Y = ax 1 b1 X 2 b2...x k bk e u InY = Ina + b 1 InX 1 + b 2 InX 2 +...+ b k InX k + u X 1 Y b = ab 1 X 1 1 b 1 X 2 2...X bk k e u = b 1 (ax b1 1 X b2 2...X bk k e u ) / X 1 = b 1 Y / X 1 X 1 X 1 q YX1 = Y X 1 X 1 Y q YX1 = b 1
InY = Ina + b 1 InX 1 + b 2 InX 2 +...+ b k InX k + b k+1 X K+1 +...+ b q X q + u
InY = a 1 InX 1 + a 2 InX 2 + a 3 InX 3 + a 4 InX 4 + d 1 D 1 +U
GDP 0.253 (3.23)** -0.291 (6.67)** 12.115 (1.05) 10.527 (0.92) -0.002 (0.01) _cons -43.006 (0.81) R2 0.32 N 108 * p<0.05; ** p<0.01
GDP 1.588 (11.31)** -1.278 (5.34)** 3.812 (2.17)* 4.226 (2.31)* -0.272 (5.47)** 2.106 (6.32)** -3.696 (5.76)** 4.650 (8.73)** 0.791 (3.02)** 1.304 (4.38)** -3.792 (2.76)** 3.411 (10.85)** 1.301 (4.83)** _cons -53.543 (5.83)** R2 0.99 N 108
Variable Obs Mean Std. Dev. Min Max GDP 12 12548.12 4191.977 6781.19 19261.54 ~ 12 97.11917 10.69143 81.82 113.24 12 1.048314.1153625.9010177 1.23075 ~ 12 14.17743 1.459845 12.3489 17.2461 ~ 12 1200007 693999.2 448782 2829821 12.0833333.2886751 0 1 Source SS df MS Number of obs = 12 F(5, 6) = 34.72 Model 2.93228609 5.586457217 Prob > F = 0.0002 Residual.10134125 6.016890208 R-squared = 0.9666 Adj R-squared = 0.9388 Total 3.03362734 11.275784303 Root MSE =.12996 ~ Coef. Std. Err. t P> t [95% Conf. Interval] GDP.9520197.8679716 1.10 0.315-1.17183 3.07587 ~.557806 6.530264 0.09 0.935-15.42117 16.53679 -.8698961 6.51889-0.13 0.898-16.82105 15.08125 ~ 1.026013.6426238 1.60 0.161 -.5464308 2.598457 -.2784234.1653722-1.68 0.143 -.6830747.1262279 _cons -.2728607 28.55692-0.01 0.993-70.14912 69.6034
Variable Obs Mean Std. Dev. Min Max GDP 12 1192336 156265.9 948796.1 1426540 ~ 12 95.65808 9.82532 80.924 109.039 12 1.062976.1109702.9291612 1.244377 ~ 12.0938583.0187373.0709.1267 ~ 12 2069526 452261.2 1459333 2755313 12.0833333.2886751 0 1 Source SS df MS Number of obs = 12 F(5, 6) = 23.66 Model.519062385 5.103812477 Prob > F = 0.0007 Residual.02632726 6.004387877 R-squared = 0.9517 Adj R-squared = 0.9115 Total.545389645 11.049580877 Root MSE =.06624 Coef. Std. Err. t P> t [95% Conf. Interval] GDP 11.06859 2.60297 4.25 0.005 4.699354 17.43783 -.1395512.264593-0.53 0.617 -.786987.5078846 1.021368 2.619198 0.39 0.710-5.387579 7.430315-12.00036 4.113821-2.92 0.027-22.06652-1.934199 -.2738573.0789499-3.47 0.013 -.4670408 -.0806738 _cons -85.95013 25.14751-3.42 0.014-147.4839-24.41639
Variable Obs Mean Std. Dev. Min Max GDP 12 1842.612 256.6185 1375.87 2192.153 ~ 12 100.2791 10.46497 89.325 120.175 12 1.013559.0999327.8552527 1.127232 ~ 12 13.03707 1.740989 10.2528 15.0933 ~ 12 472534.3 195614.6 260214 925975 12.0833333.2886751 0 1 Source SS df MS Number of obs = 12 F(5, 6) = 31.80 Model 1.51130842 5.302261683 Prob > F = 0.0003 Residual.057025405 6.009504234 R-squared = 0.9636 Adj R-squared = 0.9333 Total 1.56833382 11.142575802 Root MSE =.09749 Coef. Std. Err. t P> t [95% Conf. Interval] GDP 1.581736.4875137 3.24 0.018.3888332 2.774639 10.68854 4.280096 2.50 0.047.2155228 21.16156 9.26098 4.424324 2.09 0.081-1.564951 20.08691.2374337.3796709 0.63 0.555 -.6915876 1.166455 -.3354623.1210107-2.77 0.032 -.6315649 -.0393597 _cons -48.74367 18.91867-2.58 0.042-95.03599-2.451348
