Econometria: Exercício soja (apostila) em Python

Abstract

This is an undergrad student level exercise for class use. We analyse soy data, 117 observations.

Licença

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

License: CC BY-SA 4.0

Citação

Sugestão de citação: FIGUEIREDO, Adriano Marcos Rodrigues. Econometria: Exercício soja (apostila) em Python. Campo Grande-MS,Brasil: RStudio/Rpubs, 2022. Disponível em http://rpubs.com/amrofi/exercicio_soja_apostila_python.

1 Introdução

Este exercício acompanha o publicado em Figueiredo (2020), mas agora executado em Python no Rmarkdown que pode ser baixado no alto do post. Os dados foram inicialmente carregados do Excel e depois incorporados no script abaixo.

import numpy as np
import pandas as pd
# Carrega os dados

# precisei instalar openpyxl (para xlsx) e xlrd (para xls)
df = pd.read_excel (r'soja_apostila.xlsx', sheet_name='dados')

#data_as_dict= print(df.to_dict())
#df = pd.DataFrame.from_dict(data_as_dict)
import pandas as pd
dados = pd.DataFrame.from_dict(
  {'OBS': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20, 20: 21, 21: 22, 22: 23, 23: 24, 24: 25, 25: 26, 26: 27, 27: 28, 28: 29, 29: 30, 30: 31, 31: 32, 32: 33, 33: 34, 34: 35, 35: 36, 36: 37, 37: 38, 38: 39, 39: 40, 40: 41, 41: 42, 42: 43, 43: 44, 44: 45, 45: 46, 46: 47, 47: 48, 48: 49, 49: 50, 50: 51, 51: 52, 52: 53, 53: 54, 54: 55, 55: 56, 56: 57, 57: 58, 58: 59, 59: 60, 60: 61, 61: 62, 62: 63, 63: 64, 64: 65, 65: 66, 66: 67, 67: 68, 68: 69, 69: 70, 70: 71, 71: 72, 72: 73, 73: 74, 74: 75, 75: 76, 76: 77, 77: 78, 78: 79, 79: 80, 80: 81, 81: 82, 82: 83, 83: 84, 84: 85, 85: 86, 86: 87, 87: 88, 88: 89, 89: 90, 90: 91, 91: 92, 92: 93, 93: 94, 94: 95, 95: 96, 96: 97, 97: 98, 98: 99, 99: 100, 100: 101, 101: 102, 102: 103, 103: 104, 104: 105, 105: 106, 106: 107, 107: 108, 108: 109, 109: 110, 110: 111, 111: 112, 112: 113, 113: 114, 114: 115, 115: 116, 116: 117}, 'QSOJA': {0: 436.631327347, 1: 373.648319403, 2: 394.422208122, 3: 343.569529223, 4: 303.766149519, 5: 301.164159253, 6: 288.948162961, 7: 330.653425923, 8: 312.790481897, 9: 326.337437514, 10: 393.924244131, 11: 472.095484821, 12: 506.519816219, 13: 351.622349614, 14: 381.683735178, 15: 383.16244294, 16: 411.039886175, 17: 393.721292241, 18: 434.570723074, 19: 433.61603289, 20: 397.521061235, 21: 392.667303139, 22: 388.161060061, 23: 370.962499467, 24: 392.989989558, 25: 364.608287145, 26: 346.432408617, 27: 418.249947335, 28: 406.403616915, 29: 335.565654517, 30: 372.389277147, 31: 355.138034335, 32: 350.368666514, 33: 333.22912698, 34: 331.404160354, 35: 350.215587437, 36: 347.930917294, 37: 429.353837601, 38: 312.648633868, 39: 320.1290397, 40: 367.600375264, 41: 370.58115319, 42: 318.293875369, 43: 360.716491231, 44: 344.127888634, 45: 348.460445231, 46: 339.909909323, 47: 355.115806958, 48: 333.991242698, 49: 324.352196839, 50: 326.362748629, 51: 337.522873509, 52: 326.439134587, 53: 315.883680773, 54: 309.389262881, 55: 309.992167966, 56: 294.858595183, 57: 319.126938705, 58: 321.075126328, 59: 324.617110436, 60: 326.498169984, 61: 323.024096765, 62: 306.607962724, 63: 316.685380598, 64: 306.63234033, 65: 347.051171678, 66: 281.018277888, 67: 306.438241825, 68: 310.158071775, 69: 308.554712739, 70: 317.988817729, 71: 309.3024648, 72: 301.907326808, 73: 293.695986672, 74: 286.246007121, 75: 284.741951642, 76: 281.541824884, 77: 276.076484065, 78: 225.250102468, 79: 221.579142339, 80: 222.819046328, 81: 210.465091286, 82: 204.579726173, 83: 210.208100729, 84: 214.619137203, 85: 249.68373735, 86: 234.056997721, 87: 237.782743552, 88: 247.783594823, 89: 243.326935015, 90: 250.517759798, 91: 245.477283956, 92: 242.547637962, 93: 