\[voteavoteA=\beta_0+\beta_1log(expendA)+\beta_2log(expendB)+\beta_3prtystrA+u\] Burada voteA aday A tarafından alınan oy oranı ,expendA ve expendB aday A ve B tarafından yapılan kampanya harcamaları ve prtsyrA ise aday A için parti gücünün bir ölçüsüdür(A’nın partisine en son başkanlık seçimine giden oy oranı).
Herşeyin eşit olduğunda A adayının yağtığı harcamalardaki artışın A adayının oy oranını arttırabilmesidir. β1 esnekliği pozitifdir.
\[voteavoteA=\beta_0+\beta_1log(1)+\beta_2log(1)+\beta_3prtystrA+u\]
library(wooldridge)
data("vote1")head(vote1,1-20)## state district democA voteA expendA expendB prtystrA lexpendA
## 1 AL 7 1 68 328.296 8.737 41 5.7939157
## 2 AK 1 0 62 626.377 402.477 60 6.4399524
## 3 AZ 2 1 73 99.607 3.065 55 4.6012325
## 4 AZ 3 0 69 319.690 26.281 64 5.7673516
## 5 AR 3 0 75 159.221 60.054 66 5.0702929
## 6 AR 4 1 69 570.155 21.393 46 6.3459082
## 7 CA 2 0 59 696.748 193.915 58 6.5464239
## 8 CA 3 1 71 638.688 7.695 49 6.4594159
## 9 CA 5 1 76 616.936 19.245 71 6.4247651
## 10 CA 6 1 73 351.687 50.532 64 5.8627415
## 11 CA 7 1 68 269.887 14.710 53 5.5980034
## 12 CA 11 1 71 269.510 95.575 58 5.5966053
## 13 CA 12 0 52 1440.639 1089.570 49 7.2728419
## 14 CA 16 1 79 252.336 69.563 54 5.5307617
## 15 CA 19 0 50 1470.674 1548.193 54 7.2934761
## 16 CA 23 1 64 140.486 100.956 56 4.9451079
## 17 CA 24 1 72 191.334 15.449 65 5.2540207
## 18 CA 27 1 68 398.597 15.239 54 5.9879508
## 19 CA 30 1 60 460.622 382.111 53 6.1325779
## 20 CA 32 1 67 457.410 20.608 49 6.1255803
## 21 CA 34 1 63 227.098 149.886 50 5.4253817
## 22 CA 36 1 54 532.897 218.696 47 6.2783279
## 23 CA 37 0 64 122.839 13.558 68 4.8108745
## 24 CA 40 0 67 1110.126 47.746 68 7.0122290
## 25 CA 42 0 64 494.487 11.889 65 6.2035208
## 26 CO 1 1 70 217.503 26.040 61 5.3822126
## 27 CO 2 1 63 721.647 85.095 50 6.5815363
## 28 CO 3 1 78 482.789 17.936 46 6.1795797
## 29 CO 5 0 75 183.229 0.930 67 5.2107368
## 30 CO 6 0 63 636.204 489.303 57 6.4555192
## 31 CT 2 1 64 727.919 246.903 49 6.5901899
## 32 CT 4 0 72 372.680 44.410 57 5.9207201
## 33 CT 6 0 66 399.370 128.853 53 5.9898882
## 34 DE 1 1 68 371.747 184.712 43 5.9182134
## 35 FL 1 1 67 210.940 23.912 27 5.3515739
## 36 FL 4 0 50 313.415 1069.699 36 5.7475281
## 37 FL 6 0 54 408.292 503.654 61 6.0119824
## 38 FL 14 1 55 971.883 777.988 47 6.8792353
## 39 FL 19 1 72 337.596 4.907 41 5.8218498
## 40 GA 1 1 67 337.048 40.461 39 5.8202252
## 41 GA 4 1 60 516.737 696.301 41 6.2475343
## 42 GA 5 1 78 101.540 6.047 68 4.6204529
## 43 GA 6 0 59 838.708 358.354 67 6.7318625
## 44 GA 7 1 65 382.281 60.694 29 5.9461560
## 45 GA 9 1 63 405.040 64.400 29 6.0039859
## 46 GA 10 1 64 193.123 6.760 35 5.2633271
## 47 ID 2 1 63 502.083 206.960 33 6.2187653
## 48 