.2988    0.1056    1.2444
    13  IN        |      |**    |     0.011    1.1833    0.0368    0.9912
    14  KS        |     *|      |     0.014   -0.8546    0.0846    1.1273
    15  KY        |      |*     |     0.023    0.9761    0.1056    1.1242
    16  LA        |      |      |     0.002   -0.2956    0.0926    1.2269
    17  MA        |    **|      |     0.034   -1.3487    0.0863    0.9960
    18  MD        |      |*     |     0.011    0.5959    0.1288    1.2379
    19  ME        |      |      |     0.002    0.2695    0.0947    1.2319
    20  MI        |      |      |     0.003   -0.4561    0.0613    1.1691
    21  MN        |    **|      |     0.011   -1.2163    0.0368    0.9822
    22  MO        |      |      |     0.000    0.0060    0.0322    1.1623
    23  MS        |    **|      |     0.039   -1.0840    0.1426    1.1429
    24  MT        |      |*     |     0.007    0.7953    0.0520    1.1011
    25  NC        |      |*     |     0.014    0.7718    0.1076    1.1747
    26  ND        |      |***   |     0.055    1.7364    0.0868    0.8710
    27  NE        |     *|      |     0.017   -0.6658    0.1608    1.2718
    28  NH        |      |      |     0.004   -0.4897    0.0715    1.1775
    29  NJ        |      |      |     0.002   -0.3024    0.0794    1.2087
    30  NM        |      |*     |     0.013    0.9901    0.0636    1.0704
    31  NV        |      |*     |     0.059    0.9810    0.2358    1.3143
    32  NY        |      |*     |     0.043    0.7321    0.2849    1.4764
    33  OH        |     *|      |     0.005   -0.5883    0.0718    1.1631
    34  OK        |    **|      |     0.023   -1.1462    0.0798    1.0479
    35  OR        |     *|      |     0.009   -0.9548    0.0464    1.0595
    36  PA        |      |      |     0.000   -0.0841    0.0976    1.2454
    37  RI        |  ****|      |     0.068   -2.2217    0.0698    0.6938
    38  SC        |      |      |     0.000   -0.1375    0.0663    1.2021
    39  SD        |      |***   |     0.110    1.5685    0.1876    1.0416
    40  TN        |      |      |     0.000    0.0005    0.0797    1.2223
    41  TX        |      |      |     0.000   -0.0509    0.2399    1.4794
    42  UT        |      |      |     0.004    0.3736    0.1266    1.2667
    43  VA        |      |**    |     0.028    1.3648    0.0701    0.9737
    44  VT        |      |      |     0.001   -0.2523    0.0835    1.2181
    45  WA        |      |      |     0.001   -0.1847    0.0688    1.2031
    46  WI        |    **|      |     0.010   -1.0189    0.0470    1.0446
    47  WV        |     *|      |     0.013   -0.9577    0.0676    1.0829
    48  WY        |      |******|     0.305    4.6299    0.0951    0.1581

                        Fuel Consumption across the US                       9
                     A closer look at the stepwise model

                            INTERCEP     TAX     DRIVERS     INC       POP
   Obs   STATE      Dffits   Dfbetas   Dfbetas   Dfbetas   Dfbetas   Dfbetas