235.139515392, 94: 246.077631412, 95: 300.660379261, 96: 311.547314244, 97: 311.592498254, 98: 311.661546245, 99: 313.521069724, 100: 324.623216411, 101: 325.219601572, 102: 316.051963666, 103: 315.23510561, 104: 313.039404973, 105: 311.256344161, 106: 314.759829619, 107: 319.859862035, 108: 315.86486682, 109: 313.067146865, 110: 305.235250016, 111: 299.911393983, 112: 292.819273066, 113: 288.374750217, 114: 282.574142328, 115: 280.040196223, 116: 272.093598783}, 'FERTILIZANTE': {0: 19.0271541214, 1: 17.896131535, 2: 16.7816326404, 3: 13.4907436954, 4: 9.8792199643, 5: 9.47578570764, 6: 11.3642792008, 7: 15.1279345194, 8: 15.3328667597, 9: 12.851502126, 10: 11.5137639555, 11: 12.855099231, 12: 13.0130463524, 13: 13.4551480743, 14: 14.3478259384, 15: 13.4461834272, 16: 12.8505836532, 17: 11.878680085, 18: 8.97428388969, 19: 11.2853667097, 20: 10.3459526645, 21: 10.1678109845, 22: 12.599515057, 23: 18.0635955859, 24: 22.5905514861, 25: 27.0789975599, 26: 25.8933999151, 27: 24.670302157, 28: 22.3482879799, 29: 23.0661021802, 30: 23.46202603, 31: 23.3742807993, 32: 23.6293106114, 33: 21.5085651347, 34: 20.4244350802, 35: 18.8640383209, 36: 18.2649424041, 37: 16.1258445984, 38: 15.3872613296, 39: 15.7475620647, 40: 14.8983557849, 41: 18.5713738614, 42: 19.782502768, 43: 19.9334418708, 44: 20.8217736318, 45: 20.2664704198, 46: 18.7039332243, 47: 16.9397047639, 48: 15.2224405941, 49: 15.3900606317, 50: 15.4866979181, 51: 14.1888364722, 52: 17.5057959027, 53: 18.4499760981, 54: 18.0443380567, 55: 18.7653974258, 56: 17.733992169, 57: 14.4708212634, 58: 19.1906127545, 59: 23.6107568782, 60: 22.4809389477, 61: 19.9623501966, 62: 24.292193006, 63: 23.7774100871, 64: 20.902854945, 65: 17.6135324226, 66: 18.2422805406, 67: 18.4963907183, 68: 20.1887054098, 69: 17.2164566133, 70: 18.2228548842, 71: 17.63412, 72: 17.3651340732, 73: 21.165752859, 74: 20.6546570465, 75: 20.5382250175, 76: 20.2625821575, 77: 20.0316705895, 78: 19.6747891284, 79: 19.2320746157, 80: 19.1556951795, 81: 18.6659751037, 82: 18.2573530021, 83: 18.0250472242, 84: 18.2220357618, 85: 18.1808546614, 86: 17.9427350427, 87: 17.8936494922, 88: 17.5782913467, 89: 17.4452921577, 90: 17.4075434149, 91: 17.287132673, 92: 17.0010026609, 93: 16.7956796708, 94: 16.6141444443, 95: 16.6135183413, 96: 16.5922588804, 97: 22.0744924554, 98: 22.0123280182, 99: 21.8207871467, 100: 21.4818658909, 101: 21.3918043526, 102: 21.1455500396, 103: 21.0219803014, 104: 20.9587175263, 105: 20.8135574015, 106: 22.8749876176, 107: 22.8850270408, 108: 22.7508743781, 109: 22.6733292656, 110: 22.4866071739, 111: 22.3322073706, 112: 22.1375395445, 113: 22.1331443789, 114: 22.081593902, 115: 22.1113459316, 116: 22.0611011027}, 'TRATOR': {0: 3.1712177231, 1: 2.9130726375, 2: 2.79693877341, 3: 2.89345709284, 4: 3.09884379577, 5: 3.55341964037, 6: 3.9774977203, 7: 4.86255038122, 8: 5.27067294863, 9: 5.29179499304, 10: 4.38619579258, 11: 3.61549665871, 12: 3.18096688613, 13: 3.31203644906, 14: 3.58695648459, 15: 3.36154585679, 16: 2.79360514201, 17: 3.25443289999, 18: 2.69228516691, 19: 2.90195143963, 20: 2.95598647557, 21: 2.98255788878, 22: 3.23987530037, 23: 3.18769333868, 24: 3.80472446082, 25: 4.16599962459, 26: 4.25644930111, 27: 3.65485957882, 28: 3.42843054238, 29: 3.56476124603, 30: 4.10585455524, 31: 4.23376550096, 32: 4.21951975203, 33: 4.45534563505, 34: 4.22104991658, 35: 3.77280766418, 36: 4.05887608981, 37: 4.35397804157, 38: 3.71858815465, 39: 3.9194002239, 40: 3.86253116707, 41: 3.4489694314, 42: 3.40698658782, 43: 3.10590838452, 44: 3.40719932157, 45: 3.89739815766, 46: 3.58705568686, 47: 3.06139242721, 48: 2.56377946849, 49: 3.27038788423, 50: 3.61356284755, 51: 2.9212310384, 52: 