IL 4 1 50 359.942 348.339 44 5.8859429
## 49 IL 5 1 61 165.144 48.940 48 5.1068177
## 50 IL 6 0 74 281.229 26.555 68 5.6391692
## 51 IL 9 1 66 122.900 28.324 61 4.8113708
## 52 IL 11 1 65 239.158 41.259 46 5.4771242
## 53 IL 17 1 65 471.233 124.133 53 6.1553526
## 54 IL 19 1 64 193.205 16.241 45 5.2637520
## 55 IL 20 1 69 251.634 57.708 49 5.5279756
## 56 IL 21 1 53 394.412 69.486 54 5.9773960
## 57 IN 2 1 53 444.422 332.880 35 6.0967746
## 58 IN 5 1 56 689.086 244.985 35 6.5353661
## 59 IN 6 0 73 333.723 11.743 69 5.8103113
## 60 IN 8 1 62 551.484 130.243 42 6.3126130
## 61 IN 10 1 61 35.786 24.919 51 3.5775568
## 62 IA 5 0 64 420.730 115.701 47 6.0419912
## 63 IA 6 0 64 523.108 175.951 50 6.2597880
## 64 KS 2 1 73 388.866 119.263 46 5.9632349
## 65 KS 3 0 74 234.583 13.483 54 5.4578094
## 66 KS 4 1 64 545.755 149.035 43 6.3021703
## 67 KY 2 1 61 8.397 84.102 41 2.1278746
## 68 KY 3 1 70 371.431 4.931 53 5.9173632
## 69 KY 4 0 74 468.870 23.636 65 6.1503253
## 70 KY 7 1 59 411.699 432.403 55 6.0202923
## 71 ME 2 0 66 202.317 68.390 55 5.3098359
## 72 MD 3 1 73 354.701 18.893 54 5.8712749
## 73 MA 4 1 60 343.097 34.368 57 5.8380132
## 74 MA 5 1 84 344.930 15.396 47 5.8433414
## 75 MA 6 1 70 337.199 63.013 50 5.8206735
## 76 MA 10 1 67 235.946 121.056 51 5.4636030
## 77 MI 2 0 54 876.779 750.493 58 6.7762551
## 78 MI 3 1 57 600.940 164.856 45 6.3984952
## 79 MI 4 0 71 323.829 8.577 63 5.7802157
## 80 MI 7 1 76 150.594 1.310 55 5.0145874
## 81 MI 8 1 72 128.400 2.188 50 4.8551502
## 82 MI 9 0 70 450.801 14.866 62 6.1110258
## 83 MI 11 0 60 680.819 415.660 52 6.5232964
## 84 MI 12 1 54 434.200 143.886 39 6.0735054
## 85 MI 14 1 63 137.560 3.537 44 4.9240603
## 86 MI 15 1 64 234.435 7.993 45 5.4571781
## 87 MI 18 1 23 9.459 77.103 30 2.2469666
## 88 MN 2 1 42 152.295 623.776 49 5.0258193
## 89 MN 4 0 28 35.789 216.172 39 3.5776405
## 90 MN 5 0 28 16.915 281.455 35 2.8282008
## 91 MN 6 0 35 100.941 320.219 49 4.6145363
## 92 MN 8 0 25 7.743 157.802 40 2.0467892
## 93 MO 3 0 37 202.524 512.206 53 5.3108582
## 94 MO 6 1 41 198.617 341.344 50 5.2913785
## 95 MO 7 1 47 215.064 338.125 39 5.3709354
## 96 MO 8 1 42 516.239 768.792 45 6.2465696
## 97 MO 9 0 32 9.565 210.841 55 2.2581105
## 98 MT 1 0 39 58.204 250.276 52 4.0639539
## 99 MT 2 1 45 394.102 380.928 46 5.9766097
## 100 NE 1 1 33 96.278 221.530 44 4.5672398
## 101 NE 2 0 49 1158.294 858.762 58 7.0547032
## 102 NV 1 0 36 147.891 652.199 58 4.9964757
## 103 NJ 3 0 48 981.865 678.647 63 6.8894539
## 104 NJ 4 1 34 53.964 252.823 45 3.9883173
## 105 NJ 6 0 38 38.919 123.632 54 3.6614826
## 106 NJ 9 0 32 57.260 403.059 54 4.0476022
## 107 NM 1 1 49 576.677 559.134 46 6.3572822
## 108 NM 3 0 27 41.669 267.633 46 3.7297573
## 109 NY 3 0 