Dataframe Ames
Luis Reynoso
09 abril, 2024
1 Dataframe Ames
#install.packages("modeldata")
dim(ames)## [1] 2930 74El conjunto de datos Ames proporcionado por el paquete modeldata contiene información sobre propiedades residenciales vendidas en Ames, Iowa, entre 2006 y 2010. Este conjunto de datos se utiliza comúnmente en la práctica de la ciencia de datos y el análisis predictivo para comprender las características que influyen en el precio de las viviendas y para construir modelos de predicción de precios de viviendas.
El conjunto de datos contiene información sobre 2930 propiedades en Ames, Iowa, incluidas columnas relacionadas con:
- Características de la casa (dormitorios, garaje, chimenea, piscina, porche, etc.)
- ubicación (barrio) y latitud-longitud.
- información del lote (zonificación, forma, tamaño, etc.)
- calificaciones de condición y calidad
- precio de venta
Aquí hay una explicación de los atributos más importantes del conjunto de datos “Ames”:
Order: Un identificador único para cada fila del conjunto de datos.
PID: Un identificador único para cada propiedad.
MS_SubClass: La clase de construcción de la propiedad.
MS_Zoning: La clasificación de zonificación de la propiedad.
Lot_Frontage: La longitud de la línea de frente de la propiedad (en pies).
Lot_Area: El tamaño del lote de la propiedad (en pies cuadrados).
Street: El tipo de acceso a la propiedad (pavimentado o no pavimentado).
Alley: Tipo de acceso a través del callejón (pavimentado, no pavimentado o sin callejón).
Lot_Shape: Forma general del lote de la propiedad.
Land_Contour: Contorno plano de la propiedad.
Utilities: Disponibilidad de servicios públicos (agua, electricidad, gas, etc.).
Lot_Configuration: Configuración del lote en relación con la vecindad.
Land_Slope: Pendiente de la propiedad.
Neighborhood: Vecindario en el que se encuentra la propiedad.
Condition_1 y Condition_2: Condiciones de proximidad a diversas características (carreteras, ferrocarriles, etc.).
Bldg_Type: Tipo de vivienda (unifamiliar, dúplex, etc.).
House_Style: Estilo de la casa (un piso, dos pisos, etc.).
Overall_Qual: Calidad general de la casa.
Overall_Cond: Condición general de la casa.
Year_Built: Año de construcción de la casa.
Year_Remod_Add: Año de remodelación de la casa.
Roof_Style y Roof_Matl: Estilo y material del techo.
Exterior_1st y Exterior_2nd: Revestimiento exterior de la casa.
Mas_Vnr_Type: Tipo de revestimiento de mampostería.
Mas_Vnr_Area: Área de revestimiento de mampostería en pies cuadrados.
Exter_Qual y Exter_Cond: Calidad y condición del material exterior.
Foundation: Tipo de cimentación de la casa.
Bsmt_Qual y Bsmt_Cond: Calidad y condición del sótano.
Bsmt_Exposure: Exposición del sótano.
BsmtFin_Type_1 y BsmtFin_Type_2: Calidad del acabado del sótano.
BsmtFin_SF_1 y BsmtFin_SF_2: Área acabada del sótano (en pies cuadrados).
Bsmt_Unf_SF: Área sin terminar del sótano (en pies cuadrados).
Total_Bsmt_SF: Área total del sótano (en pies cuadrados).
Heating y Heating_QC: Tipo y calidad del sistema de calefacción.
Central_Air: Si la casa tiene aire acondicionado central.
Electrical: Tipo de sistema eléctrico.
1st_Flr_SF y 2nd_Flr_SF: Área del primer y segundo piso (en pies cuadrados).
Low_Qual_Fin_SF: Área de acabado de baja calidad (en pies cuadrados).
Gr_Liv_Area: Área habitable sobre el nivel del suelo (en pies cuadrados).
Bsmt_Full_Bath y Bsmt_Half_Bath: Cantidad de baños completos y medios en el sótano.
Full_Bath y Half_Bath: Cantidad de baños completos y medios sobre el nivel del suelo.
Bedroom_AbvGr: Cantidad de dormitorios sobre el nivel del suelo.
Kitchen_AbvGr: Cantidad de cocinas sobre el nivel del suelo.
Kitchen_Qual: Calidad de la cocina.
TotRms_AbvGrd: Cantidad total de habitaciones sobre el nivel del suelo (excluyendo baños).
Functional: Funcionalidad de la casa.
Fireplaces: Cantidad de chimeneas.
Fireplace_Qu: Calidad de la chimenea.
Garage_Type: Ubicación del garaje.
Garage_Yr_Blt: Año de construcción del garaje.
Garage_Finish: Acabado interior del garaje.
Garage_Cars: Capacidad del garaje en términos de número de autos.
Garage_Area: Área del garaje (en pies cuadrados).
Garage_Qual y Garage_Cond: Calidad y condición del garaje.
Paved_Drive: Tipo de entrada pavimentada.
Wood_Deck_SF, Open_Porch_SF, Enclosed_Porch, 3Ssn_Porch, y Screen_Porch: Área de porches y terrazas (en pies cuadrados).
Pool_Area: Área de la piscina (en pies cuadrados).
Pool_QC: Calidad de la piscina.
Fence: Calidad de la valla.
Misc_Feature: Otras características no cubiertas por los campos anteriores.
Misc_Val: Valor de las características adicionales.
Mo_Sold y Yr_Sold: Mes y año de venta de la casa.
Sale_Type: Tipo de venta.
Sale_Condition: Condición de venta.
Sale_Price: Precio de venta de la propiedad (variable objetivo).
Este conjunto de datos contiene una amplia gama de características que describen diferentes aspectos de las propiedades residenciales en Ames. Es comúnmente utilizado para la construcción y evaluación de modelos de regresión para predecir el precio de venta de las viviendas.