Variable Obs Mean Std. Dev. Min Max GDP ~ 12 292.2683 61.27351 197.68 380.59 ~ 12 86.14833 9.020058 75.64 99.98 12 1.180277.1204942 1.010811 1.331306 ~ 12 69.90867 7.011412 63.48 83.5731 ~ 12 141138.6 45492.2 76896 227962 12.0833333.2886751 0 1 Source SS df MS Number of obs = 12 F(5, 6) = 22.40 Model 1.15328585 5.23065717 Prob > F = 0.0008 Residual.061780112 6.010296685 R-squared = 0.9492 Adj R-squared = 0.9068 Total 1.21506596 11.110460542 Root MSE =.10147 Coef. Std. Err. t P> t [95% Conf. Interval] GDP 2.470463.5520333 4.48 0.004 1.119686 3.82124 -.1211447.4955749-0.24 0.815-1.333773 1.091483 ~ 8.648822 4.597937 1.88 0.109-2.601925 19.89957 10.94066 4.755317 2.30 0.061 -.6951857 22.5765 -.3986708.1226847-3.25 0.017 -.6988695 -.098472 _cons -41.87367 20.43713-2.05 0.086-91.88152 8.134187
Variable Obs Mean Std. Dev. Min Max GDP ~ 12 74569.52 19479.78 47134.73 106439.8 ~ 12 156.0025 50.21777 104.05 246.84 12.7025078.1986204.4163831.967804 ~ 12 2.1384.4405458 1.4957 2.8511 ~ 12 64464.17 10542.58 47520 87967 12.0833333.2886751 0 1 Source SS df MS Number of obs = 12 F(5, 6) = 28.40 Model.272942487 5.054588497 Prob > F = 0.0004 Residual.011533403 6.001922234 R-squared = 0.9595 Adj R-squared = 0.9257 Total.28447589 11.025861445 Root MSE =.04384 Coef. Std. Err. t P> t [95% Conf. Interval] GDP.511339.2163248 2.36 0.056 -.0179887 1.040667.573736.1698535 3.38 0.015.1581193.9893526 2.077791 1.784834 1.16 0.289-2.28954 6.445121 1.726726 1.827292 0.94 0.381-2.744497 6.197949 -.1083386.0544046-1.99 0.094 -.2414618.0247846 _cons -4.796103 8.258142-0.58 0.583-25.00305 15.41084
Variable Obs Mean Std. Dev. Min Max GDP ~ 12 14726.63 747.8879 13271.1 15961.65 ~ 12 212.4317 17.33756 184 236.71 12.4771685.0403296.4294299.55 ~ 12 101.3537 13.62996 79.7905 117.7535 ~ 12 753271.5 87222.4 565887 891668 12.0833333.2886751 0 1 Source SS df MS Number of obs = 12 F(5, 6) = 25.30 Model.155217223 5.031043445 Prob > F = 0.0006 Residual.007361804 6.001226967 R-squared = 0.9547 Adj R-squared = 0.9170 Total.162579028 11.014779912 Root MSE =.03503 Coef. Std. Err. t P> t [95% Conf. Interval] GDP 3.910873.9553255 4.09 0.006 1.573275 6.24847.0668429.1997426 0.33 0.749 -.4219096.5555954 -.2543234 1.549699-0.16 0.875-4.046301 3.537654 1.705449 1.690008 1.01 0.352-2.429851 5.84075 -.231829.0440164-5.27 0.002 -.3395333 -.1241247 _cons -21.66171 9.468939-2.29 0.062-44.83137 1.507953
Variable Obs Mean Std. Dev. Min Max GDP ~ 12 1596.12 65.22482 1471.09 1705 ~ 12 111.0133 11.1343 96.68 127.97 12.9152987.0909023.7931499 1.04158 ~ 12 132.7079 16.84337 102.5996 161.2446 ~ 12 197851.9 24833.69 140099 221945 12.0833333.2886751 0 1 Source SS df MS Number of obs = 12 F(5, 6) = 10.08 Model.181811578 5.036362316 Prob > F = 0.0070 Residual.02164792 6.003607987 R-squared = 0.8936 Adj R-squared = 0.8049 Total.203459498 11.018496318 Root MSE =.06007 Coef. Std. Err. t P> t [95% Conf. Interval] GDP.9247671 1.302589 0.71 0.504-2.262554 4.112088.2552105.3546954 0.72 0.499 -.612698 1.123119 1.694246 2.778525 0.61 0.564-5.104559 8.493051 2.304465 2.963691 0.78 0.466-4.947425 9.556355 -.2578325.0710286-3.63 0.011 -.4316332 -.0840317 _cons -3.613573 15.07608-0.24 0.819-40.50342 33.27627