     1  AL         -0.1630   -0.1312    0.0700    0.0708    0.0751    0.0149
     2  AR          0.0781    0.0399   -0.0093   -0.0093   -0.0510   -0.0018
     3  AZ         -0.0531   -0.0118    0.0280    0.0014   -0.0145    0.0239
     4  CA          0.2074   -0.0825    0.0386    0.1052   -0.0518    0.1891
     5  CO         -0.2901    0.0293    0.1053   -0.0805   -0.0777    0.0750
     6  CT          0.1246   -0.0704    0.0766    0.0005    0.0686   -0.0235
     7  DE         -0.2453    0.0437    0.0103    0.0429   -0.1941    0.1566
     8  FL          0.1012   -0.0311    0.0468    0.0380   -0.0438    0.0698
     9  GA          0.0664    0.0007    0.0068    0.0258   -0.0451    0.0300
    10  IA          0.0396    0.0149   -0.0241   -0.0083    0.0127   -0.0175
    11  ID         -0.4586    0.2847   -0.2764   -0.3781    0.2784   -0.1791
    12  IL          0.1027    0.0066   -0.0160   -0.0345    0.0557    0.0192
    13  IN          0.2312    0.0655    0.0041   -0.1276    0.0785   -0.0437
    14  KS         -0.2597    0.1071    0.0365   -0.1479   -0.0489    0.0158
    15  KY          0.3354    0.0692    0.1557   -0.1049   -0.1247    0.0037
    16  LA         -0.0944   -0.0627    0.0056    0.0547    0.0317    0.0123
    17  MA         -0.4146   -0.1516    0.1593    0.2775   -0.3157    0.1819
    18  MD          0.2291   -0.0026    0.0573   -0.1224    0.1502   -0.0951
    19  ME          0.0872    0.0063    0.0461   -0.0130   -0.0342   -0.0089
    20  MI         -0.1166    0.0025    0.0363   -0.0024   -0.0401   -0.0367
    21  MN         -0.2377    0.0012    0.0919   -0.0684   -0.0157    0.0055
    22  MO          0.0011    0.0005   -0.0006   -0.0002    0.0000   -0.0001
    23  MS         -0.4421    0.0107   -0.1473   -0.1806    0.3978   -0.1704
    24  MT          0.1863    0.0946   -0.1010   -0.0326   -0.0111   -0.0913
    25  NC          0.2679   -0.0832    0.2011    0.0825   -0.1654    0.1332
    26  ND          0.5355    0.4364   -0.3231   -0.3145   -0.0027   -0.3115
    27  NE         -0.2914    0.2406   -0.1784   -0.2462    0.0650   -0.0824
    28  NH         -0.1359    0.0516   -0.0949   -0.0190    0.0103    0.0218
    29  NJ         -0.0888    0.0153   -0.0043    0.0232   -0.0659    0.0083
    30  NM          0.2581    0.1764   -0.1360   -0.0790   -0.0652   -0.1010
    31  NV          0.5449    0.0082   -0.3094   -0.0025    0.3574   -0.2753
    32  NY          0.4621    0.0245    0.0244   -0.1480    0.1279    0.2025
    33  OH         -0.1636   -0.0157    0.0355   -0.0079    0.0115   -0.0997
    34  OK         -0.3375   -0.0271    0.1145   -0.1586    0.1581   -0.0511
    35  OR         -0.2106    0.0103    0.0755   -0.0666   -0.0212    0.0446
    36  PA         -0.0277    0.0052   -0.0092   -0.0041    0.0068   -0.0216
    37  RI         -0.6085   -0.2127    0.1069    0.3826   -0.3505    0.4644
    38  SC         -0.0367   -0.0085   -0.0085   -0.0019    0.0268   -0.0059
    39  SD          0.7537   -0.4399    0.0189    0.5447    0.0812    0.0033
    40  TN          0.0001    0.0001   -0.0001   -0.0001   -0.0000   -0.0000
    41  TX         -0.0286   -0.0134    0.0194    0.0004    0.0069   -0.0106
    42  UT          0.1422    0.1263   -0.0872   -0.1087    0.0161   -0.0856
    43  VA          0.3746   -0.0383    0.2247   -0.1002    0.0176    0.0024
    44  VT         -0.0762    0.0304   -0.0556   -0.0227    0.0249    0.0008
    45  WA         -0.0502    0.0284   -0.0381   -0.0095   -0.0067   -0.0015
    46  WI         -0.2262   -0.1623    0.1520    0.1301   -0.0505    0.0770
    47  WV         -0.2579    0.0046   -0.0492    0.1074   -0.1539    0.1497
    48  WY          1.5007   -0.5277   -0.1930    0.8816    0.0565   -0.2092

                        Fuel Consumption across the US                      10
                     A closer look at the stepwise model

Sum of Residuals                      0
Sum of Squared Residuals    179105.6964
Predicted Resid SS (Press)  219548.7409

                        Fuel Consumption across the US                      11
                     A closer look at the stepwise model

                       Partial Regression Residual Plot

       --+----------+----------+----------+----------+----------+----------+--
  FUEL |                                                                     |
       |                                                                     |
   250 +                                                                     +
       |                                                                     |
       |                                                                     |
       |                         W                                           |
       |                                                                     |
   200 +                                                                     +
       |                                                                     |
F      |                                                                     |
u      |                                                                     |
e      |                                                                     |
l  150 +                                                                     +
       |                                                      N              |
c      |                                                                     |
o      |                                                                     |
n      |                                                                     |
s  100 +                                                                     +
u      |                                                 N                   |
m      |                                V      I                             |
p      |                                        K   M                U       |
t      |                                   N                                 |
i   50 +             S                                                       +
o      |                                  M N         A       T              |
n      |                         N                           T               |
       |                            F     G ?   I                            |
(      |                                         M         L    A            |
/    0 +                                       S                             +
p      |                             P        A                              |
e      |                                                                     |
r      |           CC           V     N   M O                                |
s      |                     W                         W                     |
o  -50 +                         N   D                                       +
n      |                                 OW        M                         |
)      |                        K        M  O                                |
       |                                C M                                  |
       |      N                                                              |
  -100 +           I                                                         +
       |                                                                     |
       |                                          R                          |
       |                                                                     |
       |                                                                     |
  -150 +                                                                     +
       |                                                                     |
       |                                                                     |
       --+----------+----------+----------+----------+----------+----------+--
       -0.15      -0.10      -0.05      0.00       0.05       0.10       0.15