2 Grafico
2.1 Ploteo básico
plot(ames$Longitude, ames$Latitude, xlab = "Longitud",
ylab = "Latitud",
main = "Ubicación de propiedades en Ames",
col = as.integer(ames$Neighborhood))
2.2 leaflet de un barrio
levels(ames$Neighborhood)## [1] "North_Ames"
## [2] "College_Creek"
## [3] "Old_Town"
## [4] "Edwards"
## [5] "Somerset"
## [6] "Northridge_Heights"
## [7] "Gilbert"
## [8] "Sawyer"
## [9] "Northwest_Ames"
## [10] "Sawyer_West"
## [11] "Mitchell"
## [12] "Brookside"
## [13] "Crawford"
## [14] "Iowa_DOT_and_Rail_Road"
## [15] "Timberland"
## [16] "Northridge"
## [17] "Stone_Brook"
## [18] "South_and_West_of_Iowa_State_University"
## [19] "Clear_Creek"
## [20] "Meadow_Village"
## [21] "Briardale"
## [22] "Bloomington_Heights"
## [23] "Veenker"
## [24] "Northpark_Villa"
## [25] "Blueste"
## [26] "Greens"
## [27] "Green_Hills"
## [28] "Landmark"
## [29] "Hayden_Lake"boxplot(ames$Lot_Frontage)
summary(ames$Lot_Frontage)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 43.00 63.00 57.65 78.00 313.00ames7 <- ames %>%
filter(Lot_Frontage >= 100)
viviendasPrecioAlto <- ames %>%
filter(Sale_Price >= 213500)
viviendasPrecioAlto <- viviendasPrecioAlto %>%
select(Neighborhood, Sale_Price)
tablaPorBarrio <- viviendasPrecioAlto%>%
group_by(Neighborhood)%>%
summarise( cantidad = n(),
Minimo_Valor = min(Sale_Price,na.rm = TRUE),
Maximo_Valor = max(Sale_Price,na.rm = TRUE),
Valor_Promedio = mean(Sale_Price,na.rm = TRUE))
ames$Latitude## [1] 42.05403 42.05301 42.05266 42.05125 42.06090 42.06078 42.06298 42.06073
## [9] 42.06112 42.05919 42.05848 42.05742 42.05815 42.05727 42.05917 42.06124
## [17] 42.06035 42.05885 42.05667 42.05445 42.05035 42.05027 42.04930 42.05515
## [25] 42.05459 42.05523 42.05340 42.05638 42.05532 42.05183 42.05168 42.05168
## [33] 42.04967 42.05068 42.05068 42.04981 42.06235 42.06211 42.06113 42.06129
## [41] 42.06087 42.06081 42.06088 42.06030 42.05962 42.05839 42.05860 42.05710
## [49] 42.05716 42.05825 42.05718 42.06193 42.06257 42.06230 42.06144 42.06098
## [57] 42.06119 42.06094 42.05710 42.05439 42.05324 42.05172 42.05167 42.05246
## [65] 42.05244 42.05091 42.05306 42.05183 42.05165 42.05008 42.05235 42.05143
## [73] 42.03625 42.03611 42.03603 42.03548 42.03666 42.03459 42.03470 42.03663
## [81] 42.03455 42.03468 42.03608 42.03654 42.03479 42.03569 42.03486 42.03457
## [89] 42.03533 42.03460 42.04825 42.04682 42.04577 42.04745 42.04809 42.04857
## [97] 42.04790 42.04788 42.04778 42.04717 42.04615 42.04615 42.04642 42.04611
## [105] 42.04703 42.04638 42.04257 42.04370 42.03456 42.04861 42.04632 42.04304
## [113] 42.04331 42.04331 42.04333 42.04382 42.04382 42.04657 42.04221 42.04336
## [121] 42.03909 42.03897 42.04033 42.04115 42.04039 42.04184 42.03921 42.03921
## [129] 42.03854 42.03526 42.03548 42.03594 42.03610 42.03742 42.04849 42.04594
## [137] 42.04951 42.04745 42.04489 42.04398 42.04291 42.04308 42.04485 42.04397
## [145] 42.04405 42.04418 42.04488 42.04359 42.04231 42.04040 42.04137 42.03851
## [153] 42.03984 42.03844 42.03852 42.03825 42.03813 42.03587 42.03721 42.04008
## [161] 42.04112 42.03587 42.03594 42.03476 42.03485 42.03475 42.03485 42.03687
## [169] 42.03709 42.03331 42.03213 42.03136 42.03138 42.03038 42.03328 42.03364
## [177] 42.03239 42.03128 42.03031 42.03038 42.03047 42.03039 42.03033 42.02810
## [185] 42.02915 42.02815 42.02808 42.03005 42.02816 42.02916 42.02817 42.03364
## [193] 42.03019 42.03362 42.03356 42.03360 42.03366 42.03363 42.03156 42.03134
## [201] 42.03230 42.02799 42.02889 42.02887 42.02691 42.02069 42.02414 42.02674
## [209] 42.03345 42.03243 42.02826 42.02675 42.02616 42.02526 42.02282 42.03445
## [217] 42.03339 42.03339 42.03301 42.03237 42.02987 42.03069 42.02992 42.02973
## [225] 42.03052 42.03119 42.03136 42.03128 42.03008 42.03009 42.03387 42.03216
## [233] 42.02655 42.02467 42.02308 42.02823 42.02653 42.02421 42.02517 42.02526
## [241] 42.02475 42.02413 42.02502 42.02416 42.03374 42.03208 42.03378 42.03068
## [249] 42.03112 42.02575 42.02461 42.02460 42.02460 42.03060 42.02985 42.02432
## [257] 42.02132 42.01841 42.01867 42.02219 42.02204 42.02139 42.02113 42.01866
## [265] 42.01907 42.01612 42.01872 42.01775 42.01628 42.01625 42.01404 42.01409
## [273] 42.01402 42.02036 42.02125 42.02104 42.02063 42.02116 42.02031 42.01985
## [281] 42.01963 42.02020 42.02179 42.02158 42.01773 42.02267 42.02270 42.02209
## [289] 42.01774 42.01780 42.01639 42.01909 42.01909 42.01623 42.01494 42.01468
## [297] 42.01100 42.01061 42.00935 42.00934 42.01080 42.02277 42.02141 42.02147
## [305] 42.02146 42.02265 42.02133 42.02152 42.00869 41.99706 41.99705 41.99607
## [313] 41.99478 41.99401 41.99774 41.99535 41.99528 41.99428 41.99353 41.99549
## [321] 41.99435 41.99299 41.99321 41.99093 41.99325 41.99100 41.99186 41.99176
## [329] 41.99188 41.99221 41.99212 41.99170 41.99182 41.99156 41.98873 41.98894
## [337] 41.98766 41.98665 41.99130 41.98985 41.98918 42.05304 42.05139 42.04932
## [345] 42.05996 42.06329 42.06090 42.06296 42.06060 42.06290 42.06198 42.06163
## [353] 42.06118 42.05928 42.05913 42.05916 42.05827 42.05806 42.05965 42.05819
## [361] 42.05793 42.05817 42.05785 42.05820 42.05875 42.05924 42.06027 42.05982
## [369] 42.05844 42.05680 42.05353 42.05541 42.05508 42.05557 42.05184 42.05251
## [377] 42.05210 42.05272 42.05288 42.05291 42.05035 42.04965 42.04939 42.04911
## [385] 42.05162 42.05038 42.04941 42.05317 42.05235 42.05245 42.05267 42.04891
## [393] 42.05640 42.05463 42.05523 42.05518 42.05515 42.05337 42.05331 42.05331
## [401] 42.05644 42.05646 42.05276 42.05234 42.05168 42.05166 42.05182 42.05182
## [409] 42.05062 42.05071 42.05071 42.05068 42.05053 42.05021 42.05009 42.05013
## [417] 42.05022 42.05040 42.04889 42.04849 42.06231 42.06330 42.06303 42.06190
## [425] 42.06128 42.06299 42.06299 42.06299 42.06294 42.06226 42.06226 42.06278
## [433] 42.06279 42.06240 42.06211 42.06093 42.06035 42.06138 42.06144 42.06058
## [441] 42.06058 42.06168 42.06043 42.06018 42.05991 42.05990 42.06140 42.05924
## [449] 