# install.packages( "AER" ) # library( AER ) # library( dplyr ) # # # data( "CASchools" ) # # ## variable transformations # # CASchools <- mutate( CASchools, # student.teacher.ratio = students/teachers, # test.score = (math + read)/2 ) # # # plot( CASchools$expenditure, CASchools$test.score ) # # plot( CASchools$student.teacher.ratio, CASchools$test.score ) # # plot( CASchools$lunch, CASchools$test.score ) # # # dput( CASchools$test.score ) # dput( CASchools$expenditure ) # dput( CASchools$student.teacher.ratio ) # dput( CASchools$lunch ) test <- c(690.799987792969, 661.200012207031, 643.600006103516, 647.700012207031, 640.850006103516, 605.550018310547, 606.75, 609, 612.5, 612.650024414062, 615.75, 616.299987792969, 616.299987792969, 616.299987792969, 616.450012207031, 617.350006103516, 618.050018310547, 618.300018310547, 619.799987792969, 620.299987792969, 620.5, 621.400024414062, 621.75, 622.050018310547, 622.600006103516, 623.100006103516, 623.200012207031, 623.450012207031, 623.599975585938, 624.150024414062, 624.550018310547, 624.950012207031, 625.299987792969, 625.849975585938, 626.100006103516, 626.800018310547, 626.899993896484, 627.100006103516, 627.25, 627.299987792969, 628.25, 628.399993896484, 628.550018310547, 628.649993896484, 628.75, 629.800018310547, 630.350006103516, 630.400024414062, 630.549987792969, 630.549987792969, 631.050018310547, 631.399993896484, 631.850006103516, 631.899993896484, 631.950012207031, 632, 632.200012207031, 632.25, 632.449981689453, 632.850006103516, 632.950012207031, 633.049987792969, 633.149993896484, 633.650024414062, 633.899993896484, 634, 634.050018310547, 634.100006103516, 634.100006103516, 634.149993896484, 634.199981689453, 634.399993896484, 634.549987792969, 634.700012207031, 634.899993896484, 634.949981689453, 635.049987792969, 635.199981689453, 635.450012207031, 635.599975585938, 635.600006103516, 635.75, 635.950012207031, 636.100006103516, 636.5, 636.600006103516, 636.699981689453, 636.900024414062, 636.950012207031, 637, 637.100006103516, 637.350006103516, 637.650024414062, 637.949981689453, 637.950012207031, 638, 638.200012207031, 638.300018310547, 638.300018310547, 638.349975585938, 638.549987792969, 638.700012207031, 639.25, 639.300018310547, 639.350006103516, 639.5, 639.75, 639.799987792969, 639.850006103516, 639.899993896484, 640.100006103516, 640.150024414062, 640.5, 640.75, 640.900024414062, 641.100006103516, 641.449981689453, 641.449981689453, 641.549987792969, 641.800018310547, 642.199981689453, 642.200012207031, 642.399993896484, 642.75, 643.049987792969, 643.199981689453, 643.25, 643.400024414062, 643.399993896484, 643.5, 643.5, 643.699981689453, 643.700012207031, 644.199981689453, 644.200012207031, 644.399993896484, 644.450012207031, 644.450012207031, 644.5, 644.549987792969, 644.699981689453, 644.950012207031, 645.100006103516, 645.25, 645.549987792969, 645.550018310547, 645.600006103516, 645.75, 645.75, 646, 646.200012207031, 646.350006103516, 646.399993896484, 646.5, 646.549987792969, 646.700012207031, 646.899993896484, 646.949981689453, 647.049987792969, 647.25, 647.299987792969, 647.600006103516, 647.599975585938, 648, 648.200012207031, 648.25, 648.349975585938, 648.700012207031, 648.949981689453, 649.149993896484, 649.300018310547, 649.5, 649.699981689453, 649.849975585938, 650.449981689453, 650.549987792969, 650.600006103516, 650.649993896484, 650.899993896484, 650.899993896484, 651.149993896484, 651.200012207031, 651.350006103516, 651.399993896484, 651.450012207031, 651.800018310547, 651.850006103516, 651.899993896484, 652, 652.100006103516, 652.099975585938, 652.299987792969, 652.300018310547, 652.350006103516, 652.399993896484, 652.399993896484, 