                                      INTERCEP

                        Fuel Consumption across the US                      12
                     A closer look at the stepwise model

                       Partial Regression Residual Plot

       -------+------+------+------+------+------+------+------+------+-------
  FUEL |                                                                     |
       |                                                                     |
   250 +                                                                     +
       |                               W                                     |
       |                                                                     |
       |                                                                     |
       |                                                                     |
   200 +                                                                     +
       |                                                                     |
F      |                                                                     |
u      |                                                                     |
e      |                                                                     |
l  150 +                                                                     +
       |                    N                                                |
c      |                                                                     |
o      |                                                                     |
n      |            N                                                        |
s  100 +                                                                     +
u      |                       N           S                                 |
m      |                        M                                            |
p      |       T        U                 I                                  |
t      |                                                                     |
i   50 +                                               V                     +
o      |                        I                                            |
n      |                      T       I     N         K                      |
       |                          M    A    G    M                           |
(      |                         A                F                          |
/    0 +                       A                              N              +
p      |                            M    L          C                        |
e      |                             O     N   S       M                     |
r      |                      W                   P                          |
s      |                            O  K D                                   |
o  -50 +                          O                       W       C          +
n      |                         M CM                      V                 |
)      |                                      W          N                   |
       |                                                                     |
       |                                            M         N              |
  -100 +                                                                     +
       |                                                        I            |
       |                              R                                      |
       |                                                                     |
       |                                                                     |
  -150 +                                                                     +
       |                                                                     |
       |                                                                     |
       -------+------+------+------+------+------+------+------+------+-------
            -2.0   -1.5   -1.0   -0.5    0.0    0.5    1.0    1.5    2.0

                          Motor fuel tax (cents/gal.)   TAX

                        Fuel Consumption across the US                      13
                     A closer look at the stepwise model

                       Partial Regression Residual Plot

       -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
  FUEL |                                                                     |
       |                                                                     |
       |                                                                     |
       |                                                                     |
       |                                                                     |
   300 +                                            W                        +
       |                                                                     |
       |                                                                     |
       |                                                                     |
F      |                                                                     |
u      |                                                                     |
e      |                                                                     |
l  200 +                                                        S            +
       |                                                                     |
c      |                                                                     |
o      |                                                                     |
n      |                                                                     |
s      |                                                         C           |
u      |                                                                     |
m  100 +                                                                     +
p      |                                     N                               |
t      |                                                          N  I       |
i      |                      V     N      F                                 |
o      |             N     I    M          G                                 |
n      |                   K N                                               |
       |                            C   P   V                                |
(    0 +                        ?A T S  W          K                         +
/      |             N    I      M  A  N          M                          |
p      |           M                MO          O                            |
e      |                     N            O                                  |
r      |              T        D         MC                                  |
s      |    U          A                                                     |
o      |            L                                                        |
n -100 +                  W                                                  +
)      |                 W                                                   |
       |                                                                     |
       |                                                                     |
       |          M                                                          |
       |                                                                     |
       |             R                                                       |
  -200 +                                                                     +
       |                                                                     |
       |                                                                     |
       |                                                                     |
       |                                                                     |
       -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
          -0.08 -0.06 -0.04 -0.02 0.00  0.02  0.04  0.06  0.08  0.10  0.12

                        Proportion licensed drivers   DRIVERS

                        Fuel Consumption across the US                      14
                     A closer look at the stepwise model