42.05878 42.05889 42.05920 42.05918 42.05918 42.05918 42.05834 42.05834
## [457] 42.05718 42.05851 42.05716 42.05709 42.05702 42.05698 42.05728 42.05747
## [465] 42.06232 42.06318 42.06206 42.06240 42.06256 42.06256 42.06230 42.06227
## [473] 42.06208 42.06209 42.06156 42.05938 42.06174 42.06115 42.06111 42.06166
## [481] 42.06137 42.06328 42.05837 42.05859 42.05948 42.05907 42.05960 42.05784
## [489] 42.05783 42.05783 42.05710 42.05709 42.05696 42.05867 42.05375 42.05391
## [497] 42.05563 42.05344 42.05304 42.05267 42.05041 42.04970 42.05161 42.05022
## [505] 42.04992 42.05097 42.05428 42.05504 42.05430 42.05415 42.05415 42.05321
## [513] 42.05326 42.05311 42.05180 42.05180 42.05179 42.05165 42.05165 42.05165
## [521] 42.05041 42.05172 42.05179 42.05234 42.05235 42.05213 42.05142 42.05138
## [529] 42.05212 42.05141 42.05125 42.05125 42.05089 42.03756 42.03761 42.03766
## [537] 42.03600 42.03601 42.03528 42.03792 42.03813 42.03776 42.03743 42.03685
## [545] 42.03607 42.03690 42.03658 42.03453 42.03552 42.03761 42.03597 42.03576
## [553] 42.03654 42.03529 42.03581 42.03475 42.03462 42.03529 42.03466 42.03533
## [561] 42.03460 42.03460 42.03458 42.03724 42.04767 42.04763 42.04842 42.04849
## [569] 42.04734 42.04725 42.04710 42.04614 42.04642 42.04717 42.04378 42.04265
## [577] 42.04355 42.04302 42.03451 42.04771 42.04801 42.04896 42.04876 42.04876
## [585] 42.04765 42.04648 42.04648 42.04581 42.04580 42.04324 42.04384 42.04367
## [593] 42.04469 42.04880 42.04671 42.04664 42.04482 42.04393 42.04315 42.04313
## [601] 42.04224 42.04484 42.04477 42.04493 42.04488 42.04064 42.03849 42.04073
## [609] 42.04001 42.03990 42.04089 42.04110 42.03946 42.03860 42.03549 42.03544
## [617] 42.03464 42.03618 42.03474 42.03745 42.03595 42.03618 42.04931 42.04829
## [625] 42.04683 42.04861 42.04872 42.04806 42.04579 42.04489 42.04397 42.04413
## [633] 42.04399 42.04408 42.04547 42.04491 42.04297 42.04223 42.04324 42.04093
## [641] 42.04086 42.04046 42.03967 42.03853 42.03836 42.03840 42.03712 42.03722
## [649] 42.03492 42.03469 42.03475 42.03622 42.03583 42.03475 42.03807 42.03768
## [657] 42.03714 42.03733 42.03601 42.03600 42.03467 42.03457 42.03476 42.03474
## [665] 42.03526 42.03528 42.04179 42.04015 42.04030 42.04124 42.03851 42.03835
## [673] 42.03905 42.04077 42.03881 42.03713 42.03571 42.03579 42.03584 42.03723
## [681] 42.03602 42.03597 42.03572 42.03571 42.03721 42.03475 42.03486 42.03705
## [689] 42.03895 42.03826 42.03529 42.03422 42.03327 42.03207 42.03233 42.03240
## [697] 42.03220 42.03211 42.03191 42.03131 42.03047 42.03033 42.03035 42.03028
## [705] 42.03106 42.03338 42.03358 42.03205 42.03230 42.03223 42.03052 42.03020
## [713] 42.02967 42.02901 42.02904 42.02896 42.02931 42.02900 42.02811 42.02810
## [721] 42.02770 42.02856 42.02820 42.02706 42.02720 42.02723 42.02322 42.02322
## [729] 42.03400 42.03356 42.03338 42.03156 42.03154 42.03341 42.03362 42.03329
## [737] 42.03335 42.03350 42.03347 42.03140 42.03252 42.03246 42.03236 42.03129
## [745] 42.03238 42.03235 42.03109 42.03006 42.02676 42.02895 42.02785 42.02800
## [753] 42.02704 42.02696 42.02531 42.02309 42.02580 42.02603 42.02425 42.02414
## [761] 42.02283 42.03268 42.02810 42.02810 42.02805 42.02696 42.02282 42.02298
## [769] 42.03338 42.03363 42.03237 42.03239 42.02986 42.03134 42.03063 42.03114
## [777] 42.03343 42.03328 42.03230 42.03265 42.03256 42.03250 42.02655 42.02323
## [785] 42.02403 42.02847 42.02766 42.02751 42.02448 42.02398 42.02392 42.02613
## [793] 42.02600 42.02631 42.02499 42.02469 42.02472 42.02355 42.02275 42.03418
## [801] 42.03371 42.03184 42.03254 42.03063 42.03062 42.03068 42.03252 42.03162
## [809] 42.03183 42.03162 42.03155 42.03147 42.03146 42.03128 42.03057 42.03053
## [817] 42.03109 42.03093 42.02663 42.02648 42.02641 42.02637 42.02571 42.02529
## [825] 42.02558 42.02463 42.02460 42.02461 42.02477 42.02433 42.02440 42.02322
## [833] 42.02977 42.02792 42.02555 42.02117 42.02118 42.02121 42.02082 42.01978
## [841] 42.01900 42.01972 42.01860 42.01757 42.01690 42.01867 42.01686 42.01640
## [849] 42.01571 42.01655 42.01613 42.01571 42.02138 42.02009 42.01918 42.01970
## [857] 42.01955 42.01969 42.02067 42.02099 42.02179 42.02084 42.01711 42.01872
## [865] 42.01885 42.01877 42.01870 42.01697 42.01698 42.01815 42.01888 42.01887
## [873] 42.01801 42.01786 42.01786 42.01682 42.01680 42.01627 42.01627 42.01647
## [881] 42.01396 42.01405 42.01351 42.01339 42.02012 42.02125 42.02122 42.01899
## [889] 42.01865 42.01967 42.01893 42.01703 42.01896 42.02248 42.01942 42.02032
## [897] 42.02180 42.02150 42.01900 42.01822 42.01938 42.01859 42.02209 42.02209
## [905] 42.02209 42.02012 42.01971 42.01756 42.01692 42.01618 42.01909 42.01893
## [913] 42.01789 42.01783 42.01893 42.01694 42.01684 42.01696 42.01607 42.01913
## [921] 42.01918 42.01871 42.01758 42.01757 42.01668 42.01585 42.01615 42.01469
## [929] 42.01317 42.01494 42.01375 42.01250 42.00949 42.00949 42.00949 42.00949
## [937] 42.01064 42.01141 42.00913 42.02272 42.02143 42.02160 42.02018 42.02000
## [945] 42.00868 42.01830 41.99689 41.99667 41.99712 41.99539 41.99707 41.99707
## [953] 41.99692 41.99591 41.99607 42.00125 42.00138 41.99503 41.99506 41.99376
## [961] 41.99473 41.99470 41.99768 41.99895 41.99817 41.99633 41.99609 41.99536
## [969] 41.99296 41.99354 41.99219 41.99313 41.99212 41.99179 41.99292 41.99218
## [977] 41.99282 41.99217 41.99254 41.99179 41.99137 41.98754 41.98878 41.98822
## [985] 41.98766 41.98650 41.98651 41.99149 41.99095 42.05255 42.05145 42.04959
## [993] 42.05996 42.06123 42.06077 42.06082 42.06037 42.06064 42.06230 42.06298
## [1001] 42.06137 42.06086 42.06076 42.05941 42.05936 42.05941 42.05844 42.05701
## [1009] 42.05952 42.05964 42.06139 42.06056 42.06024 42.05979 42.05890 42.05867
## [1017] 42.05602 42.05451 42.05456 42.05444 42.05536 42.05450 42.05445 42.05421
## [1025] 42.05543 42.05254 42.05033 42.05147 42.05068 42.04945 42.04986 42.04961
## [1033] 42.05107 42.05631 42.05539 42.05530 42.05433 42.05643 