Variable Obs Mean Std. Dev. Min Max GDP ~ 12 2560.827 123.464 2379.69 2734.26 ~ 12 106.585 6.67807 96.37 116.22 12.9480849.0599128.8675744 1.044931 ~ 12 132.7106 16.84393 102.5996 161.2446 ~ 12 114315.5 15866.85 80772 140254 12.0833333.2886751 0 1 Source SS df MS Number of obs = 12 F(5, 6) = 8.00 Model.209222741 5.041844548 Prob > F = 0.0125 Residual.031385246 6.005230874 R-squared = 0.8696 Adj R-squared = 0.7609 Total.240607987 11.021873453 Root MSE =.07232 Coef. Std. Err. t P> t [95% Conf. Interval] GDP.2712726 1.466398 0.18 0.859-3.316874 3.859419.4678765.2931934 1.60 0.162 -.2495419 1.185295 1.805234 3.307273 0.55 0.605-6.287372 9.89784.6494937 3.383721 0.19 0.854-7.630174 8.929161 -.3409733.0904819-3.77 0.009 -.5623746 -.119572 _cons -1.136692 16.04153-0.07 0.946-40.38891 38.11553
Variable Obs Mean Std. Dev. Min Max GDP ~ 12 1985.127 69.75619 1841.5 2060.87 ~ 12 106.4608 6.662374 95.89 115.58 12.9492066.0603017.8708217 1.050162 ~ 12 132.7106 16.84393 102.5996 161.2446 ~ 12 128969.3 28303.5 85179 178580 12.0833333.2886751 0 1 Source SS df MS Number of obs = 12 F(5, 6) = 13.68 Model.525827763 5.105165553 Prob > F = 0.0031 Residual.04613811 6.007689685 R-squared = 0.9193 Adj R-squared = 0.8521 Total.571965873 11.051996898 Root MSE =.08769 Coef. Std. Err. t P> t [95% Conf. Interval] GDP.7435898 3.161159 0.24 0.822-6.991488 8.478667.5704454.513168 1.11 0.309 -.6852315 1.826122 3.806313 4.125029 0.92 0.392-6.287269 13.89989.7621682 5.000029 0.15 0.884-11.47246 12.9968 -.3629644.1113469-3.26 0.017 -.6354204 -.0905085 _cons -14.37631 31.05691-0.46 0.660-90.36984 61.61722
Source SS df MS Number of obs = 108 F(5, 102) = 9.52 Model 44.9792649 5 8.99585299 Prob > F = 0.0000 Residual 96.3656086 102.944760868 R-squared = 0.3182 Adj R-squared = 0.2848 Total 141.344874 107 1.32098013 Root MSE =.97199 Coef. Std. Err. t P> t [95% Conf. Interval] GDP.2526574.0781313 3.23 0.002.0976844.4076304 -.2906625.0435581-6.67 0.000 -.3770598 -.2042652 12.11545 11.52387 1.05 0.296-10.7421 34.973 10.52657 11.48438 0.92 0.362-12.25265 33.30578 -.0021178.3655688-0.01 0.995 -.7272219.7229862 _cons -43.00583 52.78905-0.81 0.417-147.7127 61.70101
Source SS df MS Number of obs = 108 F(13, 94) = 665.43 Model 139.825497 13 10.7558074 Prob > F = 0.0000 Residual 1.51937698 94.016163585 R-squared = 0.9893 Adj R-squared = 0.9878 Total 141.344874 107 1.32098013 Root MSE =.12714 Coef. Std. Err. t P> t [95% Conf. Interval] GDP 1.588445.1404547 11.31 0.000 1.309569 1.867321-1.278109.2393313-5.34 0.000-1.753307 -.8029115 3.812334 1.757284 2.17 0.033.323206 7.301462 4.226496 1.830402 2.31 0.023.5921888 7.860802 -.2720524.0497263-5.47 0.000 -.370785 -.1733197 2.106373.3334624 6.32 0.000 1.444275 2.76847-3.696242.6414299-5.76 0.000-4.969816-2.422668 4.650314.5327059 8.73 0.000 3.592613 5.708014.7913953.2620214 3.02 0.003.2711457 1.311645 1.303704.297563 4.38 0.000.712886 1.894523-3.791913 1.375454-2.76 0.007-6.52291-1.060917 3.411129.3145276 10.85 0.000 2.786627 4.035631 1.300932.2692331 4.83 0.000.7663637 1.835501 _cons -53.54337 9.17923-5.83 0.000-71.76895-35.3178