                       Partial Regression Residual Plot

       --+----------+----------+----------+----------+----------+----------+--
  FUEL |                                                                     |
       |                                                                     |
       |                                                                     |
       |                                                                     |
   250 +                                                                     +
       |                                   W                                 |
       |                                                                     |
       |                                                                     |
   200 +                                                                     +
F      |                                                                     |
u      |                                                                     |
e      |                                                                     |
l  150 +                                                                     +
       |                                                                     |
c      |                                                                     |
o      |                                                                     |
n  100 +                                  N                                  +
s      |                                   V S                               |
u      |                    N    K   N                                       |
m      |                                       I                             |
p   50 +                     A     F     M                                   +
t      |                       CGM                                           |
i      |                     S                                               |
o      |                          T  ?       U       N                       |
n    0 +                       A   ?      M    I           M     N           +
       |          M    I                    W          I                     |
(      |                            N    N    A              C               |
/      |                                 O      M                            |
p  -50 +                         O                       N                   +
e      |                                    O K                              |
r      |                                   M W                               |
s      |                                      C      W       D               |
o -100 +                                                                     +
n      |                                                  M                  |
)      |                                                                     |
       |                                                                     |
  -150 +                                                                     +
       |                                             R                       |
       |                                                                     |
       |                                                                     |
  -200 +                                                                     +
       |                                                                     |
       |                                                                     |
       |                                                                     |
       |                                                                     |
       --+----------+----------+----------+----------+----------+----------+--
       -1500      -1000      -500         0         500       1000       1500

                        Per Capita Personal income ($)   INC

                        Fuel Consumption across the US                      15
                     A closer look at the stepwise model

                       Partial Regression Residual Plot

       -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
  FUEL |                                                                     |
       |                                                                     |
   250 +                                                                     +
       |                   W                                                 |
       |                                                                     |
       |                                                                     |
       |                                                                     |
   200 +                                                                     +
       |                                                                     |
F      |                                                                     |
u      |                                                                     |
e      |                                                                     |
l  150 +                                                                     +
       |                                                                     |
c      |                                                                     |
o      |          N                                                          |
n      |                                                                     |
s  100 +                                                                     +
u      |                      S                                              |
m      |     N              I V                                              |
p      |               N                                                     |
t      |              M       K                                              |
i   50 +       U    M                                                        +
o      |                                                                     |
n      |                                 N                                   |
       |                ?   M A                                              |
(      |                   T      I G   F     N                              |
/    0 +                     M                                               +
p      |                A  L   W S                                           |
e      |        D           N V           T                                  |
r      |                   NA                  P                             |
s      |            W              M                                         |
o  -50 +                     K        N  O                            C      +
n      |                 W O                                                 |
)      |             M    C               I                                  |
       |                      M  O      M                                    |
       |                                                                     |
  -100 +                                                                     +
       |        R                                                            |
       |                                                                     |
       |                                                                     |
       |                                                                     |
  -150 +                                                                     +
       |                                                                     |
       |                                                                     |
       -----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----
          -6000 -4000 -2000   0   2000  4000  6000  8000  10000 12000 14000

                              Population (1000s)   POP

                        Fuel Consumption across the US                      16
                     A closer look at the stepwise model

           ---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---
  RESIDUAL |                                                                 |
           |                                                                 |
       250 +                                                                 +
           |                                                                 |
           |                                                      W          |
           |                                                                 |
           |                                                                 |
       200 +                                                                 +
           |                                                                 |
           |                                                                 |
           |                                                                 |
           |                                                                 |
       150 +                                                                 +
           |                                                                 |
           |                                                                 |
           |                                                                 |
           |                                                                 |
       100 +                                       N                         +
R          |                                                           S     |
e          |                      V                                          |
s          |                           I                                     |
i          |                       K                  N          N           |
d       50 +                            N               M                    +
u          |  N              M                                               |
a          |                               F                                 |
l          |                    I        M    U    ?                         |
           |                   C       C             I                       |
         0 +                                   T  M    T                     +
           |                      P      W      S                            |
           |                        N  L       V        A                    |
           |                                MN  A                            |
           |                              O     D           N                |
       -50 +                                                  ?              +
           |                            W      W       M  O                  |
           |                                                    O            |
           |                          M                M  C                  |
           |                                                                 |
      -100 +                                                                 +
           |                                                                 |
           |                                                                 |
           |                               R                                 |
           |                                                                 |
      -150 +                                                                 +
           |                                                                 |
           |                                                                 |
           ---+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+---
             300   350   400   450   500   550   600   650   700   750   800

                         Predicted Value of FUEL       PRED

                        Fuel Consumption across the US                      17
                     A closer look at the stepwise model