3.72808616447, 53: 4.09999468846, 54: 4.00985290148, 55: 3.12756623763, 56: 3.66502504826, 57: 3.61770531584, 58: 2.74151610779, 59: 3.07966394064, 60: 2.24809389477, 61: 2.21803891073, 62: 3.23895906746, 63: 3.26939388698, 64: 2.71737114285, 65: 3.52270648453, 66: 2.63499607808, 67: 2.84559857204, 68: 3.02830581147, 69: 2.75463305812, 70: 3.79642810087, 71: 3.673775, 72: 4.3412835183, 73: 4.23315057181, 74: 5.50790854573, 75: 5.47686000466, 76: 5.40335524199, 77: 6.67722352984, 78: 6.5582630428, 79: 6.41069153856, 80: 6.3852317265, 81: 6.22199170124, 82: 6.08578433403, 83: 6.00834907473, 84: 6.07401192061, 85: 6.06028488713, 86: 5.98091168091, 87: 5.96454983075, 88: 5.85943044889, 89: 5.8150973859, 90: 5.80251447164, 91: 5.76237755766, 92: 5.66700088697, 93: 5.59855989028, 94: 5.53804814809, 95: 5.53783944709, 96: 5.53075296013, 97: 5.51862311384, 98: 5.50308200454, 99: 5.45519678667, 100: 5.37046647273, 101: 5.34795108814, 102: 5.28638750989, 103: 5.25549507535, 104: 5.23967938158, 105: 5.20338935039, 106: 5.19886082219, 107: 5.20114250927, 108: 5.17065326775, 109: 5.15302937855, 110: 5.11059253952, 111: 5.07550167513, 112: 6.03751078486, 113: 6.03631210335, 114: 6.02225288236, 115: 6.03036707224, 116: 6.01666393711}, 'MO': {0: 0.0680761131536, 1: 0.0680761131536, 2: 0.0680761131536, 3: 0.0680761131536, 4: 0.0715237353179, 5: 0.0833559863149, 6: 0.0985723372523, 7: 0.111410334113, 8: 0.114487135409, 9: 0.102686021888, 10: 0.121305727388, 11: 0.123194700963, 12: 0.113382190903, 13: 0.0988435877764, 14: 0.0807663035114, 15: 0.0622686351567, 16: 0.083800394246, 17: 0.0765243736067, 18: 0.0574877668834, 19: 0.0653655605136, 20: 0.0725099376921, 21: 0.0780548956575, 22: 0.0806568955951, 23: 0.0816669323964, 24: 0.0822771664653, 25: 0.0801052294483, 26: 0.0750435658726, 27: 0.0703103611476, 28: 0.0796030780377, 29: 0.0830484524405, 30: 0.093584156327, 31: 0.100913962297, 32: 0.108669511694, 33: 0.111606408158, 34: 0.118828985067, 35: 0.120133794043, 36: 0.118234214897, 37: 0.105740298613, 38: 0.093457488034, 39: 0.0841934657141, 40: 0.0798233440708, 41: 0.0747407520408, 42: 0.0708495225001, 43: 0.0672990598108, 44: 0.0611103807825, 45: 0.055394759321, 46: 0.0660366632049, 47: 0.0689438046948, 48: 0.0669589093824, 49: 0.0638618759693, 50: 0.0596771157157, 51: 0.0549263770463, 52: 0.073413760912, 53: 0.0823331322263, 54: 0.0834334103063, 55: 0.079906745817, 56: 0.0716246518416, 57: 0.0633701381158, 58: 0.0934971222594, 59: 0.104075531949, 60: 0.100833255886, 61: 0.0930097649901, 62: 0.0813417334974, 63: 0.0695736926403, 64: 0.21049581374, 65: 0.261260874072, 66: 0.258725366517, 67: 0.236599269382, 68: 0.206871841743, 69: 0.167746823366, 70: 0.126327870706, 71: 0.114329213918, 72: 0.104788717578, 73: 0.0945762804116, 74: 0.0848737411962, 75: 0.0770183438155, 76: 0.0741085180759, 77: 0.071409196083, 78: 0.0683152400292, 79: 0.0649972892104, 80: 0.0629654795252, 81: 0.0596274204703, 82: 0.0578149511733, 83: 0.0565786204537, 84: 0.0566907779257, 85: 0.0560576352059, 86: 0.0548250237417, 87: 0.0541779942959, 88: 0.0539450091897, 89: 0.0542532433056, 90: 0.0548506857575, 91: 0.0551811677564, 92: 0.0549659731863, 93: 0.0549918545222, 94: 0.0547197615699, 95: 0.0550399709491, 96: 0.0552913982385, 97: 0.0554912883605, 98: 0.0556552669895, 99: 0.0554884433151, 100: 0.0541104333052, 101: 0.0533695807757, 102: 0.0522471298894, 103: 0.0514366981903, 104: 0.0507783150735, 105: 0.049926520817, 106: 0.049902565317, 107: 0.0499439709453, 108: 0.0496705879533, 109: 0.0495206123279, 110: 0.0491319590269, 111: 0.0488136373605, 112: 0.0483839405954, 113: 0.0483701426115, 114: 0.0482533012199, 115: 0.0483141284115, 116: 0.0482001633184}})
dados