42.05469 42.05279
## [1041] 42.05275 42.05148 42.05233 42.05168 42.05169 42.05166 42.05000 42.05068
## [1049] 42.05026 42.04845 42.06205 42.06327 42.06313 42.06292 42.06226 42.06241
## [1057] 42.06243 42.06113 42.06027 42.06043 42.06077 42.06043 42.05990 42.05848
## [1065] 42.05868 42.05857 42.05865 42.05703 42.05869 42.05716 42.05796 42.05820
## [1073] 42.05677 42.05702 42.05745 42.05718 42.05712 42.05747 42.05709 42.05662
## [1081] 42.06334 42.06230 42.06229 42.06200 42.06330 42.06132 42.05964 42.06154
## [1089] 42.06098 42.06132 42.06131 42.05838 42.05799 42.05859 42.06001 42.05951
## [1097] 42.05695 42.05858 42.05388 42.05367 42.05575 42.05578 42.05223 42.05227
## [1105] 42.05038 42.05162 42.04950 42.04970 42.05069 42.04948 42.05424 42.05516
## [1113] 42.05510 42.05441 42.05437 42.05431 42.05432 42.05552 42.05423 42.05318
## [1121] 42.05165 42.05165 42.05031 42.05228 42.05246 42.05228 42.05205 42.05138
## [1129] 42.05217 42.05122 42.05090 42.03784 42.03527 42.03513 42.03792 42.03781
## [1137] 42.03805 42.03652 42.03726 42.03587 42.03588 42.03588 42.03499 42.03609
## [1145] 42.03453 42.03567 42.03684 42.03650 42.03647 42.03604 42.03518 42.03461
## [1153] 42.03569 42.03570 42.03459 42.03750 42.03453 42.04767 42.04861 42.04747
## [1161] 42.04809 42.04819 42.04781 42.04757 42.04755 42.04710 42.04710 42.04638
## [1169] 42.04638 42.04637 42.04609 42.04608 42.04696 42.04696 42.04665 42.04717
## [1177] 42.04717 42.04717 42.04501 42.04442 42.04464 42.04469 42.03673 42.03758
## [1185] 42.04873 42.04793 42.04925 42.04914 42.04876 42.04640 42.04294 42.04378
## [1193] 42.04585 42.04710 42.04658 42.04754 42.04818 42.04536 42.04426 42.04406
## [1201] 42.04485 42.04314 42.04384 42.04410 42.04240 42.04477 42.04477 42.04123
## [1209] 42.04066 42.03923 42.04011 42.04178 42.04178 42.04181 42.03832 42.04102
## [1217] 42.04187 42.04117 42.04030 42.03558 42.03557 42.03456 42.03574 42.03806
## [1225] 42.03618 42.03610 42.03713 42.03468 42.04895 42.04778 42.04709 42.04708
## [1233] 42.04693 42.04657 42.04237 42.04230 42.04474 42.04399 42.04479 42.04485
## [1241] 42.04430 42.04219 42.04382 42.04202 42.04230 42.04048 42.04030 42.04039
## [1249] 42.04044 42.03953 42.03852 42.03945 42.03720 42.03471 42.03730 42.03746
## [1257] 42.03589 42.03572 42.03594 42.03522 42.04002 42.04014 42.04117 42.03869
## [1265] 42.03999 42.03957 42.03807 42.03713 42.03710 42.03581 42.03716 42.03701
## [1273] 42.03729 42.03481 42.03456 42.03479 42.03469 42.03473 42.03464 42.03480
## [1281] 42.03697 42.03702 42.03572 42.03422 42.03413 42.03338 42.03261 42.03306
## [1289] 42.03239 42.03242 42.03136 42.03043 42.03041 42.03042 42.03048 42.03216
## [1297] 42.03227 42.03041 42.03036 42.03343 42.03357 42.03325 42.03201 42.03209
## [1305] 42.03238 42.03110 42.03048 42.02903 42.02906 42.02928 42.02925 42.02928
## [1313] 42.02829 42.02793 42.02707 42.02703 42.02908 42.02813 42.02883 42.02878
## [1321] 42.02840 42.02921 42.02740 42.02725 42.02774 42.02669 42.02727 42.03361
## [1329] 42.03431 42.03338 42.03047 42.03346 42.03357 42.03370 42.03337 42.03351
## [1337] 42.03332 42.03347 42.03337 42.03349 42.03135 42.03129 42.03149 42.03248
## [1345] 42.03146 42.03150 42.03147 42.03143 42.03105 42.03039 42.03106 42.02940
## [1353] 42.02843 42.02827 42.02707 42.02956 42.02903 42.02904 42.02863 42.02552
## [1361] 42.02411 42.02426 42.02499 42.02426 42.02257 42.02295 42.02648 42.02626
## [1369] 42.02488 42.02423 42.02372 42.03439 42.03441 42.03342 42.03128 42.02393
## [1377] 42.03360 42.03323 42.03236 42.03157 42.03125 42.03112 42.03135 42.03156
## [1385] 42.03055 42.03443 42.03443 42.03345 42.03383 42.03441 42.03249 42.03257
## [1393] 42.03216 42.03392 42.03369 42.03265 42.03356 42.02945 42.02466 42.02430
## [1401] 42.02521 42.02857 42.02860 42.02733 42.02751 42.02755 42.02838 42.02823
## [1409] 42.02819 42.02803 42.02403 42.02572 42.02504 42.02367 42.02446 42.02290
## [1417] 42.02277 42.02283 42.03177 42.03391 42.03085 42.03108 42.03062 42.02541
## [1425] 42.02528 42.02737 42.02719 42.02944 42.03028 42.02492 42.02578 42.02117
## [1433] 42.01915 42.01915 42.01850 42.01879 42.01742 42.01752 42.01791 42.01777
## [1441] 42.01628 42.01597 42.01626 42.01595 42.02214 42.02123 42.01884 42.01977
## [1449] 42.02069 42.02107 42.02128 42.02080 42.02099 42.01873 42.01841 42.01835
## [1457] 42.01871 42.01760 42.01801 42.01727 42.01748 42.01819 42.01698 42.01621
## [1465] 42.01634 42.01443 42.01671 42.01787 42.01628 42.01625 42.01785 42.01626
## [1473] 42.01455 42.01395 42.01391 42.01364 42.01362 42.01360 42.01597 42.01537
## [1481] 42.01383 42.01593 42.01593 42.01612 42.01612 42.01975 42.01994 42.02090
## [1489] 42.02124 42.02000 42.02000 42.02099 42.01986 42.01899 42.01885 42.01891
## [1497] 42.01883 42.01739 42.01680 42.01890 42.02048 42.02029 42.02039 42.01954
## [1505] 42.02011 42.02158 42.01797 42.01796 42.01980 42.01996 42.01854 42.01787
## [1513] 42.02224 42.02224 42.02209 42.02145 42.01999 42.01872 42.01741 42.01708
## [1521] 42.01927 42.01909 42.01900 42.01791 42.01783 42.01769 42.01789 42.01689
## [1529] 42.01687 42.01607 42.01983 42.01962 42.01844 42.01889 42.01877 42.01753
## [1537] 42.01677 42.01601 42.01567 42.01457 42.01264 42.01249 42.00949 42.00949
## [1545] 42.02261 42.02181 42.02280 42.02252 42.02138 42.02128 42.02140 42.02038
## [1553] 42.02139 42.01881 42.02116 42.02151 42.02159 42.02246 42.02263 42.00933
## [1561] 42.00880 42.00881 42.00919 41.99507 41.99712 41.99706 41.99707 41.99692
## [1569] 41.99690 41.99599 41.99854 42.00514 41.99900 41.99514 41.99484 41.99373
## [1577] 41.99514 41.99375 41.99518 41.99981 41.99958 41.99761 41.99855 41.99551
## [1585] 41.99639 41.99423 41.99312 41.99361 41.99338 41.99334 41.99005 41.99306
## [1593] 41.99318 41.99261 41.99137 41.99090 41.99188 41.99178 41.99325 41.99213
## [1601] 41.99193 41.98868 41.98711 41.98893 41.98811 41.98808 41.98729 41.98658
## [1609] 41.98650 41.99189 42.02275 42.05130 42.05136 42.04967 42.05044 42.06127
## [1617] 42.06047 42.06166 42.06133 42.06124 