Robert Max Jackson
This page shows in detail the regression analysis to predict Buchanan vote in Palm Beach County, Florida. This page shows the actual output from the analysis, derived from an SPSS run. The analysis was done by first taking the natural log of all variables, then applying a simple linear regression. The predictors include the '00 Senate votes for all candidates by county. The graphic display at the bottom is based on taking the antilog of the predicted values from the regression. In this case, because the logging lessens other problems, the data for Palm Beach (i.e., their apparently incorrect reported votes) was included in the regression estimations.
COMPUTE lnbuch = LN(buchanan) . VARIABLE LABELS lnbuch 'LN(buchanan)' . COMPUTE lnsenref = LN(sen_ref) . VARIABLE LABELS lnsenref 'LN(sen_ref)' . COMPUTE lnsenrep = LN(sen_rep) . VARIABLE LABELS lnsenrep 'LN(sen_rep)' . COMPUTE lnsendem = LN(sen_dem) . VARIABLE LABELS lnsendem 'LN(sen_dem)' . COMPUTE lnsenlaw = LN(sen_nlaw) . VARIABLE LABELS lnsenlaw 'LN(sen_nlaw)' . COMPUTE lnsenlog = LN(sen_log) . VARIABLE LABELS lnsenlog 'LN(sen_log)' . COMPUTE lnsenmar = LN(sen_mar) . VARIABLE LABELS lnsenmar 'LN(sen_mar)' . COMPUTE lnsenmcc = LN(sen_mcc) . VARIABLE LABELS lnsenmcc 'LN(sen_mcc)' . REGRESSION /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA ZPP /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT lnbuch /METHOD=ENTER lnsenref lnsenrep lnsendem lnsenlaw lnsenlog lnsenmar lnsenmcc /RESIDUALS DURBIN ID( county ) /CASEWISE PLOT(ZRESID) OUTLIERS(3) /SAVE pred (presenln) ADJPRED (adjsenln) .
| Input | Data | E:\PalmBeach\FloridaAll.sav |
|---|---|---|
| Filter | <none> | |
| Weight | <none> | |
| Split File | <none> | |
| N of Rows in Working Data File | 67 | |
| Missing Value Handling | Definition of Missing | User-defined missing values are treated as missing. |
| Cases Used | Statistics are based on cases with no missing values for any variable used. | |
| Syntax | REGRESSION /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA ZPP /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT lnbuch /METHOD=ENTER lnsenref lnsenrep lnsendem lnsenlaw lnsenlog lnsenmar lnsenmcc /RESIDUALS DURBIN ID( county ) /CASEWISE PLOT(ZRESID) OUTLIERS(3) /SAVE pred (presenln) ADJPRED (adjsenln) . |
|
| Variables Created or Modified | PRESENLN | Predicted Value |
| ADJSENLN | Adjusted Predicted Value | |
| Mean | Std. Deviation | N | |
|---|---|---|---|
| LNBUCH LN(buchanan) | 4.8343 | 1.2005 | 67 |
| LNSENREF LN(sen_ref) | 4.4804 | 1.5535 | 67 |
| LNSENREP LN(sen_rep) | 9.6530 | 1.5290 | 67 |
| LNSENDEM LN(sen_dem) | 9.6159 | 1.5533 | 67 |
| LNSENLAW LN(sen_nlaw) | 4.6457 | 1.6690 | 67 |
| LNSENLOG LN(sen_log) | 5.9231 | 1.6406 | 67 |
| LNSENMAR LN(sen_mar) | 4.3265 | 1.4708 | 67 |
| LNSENMCC LN(sen_mcc) | 5.0530 | 1.2260 | 67 |
| LNBUCH LN(buchanan) | LNSENREF LN(sen_ref) | LNSENREP LN(sen_rep) | LNSENDEM LN(sen_dem) | LNSENLAW LN(sen_nlaw) | LNSENLOG LN(sen_log) | LNSENMAR LN(sen_mar) | LNSENMCC LN(sen_mcc) | ||
|---|---|---|---|---|---|---|---|---|---|
| Pearson Correlation | LNBUCH LN(buchanan) | 1.000 | .934 | .916 | .891 | .889 | .851 | .877 | .920 |
| LNSENREF LN(sen_ref) | .934 | 1.000 | .972 | .951 | .967 | .936 | .949 | .972 | |
| LNSENREP LN(sen_rep) | .916 | .972 | 1.000 | .960 | .960 | .946 | .953 | .957 | |
| LNSENDEM LN(sen_dem) | .891 | .951 | .960 | 1.000 | .957 | .967 | .948 | .942 | |
| LNSENLAW LN(sen_nlaw) | .889 | .967 | .960 | .957 | 1.000 | .949 | .947 | .946 | |