43 90.892 364.087 60 4.5096722
## 110 NY 5 1 35 35.627 337.792 44 3.5731037
## 111 NY 15 1 39 162.157 602.942 67 5.0885649
## 112 NY 17 0 16 2.851 170.567 22 1.0476699
## 113 NY 22 1 29 10.427 411.056 43 2.3443985
## 114 NY 23 0 38 174.790 273.505 44 5.1635852
## 115 NY 24 1 28 15.936 151.276 42 2.7685807
## 116 NY 27 1 43 645.123 594.965 48 6.4694409
## 117 NY 30 0 43 310.704 802.886 55 5.7388406
## 118 NY 31 1 47 453.462 688.382 44 6.1169114
## 119 NC 1 0 35 16.758 82.147 54 2.8188758
## 120 NC 4 0 42 745.726 1006.641 56 6.6143584
## 121 NC 5 0 47 718.015 756.115 60 6.5764904
## 122 NC 6 1 38 583.013 738.088 39 6.3682094
## 123 NC 8 0 48 242.782 581.888 62 5.4921641
## 124 NC 10 1 39 44.329 302.215 35 3.7916391
## 125 ND 1 0 29 1.154 143.210 57 0.1432342
## 126 OH 2 1 28 13.961 125.682 38 2.6362677
## 127 OH 6 1 26 43.485 884.754 36 3.7724161
## 128 OH 9 0 19 47.945 244.030 47 3.8700545
## 129 OH 11 0 38 860.766 561.070 56 6.7578225
## 130 OH 14 0 25 13.244 419.005 48 2.5835447
## 131 OH 15 1 25 6.682 211.963 38 1.8994174
## 132 OH 17 0 23 2.391 96.003 38 0.8717117
## 133 OH 19 0 30 0.522 226.086 55 -0.6500877
## 134 OK 1 1 48 253.585 484.585 39 5.5356989
## 135 OK 2 0 35 81.634 358.705 53 4.4022460
## 136 OK 5 1 28 0.302 318.822 33 -1.1973283
## 137 OR 4 0 28 58.563 279.809 46 4.0701032
## 138 PA 1 0 24 1.643 234.957 34 0.4965239
## 139 PA 3 0 37 23.101 250.480 52 3.1398759
## 140 PA 6 0 37 12.002 121.435 62 2.4850733
## 141 PA 7 1 32 203.582 507.360 40 5.3160686
## 142 PA 8 0 43 507.682 1089.612 62 6.2298551
## 143 PA 13 1 33 60.672 225.412 44 4.1054821
## 144 PA 15 1 43 355.016 752.332 45 5.8721628
## 145 PA 23 1 38 106.463 336.675 44 4.6677976
## 146 RI 1 1 44 801.289 385.402 58 6.6862216
## 147 SC 1 1 36 82.035 118.702 39 4.4071460
## 148 SC 3 0 46 354.575 641.429 67 5.8709197
## 149 SC 4 0 48 630.913 1143.351 68 6.4471679
## 150 SD 1 0 28 199.420 632.105 53 5.2954130
## 151 TN 6 0 24 12.623 454.346 61 2.5355206
## 152 TX 1 0 38 94.477 505.611 53 4.5483565
## 153 TX 5 0 39 179.201 646.218 50 5.1885080
## 154 TX 6 1 32 17.414 654.260 38 2.8572745
## lexpendB shareA
## 1 2.16756701 97.40766907
## 2 5.99763775 60.88103867
## 3 1.12004757 97.01476288
## 4 3.26884627 92.40370178
## 5 4.09524441 72.61247253
## 6 3.06306386 96.38355255
## 7 5.26741982 78.22801971
## 8 2.04057074 98.80953217
## 9 2.95725131 96.97491455
## 10 3.92260695 87.43669128
## 11 2.68852758 94.83129120
## 12 4.55991125 73.82116699
## 13 6.99353838 56.93754959
## 14 4.24223280 78.38980865
## 15 7.34484386 48.71609116
## 16 4.61468458 58.18622971
## 17 2.73754430 92.52888489
## 18 2.72385788 96.31762695
## 19 5.94571114 54.65811920
## 20 3.02567935 95.68886566
## 21 5.00987482 60.24075317
## 22 5.38768244 