42.06307 42.05959 42.05895 42.05956
## [1625] 42.05952 42.05924 42.05929 42.05701 42.05817 42.05753 42.05702 42.05938
## [1633] 42.05924 42.05931 42.05930 42.06043 42.06014 42.06120 42.06010 42.05974
## [1641] 42.05889 42.05900 42.05900 42.05437 42.05392 42.05555 42.05450 42.05439
## [1649] 42.05494 42.05522 42.05443 42.05622 42.05621 42.05235 42.05327 42.05026
## [1657] 42.04983 42.05007 42.05037 42.04996 42.05104 42.04877 42.05539 42.05526
## [1665] 42.05460 42.05341 42.05461 42.05355 42.05346 42.05350 42.05630 42.05639
## [1673] 42.05467 42.05479 42.05532 42.05267 42.05270 42.05270 42.05229 42.05183
## [1681] 42.05040 42.05057 42.05000 42.04882 42.06257 42.06330 42.06330 42.06327
## [1689] 42.06327 42.06314 42.06195 42.06198 42.06197 42.06128 42.06226 42.06282
## [1697] 42.06241 42.06243 42.06150 42.06113 42.06027 42.06027 42.06113 42.06058
## [1705] 42.06043 42.05956 42.06113 42.05976 42.05968 42.05863 42.05862 42.05921
## [1713] 42.05920 42.05920 42.05919 42.05918 42.05918 42.05918 42.05918 42.05826
## [1721] 42.05828 42.05828 42.05683 42.05712 42.05738 42.05685 42.05721 42.06339
## [1729] 42.06338 42.06248 42.06228 42.06267 42.06208 42.06207 42.06253 42.06289
## [1737] 42.06293 42.06297 42.06302 42.06311 42.06334 42.06258 42.06258 42.06295
## [1745] 42.06330 42.06171 42.06143 42.06148 42.06154 42.06153 42.06132 42.06139
## [1753] 42.06002 42.05886 42.05918 42.05798 42.05840 42.05953 42.05784 42.05890
## [1761] 42.05332 42.05336 42.05575 42.05563 42.05359 42.05344 42.05347 42.05198
## [1769] 42.05236 42.05225 42.05181 42.05048 42.04952 42.04951 42.05242 42.05441
## [1777] 42.05576 42.05432 42.05418 42.05442 42.05435 42.05431 42.05451 42.05415
## [1785] 42.05415 42.05415 42.05416 42.05318 42.05319 42.05323 42.05311 42.05303
## [1793] 42.05307 42.05180 42.05179 42.05165 42.05166 42.05021 42.05030 42.05168
## [1801] 42.05227 42.05212 42.05138 42.05227 42.05215 42.05105 42.03759 42.03764
## [1809] 42.03764 42.03722 42.03603 42.03526 42.03604 42.03507 42.03646 42.03457
## [1817] 42.03568 42.03621 42.03468 42.03595 42.03587 42.03586 42.03453 42.03472
## [1825] 42.03567 42.03465 42.03482 42.03765 42.03750 42.03466 42.03464 42.03467
## [1833] 42.04738 42.04578 42.04762 42.04742 42.04741 42.04771 42.04771 42.04770
## [1841] 42.04769 42.04767 42.04710 42.04710 42.04614 42.04615 42.04615 42.04641
## [1849] 42.04717 42.04632 42.04614 42.04613 42.04641 42.04438 42.04476 42.04499
## [1857] 42.04299 42.04375 42.04305 42.04296 42.03710 42.03497 42.04849 42.04655
## [1865] 42.04776 42.04807 42.04849 42.04762 42.04336 42.04301 42.04548 42.04259
## [1873] 42.04389 42.04217 42.04781 42.04829 42.04650 42.04476 42.04398 42.04393
## [1881] 42.04312 42.04212 42.04227 42.04404 42.04258 42.04248 42.04248 42.04492
## [1889] 42.04361 42.04363 42.03914 42.04014 42.04174 42.03907 42.04139 42.04176
## [1897] 42.04074 42.04125 42.04133 42.03921 42.03920 42.03657 42.03568 42.03602
## [1905] 42.03622 42.03462 42.03620 42.03465 42.03491 42.03475 42.04922 42.04893
## [1913] 42.04671 42.04581 42.04593 42.04688 42.04405 42.04314 42.04474 42.04393
## [1921] 42.04395 42.04231 42.04422 42.04567 42.04395 42.04323 42.04270 42.04273
## [1929] 42.04302 42.04187 42.04124 42.04077 42.04045 42.03981 42.03937 42.03948
## [1937] 42.03846 42.03837 42.03848 42.03854 42.03479 42.03472 42.03481 42.03593
## [1945] 42.03608 42.03603 42.03725 42.03810 42.03570 42.03578 42.03585 42.03488
## [1953] 42.03934 42.03998 42.04015 42.03889 42.03573 42.03592 42.03733 42.03720
## [1961] 42.03595 42.03588 42.03711 42.03586 42.03600 42.03708 42.03469 42.03461
## [1969] 42.03456 42.03695 42.03542 42.03460 42.03503 42.03440 42.03225 42.03147
## [1977] 42.03131 42.03137 42.03111 42.03341 42.03234 42.03339 42.03349 42.03331
## [1985] 42.03228 42.03236 42.03058 42.03180 42.03031 42.03013 42.02998 42.02922
## [1993] 42.02920 42.02922 42.02804 42.02808 42.02885 42.02819 42.02715 42.02820
## [2001] 42.02776 42.02609 42.02681 42.02726 42.02727 42.03331 42.03434 42.03185
## [2009] 42.03082 42.03348 42.03361 42.03334 42.03240 42.03143 42.03144 42.03142
## [2017] 42.03251 42.03239 42.03132 42.03148 42.03149 42.03045 42.02945 42.02691
## [2025] 42.02700 42.02709 42.02997 42.02911 42.02752 42.02758 42.02523 42.02543
## [2033] 42.02158 42.02500 42.02423 42.02270 42.02389 42.02296 42.02384 42.02352
## [2041] 42.02672 42.02589 42.02616 42.02295 42.03352 42.03328 42.02805 42.02800
## [2049] 42.03327 42.03243 42.03445 42.03443 42.03319 42.03238 42.03210 42.03153
## [2057] 42.03120 42.02956 42.03122 42.02968 42.03114 42.02979 42.03059 42.03442
## [2065] 42.03253 42.03442 42.03356 42.03264 42.03373 42.03402 42.03270 42.02868
## [2073] 42.02384 42.02409 42.02618 42.02323 42.02302 42.02842 42.02824 42.02495
## [2081] 42.02582 42.02500 42.02052 42.02019 42.02469 42.02387 42.02394 42.02345
## [2089] 42.02282 42.03445 42.03366 42.03358 42.03155 42.03247 42.03157 42.03080
## [2097] 42.02667 42.02664 42.02567 42.02571 42.02559 42.02526 42.02528 42.02556
## [2105] 42.02460 42.02459 42.02463 42.02461 42.02573 42.02516 42.02464 42.02448
## [2113] 42.02323 42.02969 42.02980 42.02796 42.02797 42.02473 42.02430 42.02223
## [2121] 42.02132 42.02121 42.02097 42.02091 42.01903 42.01908 42.01903 42.01838
## [2129] 42.01791 42.01783 42.01690 42.01683 42.01630 42.01621 42.02199 42.02139
## [2137] 42.02186 42.02224 42.01972 42.02116 42.02106 42.02103 42.02086 42.02174
## [2145] 42.01852 42.01842 42.01885 42.01697 42.01696 42.01621 42.01720 42.01856
## [2153] 42.01886 42.01853 42.01802 42.01786 42.01628 42.01775 42.01597 42.01404
## [2161] 42.01404 42.01482 42.01358 42.01354 42.01343 42.01347 42.01469 42.02103
## [2169] 42.02070 42.02122 42.02119 42.02103 42.02089 42.01993 42.01970 42.01990
## [2177] 42.01917 42.01828 42.01887 42.01892 42.01645 42.01664 42.01897 42.01897
## [2185] 42.02006 42.02078 42.02050 42.02266 42.02144 42.01796 42.01965 42.01894
## [2193] 42.01873 42.01994 42.01902 42.01876 42.01804 42.01804 42.01789 42.01789
## [2201] 42.01892 42.01710 42.01711 