| LNSENLOG LN(sen_log) | .851 | .936 | .946 | .967 | .949 | 1.000 | .937 | .913 | |
| LNSENMAR LN(sen_mar) | .877 | .949 | .953 | .948 | .947 | .937 | 1.000 | .953 | |
| LNSENMCC LN(sen_mcc) | .920 | .972 | .957 | .942 | .946 | .913 | .953 | 1.000 | |
| Model | Variables Entered | Variables Removed | Method |
|---|---|---|---|
| 1 | LNSENMCC LN(sen_mcc), LNSENLOG LN(sen_log), LNSENMAR LN(sen_mar), LNSENLAW LN(sen_nlaw), LNSENREP LN(sen_rep), LNSENDEM LN(sen_dem), LNSENREF LN(sen_ref)(a) | . | Enter |
| a All requested variables entered. | |||
| b Dependent Variable: LNBUCH LN(buchanan) | |||
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | Durbin-Watson |
|---|---|---|---|---|---|
| 1 | .944(a) | .891 | .878 | .4198 | 1.950 |
| a Predictors: (Constant), LNSENMCC LN(sen_mcc), LNSENLOG LN(sen_log), LNSENMAR LN(sen_mar), LNSENLAW LN(sen_nlaw), LNSENREP LN(sen_rep), LNSENDEM LN(sen_dem), LNSENREF LN(sen_ref) | |||||
| b Dependent Variable: LNBUCH LN(buchanan) | |||||
| Model | Sum of Squares | df | Mean Square | F | Sig. | |
|---|---|---|---|---|---|---|
| 1 | Regression | 84.721 | 7 | 12.103 | 68.685 | .000(a) |
| Residual | 10.396 | 59 | .176 | |||
| Total | 95.117 | 66 | ||||
| a Predictors: (Constant), LNSENMCC LN(sen_mcc), LNSENLOG LN(sen_log), LNSENMAR LN(sen_mar), LNSENLAW LN(sen_nlaw), LNSENREP LN(sen_rep), LNSENDEM LN(sen_dem), LNSENREF LN(sen_ref) | ||||||
| b Dependent Variable: LNBUCH LN(buchanan) | ||||||
| Unstandardized Coefficients | Standardized Coefficients | t | Sig. | Correlations | |||||
|---|---|---|---|---|---|---|---|---|---|
| Model | B | Std. Error | Beta | Zero-order | Partial | Part | |||
| 1 | (Constant) | -.802 | 1.058 | -.758 | .451 | ||||
| LNSENREF LN(sen_ref) | .648 | .200 | .839 | 3.248 | .002 | .934 | .389 | .140 | |
| LNSENREP LN(sen_rep) | .226 | .173 | .288 | 1.306 | .196 | .916 | .168 | .056 | |
| LNSENDEM LN(sen_dem) | .239 | .167 | .309 | 1.431 | .158 | .891 | .183 | .062 | |
| LNSENLAW LN(sen_nlaw) | -.156 | .145 | -.217 | -1.082 | .284 | .889 | -.139 | -.047 | |
| LNSENLOG LN(sen_log) | -.240 | .138 | -.328 | -1.742 | .087 | .851 | -.221 | -.075 | |
| LNSENMAR LN(sen_mar) | -.129 | .143 | -.158 | -.898 | .373 | .877 | -.116 | -.039 | |
| LNSENMCC LN(sen_mcc) | .190 | .206 | .194 | .925 | .359 | .920 | .120 | .040 | |
| a Dependent Variable: LNBUCH LN(buchanan) | |||||||||
| Case Number | COUNTY | Std. Residual | LNBUCH LN(buchanan) | Predicted Value | Residual |
|---|---|---|---|---|---|
| 50 | PALM BEACH | 3.245 | 8.13 | 6.7714 | 1.3622 |
| a Dependent Variable: LNBUCH LN(buchanan) | |||||
| Minimum | Maximum | Mean | Std. Deviation | N | |
|---|---|---|---|---|---|
| Predicted Value | 2.3531 | 7.0139 | 4.8343 | 1.1330 | 67 |
| Std. Predicted Value | -2.190 | 1.924 | .000 | 1.000 | 67 |
| Standard Error of Predicted Value | 7.088E-02 | .3133 | .1384 | 4.365E-02 | 67 |
| Adjusted Predicted Value | 2.2586 | 7.0788 | 4.8189 | 1.1652 | 67 |
| Residual | -1.1143 | 1.3622 | -2.9164E-16 | .3969 | 67 |
| Std. Residual | -2.654 | 3.245 | .000 | .945 | 67 |
| Stud. Residual | -2.711 | 3.529 | .014 | 1.047 | 67 |
| Deleted Residual | -1.1626 | 2.2187 | 1.538E-02 | .5049 | 67 |
| Stud. Deleted Residual | -2.873 | 3.939 | .024 | 1.099 | 67 |
| Mahal. Distance | .896 | 35.785 | 6.896 | 5.577 | 67 |
| Cook's Distance | .000 | 1.945 | .043 | .239 | 67 |
| Centered Leverage Value | .014 | .542 | .104 | .084 | 67 |
| a Dependent Variable: LNBUCH LN(buchanan) | |||||
Here is a chart showing the results of this regression.
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