           -+------+------+------+------+------+------+------+------+------+--
  RSTUDENT |                                                                 |
           |                                                                 |
S        5 +                                                                 +
t          |                                                                 |
u          |             W                                                   |
d          |                                                                 |
e          |                                                                 |
n        4 +                                                                 +
t          |                                                                 |
i          |                                                                 |
z          |                                                                 |
e          |                                                                 |
d        3 +                                                                 +
           |                                                                 |
R          |                                                                 |
e          |                                                                 |
s          |                                                                 |
i        2 +                                                                 +
d          |            N                                                    |
u          |                          S                                      |
a          |          V                                                      |
l          |     I                                                           |
         1 +         N     K                 N                               +
w          |       M       N                        N                        |
i          |                  M                                              |
t          |      ?           U                                              |
h          |      I   A  M I                 C                       C       |
o        0 +     M     T  P                   T                              +
u          |      A  SW VL                                                   |
t          |         MNN   A                                                 |
           |          O            N                                         |
C          |            K  D                                                 |
u       -1 +      OW W          M      I                                     +
r          |     M C   O                                                     |
r          |            M                                                    |
e          |                                                                 |
n          |                                                                 |
t       -2 +                                                                 +
           |          R                                                      |
O          |                                                                 |
b          |                                                                 |
s          |                                                                 |
        -3 +                                                                 +
           |                                                                 |
           |                                                                 |
           -+------+------+------+------+------+------+------+------+------+--
          0.00   0.05   0.10   0.15   0.20   0.25   0.30   0.35   0.40   0.45

                                   Leverage   H

                        Fuel Consumption across the US                      18
                     A closer look at the stepwise model

               Plot of FUEL*POPDEN.  Symbol is value of STATE.

       |
  1000 +
       |
       |   W
       |
       |
       |
   900 +
       |
F      |            S
u      |
e      |
l      |
   800 +
c      |       N
o      |
n      |
s      |
u      |              N
m  700 +       M      N
p      |
t      |
i      |              I           K   O
o      |                     A N      A T I    G
n      |                        O
   600 +                                     M
(      |                   U    C        M      S    I
/      |                                 M       TN F
p      |                                     A     V
e      |                             M         K      M      D
r      |                                  W    N    C
s  500 +                                       W            O
o      |                                       L
n      |                                      W          I  P    M         N
)      |                                                              C
       |
       |                                                                M R
   400 +
       |
       |
       |                                                        N
       |
       |
   300 +
       ---+------------+------------+------------+------------+------------+--
        -2.5         -2.0         -1.5         -1.0         -0.5          0.0

                                log Population Density

NOTE: 1 obs hidden.

                           Using population density                         19

              Stepwise Procedure for Dependent Variable FUEL

Step 1   Variable POPDEN Entered    R-square = 0.72698485   C(p) = 15.56115686

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       1        427733.51576606  427733.51576606     122.49   0.0001
Error           46        160632.96340060    3492.02094349
Total           47        588366.47916667

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP     388.43457835     19.03502929  1454137.6137392     416.42   0.0001
POPDEN      -157.44242028     14.22569642  427733.51576606     122.49   0.0001

Bounds on condition number:            1,            1
------------------------------------------------------------------------------

Step 2   Variable DRIVERS Entered   R-square = 0.79360972   C(p) =  3.02623415

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       2        466933.35391049  233466.67695524      86.52   0.0001
Error           45        121433.12525618    2698.51389458
Total           47        588366.47916667

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP      66.33016290     86.15234475    1599.60437257       0.59   0.4454
POPDEN      -124.26460336     15.23685272  179485.34530536      66.51   0.0001
DRIVERS      634.35269209    166.43742177   39199.83814442      14.53   0.0004

Bounds on condition number:     1.484553,     5.938211
------------------------------------------------------------------------------

Step 3   Variable TAX Entered       R-square = 0.80422424   C(p) =  2.71056288

                DF         Sum of Squares      Mean Square          F   Prob>F

Regression       3        473178.58413315  157726.19471105      60.25   0.0001
Error           44        115187.89503352    2617.90670531
Total           47        588366.47916667

                Parameter        Standard          Type II
Variable         Estimate           Error   Sum of Squares          F   Prob>F

INTERCEP     188.34947308    115.93809543    6909.24608639       2.64   0.1114
POPDEN      -117.12658632     15.70301894  145646.08929380      55.63   0.0001
TAX          -13.24738670      8.57695379    6245.23022266       2.39   0.1296
DRIVERS      613.49598980    164.48797503   36417.43164147      13.91   0.0005

                           Using population density                         20

Bounds on condition number:     1.625331,     12.94151
------------------------------------------------------------------------------

All variables left in the model are significant at the 0.1500 level.
No other variable met the 0.1500 significance level for entry into the model.

        Summary of Stepwise Procedure for Dependent Variable FUEL

       Variable        Number   Partial    Model
Step   Entered Removed     In      R**2     R**2      C(p)          F   Prob>F
       Label

   1   POPDEN               1    0.7270   0.7270   15.5612   122.4888   0.0001
       log Population Density
   2   DRIVERS              2    0.0666   0.7936    3.0262    14.5265   0.0004
       Proportion licensed drivers
   3   TAX                  3    0.0106   0.8042    2.7106     2.3856   0.1296
       Motor fuel tax (cents/gal.)