42.01628 42.01622 42.01622 42.01622 42.01685
## [2209] 42.01607 42.01995 42.01995 42.01880 42.01757 42.02004 42.01850 42.01894
## [2217] 42.01689 42.01757 42.01696 42.01629 42.01300 42.01455 42.01265 42.01249
## [2225] 42.01151 42.00949 42.01184 42.00932 42.01134 42.01033 42.01008 42.02284
## [2233] 42.02247 42.02266 42.02266 42.02257 42.02269 42.02280 42.02155 42.02128
## [2241] 42.02150 42.02016 42.02008 42.02142 42.02155 42.00940 42.00940 41.99436
## [2249] 41.99421 41.99421 41.99522 41.99597 41.99593 41.99551 41.99419 42.00569
## [2257] 42.00169 41.99854 42.00041 41.99424 41.99414 41.99410 41.99482 41.99509
## [2265] 41.99802 41.99799 41.99736 41.99713 41.99609 41.99551 41.99730 41.99534
## [2273] 41.99399 41.99735 41.99329 41.99298 41.99326 41.99005 41.99232 41.99336
## [2281] 41.99311 41.99279 41.99121 41.99292 41.99284 41.99215 41.99252 41.99248
## [2289] 41.99171 41.99164 41.99187 41.99161 41.99110 41.98958 41.99026 41.98949
## [2297] 41.99114 41.99137 41.98991 41.98761 41.98977 41.98822 41.98817 41.98651
## [2305] 41.98659 42.05341 42.05333 42.05311 42.05252 42.05051 42.05991 42.06141
## [2313] 42.06043 42.06048 42.06074 42.06188 42.06283 42.06281 42.06280 42.06280
## [2321] 42.06289 42.06296 42.06063 42.05910 42.05842 42.05820 42.05960 42.05933
## [2329] 42.05814 42.06046 42.06053 42.06052 42.06148 42.06101 42.06011 42.05996
## [2337] 42.06110 42.05939 42.05670 42.05856 42.05995 42.05882 42.05561 42.05437
## [2345] 42.05434 42.05496 42.05626 42.05327 42.05240 42.05342 42.05051 42.05018
## [2353] 42.04977 42.05108 42.05236 42.05252 42.05236 42.04977 42.04961 42.05513
## [2361] 42.05346 42.05446 42.05439 42.05532 42.05266 42.05247 42.05270 42.05180
## [2369] 42.05184 42.05169 42.05167 42.05167 42.05166 42.05060 42.04895 42.04895
## [2377] 42.05071 42.05044 42.06147 42.06331 42.06190 42.06128 42.06281 42.06211
## [2385] 42.06113 42.06034 42.06027 42.06027 42.06043 42.06083 42.06058 42.06087
## [2393] 42.06042 42.06036 42.06038 42.06154 42.06138 42.05964 42.05982 42.05854
## [2401] 42.05869 42.05922 42.05902 42.05918 42.05716 42.05823 42.05824 42.05716
## [2409] 42.05716 42.05758 42.06330 42.06244 42.06236 42.06191 42.06193 42.06303
## [2417] 42.06258 42.06198 42.06199 42.06257 42.06330 42.06333 42.06318 42.06237
## [2425] 42.06230 42.06330 42.06330 42.06330 42.06283 42.06287 42.06024 42.06029
## [2433] 42.05980 42.06173 42.06084 42.06007 42.05865 42.05853 42.05790 42.05784
## [2441] 42.05696 42.05846 42.05443 42.05384 42.05380 42.05331 42.05560 42.05315
## [2449] 42.05347 42.05178 42.04942 42.05107 42.04969 42.04953 42.05506 42.05432
## [2457] 42.05418 42.05418 42.05318 42.05303 42.05180 42.05226 42.05227 42.05235
## [2465] 42.05136 42.05143 42.05138 42.05125 42.05123 42.05122 42.03784 42.03615
## [2473] 42.03791 42.03791 42.03783 42.03661 42.03718 42.03685 42.03460 42.03674
## [2481] 42.03556 42.03563 42.03748 42.03580 42.03524 42.03605 42.03609 42.03621
## [2489] 42.03530 42.03509 42.03469 42.03570 42.03584 42.03533 42.03554 42.03457
## [2497] 42.03458 42.03466 42.03706 42.04576 42.04861 42.04837 42.04800 42.04806
## [2505] 42.04759 42.04768 42.04767 42.04764 42.04762 42.04760 42.04615 42.04643
## [2513] 42.04613 42.04611 42.04643 42.04642 42.04461 42.04378 42.04237 42.04248
## [2521] 42.04283 42.04335 42.03741 42.04563 42.04820 42.04900 42.04860 42.04647
## [2529] 42.04806 42.04355 42.04467 42.04650 42.04571 42.04573 42.04573 42.04588
## [2537] 42.04588 42.04795 42.04657 42.04568 42.04431 42.04321 42.04498 42.04211
## [2545] 42.04007 42.03843 42.04102 42.04141 42.04131 42.04027 42.04014 42.03919
## [2553] 42.03835 42.03920 42.03584 42.03537 42.03538 42.03567 42.03806 42.03461
## [2561] 42.03602 42.03746 42.03483 42.03599 42.03725 42.04930 42.04903 42.04665
## [2569] 42.04853 42.04230 42.04216 42.04313 42.04474 42.04390 42.04498 42.04498
## [2577] 42.04425 42.04210 42.04363 42.04270 42.04290 42.04182 42.04075 42.04025
## [2585] 42.03945 42.03836 42.03939 42.03860 42.03835 42.03884 42.04028 42.03935
## [2593] 42.03493 42.03462 42.03473 42.03786 42.03718 42.03700 42.03710 42.03704
## [2601] 42.03580 42.03678 42.03586 42.03457 42.03528 42.03476 42.04094 42.04081
## [2609] 42.04010 42.04008 42.04030 42.04015 42.03850 42.03850 42.03830 42.04187
## [2617] 42.04165 42.04077 42.03902 42.03610 42.03578 42.03600 42.03610 42.03605
## [2625] 42.03480 42.03471 42.03466 42.03483 42.03476 42.03471 42.03679 42.03548
## [2633] 42.03462 42.03475 42.03456 42.03327 42.03350 42.03339 42.03214 42.03235
## [2641] 42.03139 42.03151 42.03135 42.03121 42.03040 42.03046 42.03120 42.03362
## [2649] 42.03305 42.03231 42.03027 42.03206 42.03227 42.03196 42.03037 42.03146
## [2657] 42.03114 42.02914 42.02799 42.02914 42.02895 42.02928 42.02795 42.02811
## [2665] 42.02795 42.02896 42.02902 42.02799 42.02727 42.02297 42.03405 42.03179
## [2673] 42.03079 42.03331 42.03337 42.03230 42.03150 42.03240 42.03248 42.03142
## [2681] 42.03144 42.03242 42.03242 42.03108 42.03039 42.02953 42.02686 42.02854
## [2689] 42.02689 42.02689 42.02526 42.02546 42.02495 42.02424 42.02426 42.02312
## [2697] 42.02282 42.02381 42.03441 42.03458 42.03330 42.03315 42.02780 42.02800
## [2705] 42.02800 42.03352 42.03339 42.03330 42.03224 42.03230 42.03238 42.03136
## [2713] 42.03061 42.03222 42.03070 42.03136 42.03135 42.03023 42.03023 42.03328
## [2721] 42.03247 42.03229 42.03231 42.03369 42.03248 42.03164 42.03216 42.03258
## [2729] 42.02945 42.02884 42.02365 42.02470 42.02653 42.02766 42.02667 42.02661
## [2737] 42.02821 42.02819 42.02646 42.02585 42.02552 42.02510 42.02520 42.02631
## [2745] 42.02475 42.02282 42.03208 42.03249 42.03093 42.03152 42.02460 42.02464
## [2753] 42.02455 42.02461 42.02569 42.02522 42.02519 42.02437 42.02448 42.02331
## [2761] 42.02438 42.02331 42.02314 42.02988 42.02817 42.02557 42.02438 42.02459
## [2769] 42.02223 42.02208 42.02121 42.02090 42.01905 42.01804 42.01812 42.01763
## [2777] 42.01687 42.01793 42.01686 42.01622 42.01691 42.02139 42.02014 42.02007
## [2785] 42.01970 42.02181 42.02189 42.02100 42.02179 42.01834 42.01866 42.01785
## [2793] 42.01705 42.01819 42.01449 42.01698 42.01690 42.01869 42.01786 42.01787
## [2801] 42.01786 42.01719 42.01628 42.01625 42.01662 42.01591 42.01609 42.01464
## [2809] 42.01411 42.01579 42.01600 42.01397 42.01399 42.01576 42.01352 42.01459
## [2817] 42.01959 42.02099 42.02034 42.02059 42.02055 42.02111 42.01899 42.02117
## [2825] 42.01865 42.01896 42.01896 42.01896 42.01881 42.01881 42.01881 42.01881
## [2833] 42.01881 42.02011 42.02268 42.02266 42.02264 42.02143 42.01885 42.01773
## [2841] 42.02209 42.02209 42.02197 42.02156 42.02087 42.02029 42.01884 42.01828
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## [2626] -93.60905 -93.60905 -93.60689 -93.60689 -93.60674 -93.60370 -93.60584