652.5, 652.850006103516, 653.099975585938, 653.399993896484, 653.5, 653.549987792969, 653.550018310547, 653.699981689453, 653.799987792969, 653.850006103516, 653.949981689453, 654.100006103516, 654.199981689453, 654.199981689453, 654.299987792969, 654.600006103516, 654.850006103516, 654.850006103516, 654.899993896484, 655.049987792969, 655.050018310547, 655.050018310547, 655.199981689453, 655.300018310547, 655.350006103516, 655.349975585938, 655.399993896484, 655.549987792969, 655.699981689453, 655.799987792969, 655.850006103516, 656.399993896484, 656.5, 656.550018310547, 656.650024414062, 656.700012207031, 656.800018310547, 656.800018310547, 657, 657, 657.149993896484, 657.400024414062, 657.5, 657.550018310547, 657.649993896484, 657.75, 657.799987792969, 657.899993896484, 658, 658.350006103516, 658.600006103516, 658.799987792969, 659.050018310547, 659.149993896484, 659.350006103516, 659.399993896484, 659.399993896484, 659.799987792969, 659.900024414062, 660.050018310547, 660.099975585938, 660.199981689453, 660.299987792969, 660.75, 660.949981689453, 661.349975585938, 661.450012207031, 661.599975585938, 661.600006103516, 661.849975585938, 661.850006103516, 661.850006103516, 661.899993896484, 661.899993896484, 661.950012207031, 662.399993896484, 662.400024414062, 662.450012207031, 662.5, 662.550018310547, 662.550018310547, 662.649993896484, 662.700012207031, 662.75, 662.899993896484, 663.350006103516, 663.449981689453, 663.5, 663.850006103516, 663.850006103516, 663.899993896484, 664, 664, 664.149993896484, 664.149993896484, 664.299987792969, 664.400024414062, 664.449981689453, 664.700012207031, 664.75, 664.949981689453, 664.950012207031, 665.100006103516, 665.200012207031, 665.350006103516, 665.650024414062, 665.899993896484, 665.950012207031, 666, 666.050018310547, 666.100006103516, 666.150024414062, 666.149993896484, 666.449981689453, 666.550018310547, 666.600006103516, 666.649993896484, 666.649993896484, 666.699981689453, 666.850006103516, 666.850006103516, 667.149993896484, 667.199981689453, 667.450012207031, 667.450012207031, 667.600006103516, 668, 668.100006103516, 668.399993896484, 668.600006103516, 668.649993896484, 668.799987792969, 668.899993896484, 668.950012207031, 669.099975585938, 669.300018310547, 669.300018310547, 669.350006103516, 669.349975585938, 669.799987792969, 669.850006103516, 669.950012207031, 670, 670.699981689453, 671.25, 671.299987792969, 671.600006103516, 671.600006103516, 671.649993896484, 671.699981689453, 671.75, 671.899993896484, 671.899993896484, 671.949981689453, 672.049987792969, 672.050018310547, 672.299987792969, 672.349975585938, 672.450012207031, 672.550018310547, 672.699981689453, 673.049987792969, 673.25, 673.299987792969, 673.549987792969, 673.549987792969, 673.899993896484, 674.25, 675.399993896484, 675.700012207031, 676.149993896484, 676.549987792969, 676.600006103516, 676.850006103516, 676.949981689453, 677.25, 677.950012207031, 678.050018310547, 678.399993896484, 678.799987792969, 679.399993896484, 679.5, 679.649993896484, 679.75, 679.800018310547, 680.050018310547, 680.450012207031, 681.299987792969, 681.299987792969, 681.600006103516, 681.899993896484, 682.149993896484, 682.450012207031, 682.549987792969, 682.649993896484, 683.350006103516, 683.399993896484, 684.300018310547, 684.350006103516, 684.800018310547, 684.950012207031, 686.050018310547, 686.699981689453, 687.549987792969, 689.099975585938, 691.049987792969, 691.350006103516, 691.899993896484, 693.950012207031, 694.25, 694.800018310547, 695.199981689453, 695.299987792969, 696.550018310547, 698.199981689453, 698.25, 698.449981689453, 699.100006103516, 700.300018310547, 704.300018310547, 706.75, 645, 672.200012207031, 