70.90233612
## 23 2.60697675 90.05989838
## 24 3.86589527 95.87640381
## 25 2.47561359 97.65213776
## 26 3.25963378 89.30784607
## 27 4.44376850 89.45201874
## 28 2.88680983 96.41799164
## 29 -0.07257068 99.49500275
## 30 6.19298172 56.52599335
## 31 5.50899553 74.67198944
## 32 3.79346466 89.35241699
## 33 4.85867214 75.60632324
## 34 5.21879768 66.80581665
## 35 3.17438054 89.81826782
## 36 6.97513247 22.66009903
## 37 6.22188950 44.77151108
## 38 6.65671110 55.54026413
## 39 1.59066272 98.56731415
## 40 3.70033860 89.28211212
## 41 6.54578209 42.59858322
## 42 1.79956222 94.37943268
## 43 5.88152122 70.06387329
## 44 4.10584497 86.29854584
## 45 4.16511345 86.28152466
## 46 1.91102290 96.61801910
## 47 5.33252573 70.81136322
## 48 5.85317612 50.81909561
## 49 3.89059496 77.13981628
## 50 3.27921796 91.37219238
## 51 3.34370947 81.27017212
## 52 3.71986914 85.28655243
## 53 4.82135344 79.15013885
## 54 2.78753877 92.24573517
## 55 4.05539560 81.34491730
## 56 4.24112511 85.02127838
## 57 5.80778217 57.17494583
## 58 5.50119686 73.77233887
## 59 2.46325731 96.60082245
## 60 4.86940193 80.89514160
## 61 3.21563053 58.95066452
## 62 4.75100946 78.43133545
## 63 5.17020559 74.83030701
## 64 4.78133106 76.52899170
## 65 2.60142970 94.56475067
## 66 5.00418139 78.54963684
## 67 4.43203020 9.07793617
## 68 1.59554183 98.68982697
## 69 3.16277099 95.20087433
## 70 6.06935787 48.77360916
## 71 4.22522640 74.73652649
## 72 2.93879151 94.94290924
## 73 3.53712583 90.89505005
## 74 2.73410773 95.72720337
## 75 4.14334106 84.25509644
## 76 4.79625320 66.09095001
## 77 6.62073040 53.88029861
## 78 5.10507250 78.47259521
## 79 2.14908409 97.41972351
## 80 0.27002710 99.13761139
## 81 0.78298789 98.32450104
## 82 2.69907665 96.80758667
## 83 6.02986765 62.09138489
## 84 4.96902132 75.10993195
## 85 1.26327884 97.49321747
## 86 2.07856607 96.70294189
## 87 4.34514236 10.92742920
## 88 6.43579149 19.62384796
## 89 5.37607431 14.20418549
## 90 5.63997269 5.66913605
## 91 5.76900530 23.96737671
## 92 5.06134129 4.67727661
## 93 6.23872709 28.33573151
## 94 5.83289099 36.78358078
## 95 5.82341576 38.87712860
## 96 6.64482021 40.17327118
## 97 5.35110426 4.33972168
## 98 5.52256441 18.86799622
## 99 5.94261026 50.84990311
## 100 5.40055799 30.29438782
## 101 6.75549173 57.42498016
## 102 6.48034954 18.48429871
## 103 6.52010107 59.13025665
## 104 5.53268957 17.59005737
## 105 4.81730938 23.94264221
## 106 5.99908304 12.43920135
## 107 6.32638931 50.77226639
## 108 5.58961678 13.47194672
## 109 5.89739275 19.97718811
## 110 5.82243013 9.54075623
## 111 6.40182114 21.19425201
## 112 5.13912821 1.64400482
## 113 6.01872969 2.47388458
## 114 5.61132002 38.98995209
## 115 5.01910591 9.53041840
## 116 6.38850260 