## [2633] -93.60469 -93.60457 -93.60507 -93.61854 -93.61955 -93.61716 -93.61852
## [2640] -93.61714 -93.61849 -93.61951 -93.61568 -93.61880 -93.61834 -93.61833
## [2647] -93.61564 -93.61401 -93.61459 -93.61462 -93.61391 -93.60786 -93.60883
## [2654] -93.61035 -93.60894 -93.60774 -93.60680 -93.61829 -93.61689 -93.61389
## [2661] -93.61536 -93.61536 -93.61534 -93.61280 -93.61376 -93.60890 -93.61044
## [2668] -93.60967 -93.60619 -93.60687 -93.62848 -93.62602 -93.62739 -93.62558
## [2675] -93.62043 -93.62364 -93.62454 -93.62455 -93.62455 -93.62348 -93.62148
## [2682] -93.62242 -93.62041 -93.62438 -93.62239 -93.62577 -93.62277 -93.62544
## [2689] -93.62156 -93.62262 -93.62686 -93.62663 -93.62757 -93.62732 -93.62551
## [2696] -93.62842 -93.62950 -93.62659 -93.65702 -93.65565 -93.65815 -93.65783
## [2703] -93.66004 -93.65588 -93.65579 -93.67555 -93.67121 -93.67540 -93.67446
## [2710] -93.67452 -93.67541 -93.67561 -93.67646 -93.67228 -93.67439 -93.67360
## [2717] -93.67265 -93.67020 -93.67051 -93.66557 -93.66550 -93.66563 -93.66708
## [2724] -93.66954 -93.66412 -93.66839 -93.66708 -93.66204 -93.67817 -93.67635
## [2731] -93.67440 -93.67668 -93.66603 -93.66515 -93.66276 -93.66348 -93.66156
## [2738] -93.66066 -93.66023 -93.66626 -93.66719 -93.66609 -93.66610 -93.66019
## [2745] -93.66274 -93.65851 -93.68554 -93.68323 -93.68218 -93.68015 -93.68907
## [2752] -93.68982 -93.69037 -93.69123 -93.68894 -93.68892 -93.68892 -93.68949
## [2759] -93.68907 -93.68908 -93.68879 -93.68893 -93.68893 -93.68216 -93.68135
## [2766] -93.68209 -93.68388 -93.68040 -93.69190 -93.69187 -93.68830 -93.69036
## [2773] -93.69200 -93.69261 -93.69222 -93.69021 -93.69193 -93.68908 -93.68923
## [2780] -93.69124 -93.68858 -93.68663 -93.68682 -93.68716 -93.68498 -93.68347
## [2787] -93.68325 -93.68298 -93.68138 -93.68770 -93.68629 -93.68442 -93.68550
## [2794] -93.68570 -93.68767 -93.68557 -93.68372 -93.67915 -93.68148 -93.67980
## [2801] -93.68269 -93.68189 -93.68119 -93.68373 -93.68378 -93.68768 -93.68769
## [2808] -93.68783 -93.68409 -93.68412 -93.68412 -93.68537 -93.68587 -93.68343
## [2815] -93.68433 -93.68376 -93.67827 -93.67637 -93.67636 -93.67530 -93.67555
## [2822] -93.67145 -93.67238 -93.67130 -93.67161 -93.67002 -93.66998 -93.66993
## [2829] -93.67006 -93.67004 -93.66998 -93.66996 -93.66992 -93.66195 -93.65918
## [2836] -93.65922 -93.65922 -93.66012 -93.66346 -93.66200 -93.65675 -93.65670
## [2843] -93.65564 -93.65904 -93.65563 -93.64856 -93.65181 -93.65129 -93.64694
## [2850] -93.64662 -93.64644 -93.64842 -93.64842 -93.64644 -93.64471 -93.64841
## [2857] -93.64703 -93.64431 -93.64426 -93.64243 -93.64048 -93.64344 -93.64115
## [2864] -93.64232 -93.64100 -93.64167 -93.64061 -93.64288 -93.64420 -93.63962
## [2871] -93.63943 -93.64349 -93.62847 -93.62841 -93.62830 -93.62950 -93.62668
## [2878] -93.62515 -93.61531 -93.61385 -93.61501 -93.61502 -93.60434 -93.61603
## [2885] -93.61624 -93.59997 -93.60674 -93.60367 -93.60317 -93.60119 -93.60385
## [2892] -93.64453 -93.64559 -93.65108 -93.64977 -93.64610 -93.64657 -93.64617
## [2899] -93.64664 -93.64676 -93.64789 -93.64898 -93.64747 -93.61027 -93.60834
## [2906] -93.60819 -93.60819 -93.60714 -93.60439 -93.60392 -93.60352 -93.60428
## [2913] -93.60109 -93.60318 -93.60352 -93.60044 -93.60204 -93.60190 -93.60184
## [2920] -93.60161 -93.60234 -93.60447 -93.60353 -93.60869 -93.60684 -93.60478
## [2927] -93.60268 -93.60685 -93.60019 -93.60000ames1 <- ames %>%
filter(Neighborhood == "North_Ames")
ames.sf <- st_as_sf(ames1, coords = c("Longitude", "Latitude"), crs = 4326)
library(leaflet)
leaflet() %>%
addProviderTiles(providers$CartoDB.Positron)%>%
addMarkers(data = ames.sf)3 Operaciones
3.1 Cantidad de Viviendas por Barrio
cantidadviviendas <-ames%>%
group_by(barrio = Neighborhood)%>%
summarise(cantidad = n() )
ggplot(data=cantidadviviendas)+
geom_bar(aes(x=barrio,weight=cantidad))
ggplot(data=cantidadviviendas)+
geom_bar(aes(x=barrio,weight=cantidad))+
coord_flip()
Ejercicios:
- ¿Cuantos calles están pavimentadas y cuantas no pavimentadas?
3.2 seleccionamos viviendas de un barrio
barrioGilbert <- ames%>%
filter(ames$Neighborhood == "Greens")
barrioGilbert <- st_as_sf(barrioGilbert, coords = c("Longitude", "Latitude"), crs = 4326)
library(leaflet)
leaflet() %>%
addProviderTiles(providers$CartoDB.Positron)%>%
addMarkers(data = barrioGilbert)3.3 Transformación de unidad de medidas
Crear dos nuevas columnas a partir de las columnas Lot_Frontage y Lot_Area.
metros_cuadrados <- 0.3048
ames$FrenteLote <- ames$Lot_Frontage * metros_cuadrados
ames$AreaLote <- ames$Lot_Area * metros_cuadrados * metros_cuadrados
hist(ames$AreaLote)
boxplot(ames$AreaLote)
4 Arbol de Decisión
Los árboles de decisión son un potente algoritmo de aprendizaje automático que se puede utilizar tanto para tareas de clasificación como de regresión. Son fáciles de entender e interpretar y se pueden utilizar para construir modelos complejos sin necesidad de ingeniería de características.
Una vez que haya entrenado un modelo de árbol de decisión, podrá utilizarlo para hacer predicciones sobre nuevos datos. Sin embargo, también puede resultar útil trazar el árbol de decisiones para comprender mejor cómo funciona e identificar posibles problemas.