655.75) per.student.exp <- c(6384.9111328125, 5099.380859375, 5501.95458984375, 7101.8310546875, 5235.98779296875, 5580.14697265625, 5253.3310546875, 4565.74609375, 5355.54833984375, 5036.21142578125, 4547.6923828125, 5447.34521484375, 6567.1494140625, 4818.61279296875, 5621.4560546875, 6026.35986328125, 6723.23779296875, 5589.88525390625, 5064.61572265625, 5433.59326171875, 5725.5634765625, 4542.10498046875, 5107.08642578125, 4659.66162109375, 4555.46435546875, 5415.15283203125, 4997.87158203125, 5223.912109375, 5139.16455078125, 4614.251953125, 5342.2333984375, 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21.0372093023256, 19.9246234975196, 19.0098568462085, 23.8222222222222, 19.3690847073363, 19.8285714285714, 15.2588552686217, 17.1612903225806, 21.8133333333333, 19.0747133426306, 25.7851231540294, 18.212614444761, 18.166064157175, 16.972972972973, 21.5008728866294, 20.6, 16.9902909475106, 20.7795456185188, 15.5124660296439, 19.8850574712644, 21.3988234659086, 20.497512048797, 19.3637581871342, 17.659575184744, 21.0179561441264, 19.0556494863121, 22.5384615384615, 21.1078711835393, 20.0513538034642, 14.2017629244119, 18.4768683274021, 18.6354166666667, 20.9459459459459, 21.0854825556009, 18.6928802180985, 20.8680790498909, 19.8255776972916, 19.75, 19.5, 18.3908050008928, 18.7867641789278, 19.7701804862839, 19.3333333333333, 21.4639175257732, 23.0849235566616, 21.0629924423187, 18.6868694069167, 20.7702354006901, 19.3055560669781, 20.1328025598196, 20.6696349496271, 22.2815533980583, 20.6002719936284, 20.8273387010791, 19.2249242350677, 17.654770182971, 17, 16.4977277151551, 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14.7058821982578, 19.040767037723, 20.8919540229885, 19.8385070816457, 19.5219120539036, 20.6862176489988, 18.1818181818182, 18.8922429984947, 24.8888888888889, 18.5806451612903, 18.04, 17.7339901477833, 21.4545454545455, 19.9234247876565, 20.3394199785177, 22.5460750853242, 21.1034424809305, 18.1974254885637, 20.1076808229449, 19.1598356162563, 19.5454548278788, 20.8888888888889, 18.3915018503307, 19.1799030878106, 19.3977064458372, 21.6782728550361, 19.2888888888889, 20.3492739161628, 20.9641618174683, 19.4603902706826, 19.2857151615377, 20.9197933397877, 20.9002141266009, 20.5957446808511, 19.375, 19.9512232540535, 18.8497340903631, 18.1178712480167, 19.1834085642053, 22, 21.5841576006235, 20.3888888888889, 16.2931029124719, 18.2777821171534, 19.3747164524626, 18.9090909090909, 16.406926135985, 15.5913975296964, 18.7069414043726, 18.3298532783061, 17.9023506490849, 18.9115648712309, 20.3249661880789, 20.0245691799889, 24, 17.6078431372549, 19.3485337211153, 19.6784651300815, 18.7286056582498, 15.8823532381685, 20.0549127852273, 17.9882527208952, 16.9662928620368, 19.2393743182499, 19.1958581618667, 19.5990618887251, 20.5434782608696, 18.5884843645164, 15.6041861492374, 15.2930401861936, 17.6553674218923, 17.5797611320959, 22.3333333333333, 18.75, 18.1024099158844, 20.2564097610765, 18.8020749650075, 18.7723051893905, 20.405210291402, 18.6507930861339, 20.7070715049617, 22, 17.6997754983767, 21.4832888462028, 16.7010312562339, 19.5756726978814, 17.258064516129, 17.3752559601841, 17.3493114406599, 16.2622843263867, 17.7004542663956, 20.1288155606007, 18.2653941392753, 14.5421361585846, 19.1526116141991, 17.3657415845815, 15.1389850328556, 17.8426602888311, 15.407041884931, 18.8653402295668, 16.4741337274612, 17.8626250782683, 21.8858564937366, 20.2, 19.0364022585948) free.lunch <- c(2.04080009460449, 47.9166984558105, 76.3226013183594, 77.049201965332, 78.427001953125, 86.9564971923828, 94.6237030029297, 100, 93.1398010253906, 87.3163986206055, 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