52.02235794
## 117 6.68821287 27.90111542
## 118 6.53434372 39.71313095
## 119 4.40851021 16.94353485
## 120 6.91437435 42.55535507
## 121 6.62819338 48.70771408
## 122 6.60406303 44.13084412
## 123 6.36627817 29.43989563
## 124 5.71113873 12.79174042
## 125 4.96431208 0.79936981
## 126 4.83375502 9.99763489
## 127 6.78530979 4.68467712
## 128 5.49729109 16.42092896
## 129 6.32984591 60.53905106
## 130 6.03788280 3.06397247
## 131 5.35641193 3.05609894
## 132 4.56437922 2.43002319
## 133 5.42091560 0.23035431
## 134 6.18329287 34.35319519
## 135 5.88250017 18.53889465
## 136 5.76463270 0.09463501
## 137 5.63410711 17.30728149
## 138 5.45940256 0.69441986
## 139 5.52337885 8.44393158
## 140 4.79937935 8.99450684
## 141 6.22922087 28.63552856
## 142 6.99357700 31.78388214
## 143 5.41792965 21.20775604
## 144 6.62317753 32.06002045
## 145 5.81911802 24.02479553
## 146 5.95428705 67.52296448
## 147 4.77661610 40.86690521
## 148 6.46369839 35.59975433
## 149 7.04171848 35.55913544
## 150 6.44905567 23.98244476
## 151 6.11885881 2.70317841
## 152 6.22576761 15.74385834
## 153 6.47113705 21.71030426
## 154 6.48350477 2.59262848coklureg <- lm(voteA~ expendA+expendB+prtystrA,data=vote1)
summary(coklureg)##
## Call:
## lm(formula = voteA ~ expendA + expendB + prtystrA, data = vote1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -26.661 -8.385 0.362 8.536 30.814
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.267190 4.416784 7.532 2.87e-12 ***
## expendA 0.034924 0.003369 10.365 < 2e-16 ***
## expendB -0.034924 0.003001 -11.636 < 2e-16 ***
## prtystrA 0.342514 0.087952 3.894 0.000142 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.12 on 169 degrees of freedom
## Multiple R-squared: 0.5687, Adjusted R-squared: 0.561
## F-statistic: 74.27 on 3 and 169 DF, p-value: < 2.2e-16\[voteavoteA=\beta_0+\beta_1log(1)+\beta_2log(1)+\beta_3prtystrA+u\]
\[voteavoteA=33.267+0.035log(1)+(-0.035)log(1)+0343prtystrA+u\] Buna göre A ve B’nin yaptığı harcamalar sonucu aynı oranda etkiler.
reg <- lm(log(voteA)~ expendA+expendB+prtystrA,data=vote1)
summary(reg)##
## Call:
## lm(formula = log(voteA) ~ expendA + expendB + prtystrA, data = vote1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.72557 -0.15588 0.01689 0.19425 0.67449
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.431e+00 9.919e-02 34.597 < 2e-16 ***
## expendA 7.985e-04 7.567e-05 10.553 < 2e-16 ***
## expendB -6.769e-04 6.740e-05 -10.044 < 2e-16 ***
## prtystrA 7.776e-03 1.975e-03 3.937 0.00012 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2497 on 169 degrees of freedom
## Multiple R-squared: 0.5437, Adjusted R-squared: 0.5356
## F-statistic: 67.11 on 3 and 169 DF, p-value: < 2.2e-16qt (0.01,169)## [1] -2.348615