Te mostrare cómo trazar árboles de decisión en R usando los paquetes rpart y rpart.plot. Empezaremos con un ejemplo utilizando el conjunto de datos del iris y explicaremos los bloques de código en términos simples de usar.
4.1 con Iris
#Load the libraries
library(rpart)## Warning: package 'rpart' was built under R version 4.3.3library(rpart.plot)## Warning: package 'rpart.plot' was built under R version 4.3.3#Split the data into training and test sets
set.seed(123)
train_index <- sample(1:nrow(iris), size = 0.7 * nrow(iris))
train <- iris[train_index, ]
test <- iris[-train_index, ]
#Train a decision tree model
tree <- rpart(Species ~ ., data = train, method = "class")
#Plot the decision tree
rpart.plot(tree, main = "Decision Tree for the Iris Dataset")
4.1.1 Output
La salida de la función rpart.plot() es un diagrama de árbol que muestra las reglas de decisión del modelo. El nodo raíz del árbol está en la parte superior y los nodos de las hojas están en la parte inferior. Cada nodo está etiquetado con la característica que se utiliza para dividir los datos en ese nodo y el valor de la división. Los nodos hoja están etiquetados con la clase prevista para los datos que llegan a ese nodo.
4.1.2 Interpretando el árbol de decisión
Para interpretar el árbol de decisión, comience en el nodo raíz y siga las ramas hasta un nodo hoja. El nodo hoja al que llega es la clase prevista para los datos con los que comenzó.
Por ejemplo, si tiene una nueva flor de iris con una longitud de sépalo de 5,5 cm y una longitud de pétalo de 2,5 cm, comenzaría en el nodo raíz del árbol de decisión. En el nodo raíz, la característica que se utiliza para dividir los datos es la longitud del pétalo. Dado que la longitud de los pétalos de la nueva flor es superior a 2,45 cm, deberás seguir la rama derecha hasta el siguiente nodo. En el siguiente nodo, la característica que se utiliza para dividir los datos es la longitud del sépalo. Dado que la longitud del sépalo de la nueva flor es superior a 5,0 cm, deberá seguir la rama derecha hasta el nudo de la hoja. El nodo de la hoja al que llega está etiquetado como “versicolor”, por lo que la clase prevista para la nueva flor es versicolor.
4.1.3 Algoritmo de alto nivel
Para comenzar, cargue las bibliotecas rpart y rpart.plot y cargue su conjunto de datos.
Luego, divida los datos en conjuntos de entrenamiento y prueba. + Entrene un modelo de árbol de decisión utilizando la función rpart().
Finalmente, trace el árbol de decisión usando la función rpart.plot().
Una vez que haya trazado el árbol de decisión, tómese un tiempo para interpretarlo.
Intente comprender cómo el modelo hace predicciones e identifique cualquier problema potencial.
También puede intentar mejorar el modelo agregando o eliminando funciones o cambiando los hiperparámetros de la función rpart().
4.2 Arbol de decision para Ames
El precio de la vivienda puede depender de Bldg_Type y de Gr_Liv_Area
4.2.1 Gr_Liv_Area
El campo Gr_Liv_Area en el conjunto de datos de AmesHousing del paquete modeldata representa el área habitable sobre el nivel del suelo (en pies cuadrados) de cada propiedad. Es decir, incluye el área de todas las habitaciones habitables (como salas de estar, dormitorios, comedores, etc.) que están sobre el nivel del suelo, excluyendo sótanos y áreas no habitables como garajes o porches.
Este atributo es importante en el análisis de precios de viviendas, ya que el área habitable es uno de los factores clave que influyen en el precio de una propiedad. Las propiedades con áreas habitables más grandes tienden a tener precios más altos en comparación con propiedades con áreas habitables más pequeñas, siempre y cuando otros factores se mantengan constantes.
4.2.2 Bldg_Type
Cada valor de Bldg_Type indica un tipo específico de estructura de vivienda. Aquí está el significado general de cada tipo de Bldg_Type:
- 1Fam: Casa unifamiliar.
- 2FmCon: Casa con dos unidades residenciales (dúplex).
- Duplx: Casa con dos unidades residenciales (dúplex).
- TwnhsE: Casa adosada de estilo europeo (townhouse end unit).
- TwnhsI: Casa adosada de estilo interior (townhouse inside unit).
4.2.3 Ploteo
# Función para convertir pies cuadrados a metros cuadrados
convertir_pies_cuadrados_a_metros_cuadrados <- function(pies_cuadrados) {
conversion_factor <- 0.092903
metros_cuadrados <- pies_cuadrados * conversion_factor
return(metros_cuadrados)
}
# Crear una nueva columna en el dataframe 'ames' con 'Gr_Liv_Area' en metros cuadrados
ames$Gr_Liv_Area_m2 <- convertir_pies_cuadrados_a_metros_cuadrados(ames$Gr_Liv_Area)
ggplot(data = ames, aes(x = Gr_Liv_Area_m2, y = Sale_Price, color = Bldg_Type)) +
geom_point() +
labs(x = "Above Grade Living Area (sqft)", y = "Sale Price",
title = "Sale Price vs. Above Grade Living Area by Building Type")
### con facetas
# Create the plot with facets
ggplot(data = ames, aes(x = Gr_Liv_Area_m2, y = Sale_Price)) +
geom_point() +
facet_wrap(~ Bldg_Type, ncol = 2) +
labs(x = "Above Grade Living Area (sqft)", y = "Sale Price",
title = "Sale Price vs. Above Grade Living Area by Building Type")
otro grafico con colores
colors <- c("#FF5733", "#33FF57", "#3357FF", "#FF33ED", "#FF5733")
# Crea el gráfico con facetas y colores personalizados
ggplot(data = ames, aes(x = Gr_Liv_Area_m2, y = Sale_Price)) +
geom_point(aes(color = Bldg_Type), size = 3) +
facet_wrap(~ Bldg_Type, ncol = 2) +
labs(x = "Above Grade Living Area (sqft)", y = "Sale Price",
title = "Sale Price vs. Above Grade Living Area by Building Type") +
scale_color_manual(values = colors) +
theme(legend.position = "none") # Opcional: quitar la leyenda
### Dolar format
# Crea el gráfico con facetas y colores personalizados
ggplot(data = ames, aes(x = Gr_Liv_Area, y = Sale_Price)) +
geom_point(aes(color = Bldg_Type), size = 3) +
facet_wrap(~ Bldg_Type, ncol = 2) +
labs(x = "Above Grade Living Area (sqft)", y = "Sale Price (USD)",
title = "Sale Price vs. Above Grade Living Area by Building Type") +
scale_color_manual(values = colors) +
theme(legend.position = "none") + # Opcional: quitar la leyenda
scale_y_continuous(labels = scales::dollar_format())
4.2.4 Arbol
# https://cs.calvin.edu/courses/data/202/21fa/ex/ex07/ex07-modeling-inst.html
set.seed(1234)
# Split our data randomly
library(rsample)## Warning: package 'rsample' was built under R version 4.3.3ames_split <- initial_split(ames, prop = 2/3)
ames_train <- training(ames_split)
ames_test <- testing(ames_split)
#install.packages("rminer")
library(rminer)## Warning: package 'rminer' was built under R version 4.3.3# Instala y carga el paquete rpart
#install.packages("rpart")
library(rpart)
library(rpart.plot)
# Ajusta el modelo de árbol de decisión
decision_tree_fit <- rpart(Sale_Price ~ Gr_Liv_Area_m2 + Bldg_Type, data = ames_train, method = "anova", control = rpart.control(maxdepth = 3))
# Grafica el árbol de decisión
rpart.plot(decision_tree_fit, roundint = FALSE)
5 Investigar mas sobre modelos
Enlace: https://cs.calvin.edu/courses/data/202/21fa/ex/ex07/ex07-modeling-inst.html