     OBS       QSOJA  FERTILIZANTE    TRATOR        MO
0      1  436.631327     19.027154  3.171218  0.068076
1      2  373.648319     17.896132  2.913073  0.068076
2      3  394.422208     16.781633  2.796939  0.068076
3      4  343.569529     13.490744  2.893457  0.068076
4      5  303.766150      9.879220  3.098844  0.071524
..   ...         ...           ...       ...       ...
112  113  292.819273     22.137540  6.037511  0.048384
113  114  288.374750     22.133144  6.036312  0.048370
114  115  282.574142     22.081594  6.022253  0.048253
115  116  280.040196     22.111346  6.030367  0.048314
116  117  272.093599     22.061101  6.016664  0.048200

[117 rows x 5 columns]

dados.info() # Ve a estrutura dos dados

<class 'pandas.core.frame.DataFrame'>
Int64Index: 117 entries, 0 to 116
Data columns (total 5 columns):
 #   Column        Non-Null Count  Dtype  
---  ------        --------------  -----  
 0   OBS           117 non-null    int64  
 1   QSOJA         117 non-null    float64
 2   FERTILIZANTE  117 non-null    float64
 3   TRATOR        117 non-null    float64
 4   MO            117 non-null    float64
dtypes: float64(4), int64(1)
memory usage: 5.5 KB

2 Regressão inicial

import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
import statsmodels.formula.api as sm
eq1 = sm.ols(formula="QSOJA~FERTILIZANTE+TRATOR+MO", data=dados).fit()
print(eq1.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  QSOJA   R-squared:                       0.465
Model:                            OLS   Adj. R-squared:                  0.451
Method:                 Least Squares   F-statistic:                     32.75
Date:                Sat, 04 Jun 2022   Prob (F-statistic):           2.61e-15
Time:                        15:48:35   Log-Likelihood:                -599.90
No. Observations:                 117   AIC:                             1208.
Df Residuals:                     113   BIC:                             1219.
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
Intercept      494.9657     25.572     19.356      0.000     444.302     545.629
FERTILIZANTE    -0.5535      1.059     -0.523      0.602      -2.651       1.544
TRATOR         -33.6899      3.741     -9.006      0.000     -41.102     -26.278
MO            -209.1407    107.893     -1.938      0.055    -422.896       4.614
==============================================================================
Omnibus:                       14.471   Durbin-Watson:                   0.674
Prob(Omnibus):                  0.001   Jarque-Bera (JB):               16.751
Skew:                           0.745   Prob(JB):                     0.000230
Kurtosis:                       4.103   Cond. No.                         548.
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Referências

FIGUEIREDO, Adriano Marcos Rodrigues. Econometria: exercicio_soja_apostila. Campo Grande-MS,Brasil: RStudio/Rpubs, 2020. Disponível em http://rpubs.com/amrofi/exercicio_soja_apostila.