Econometria: exercicio_soja_apostila

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: exercicio_soja_apostila. Campo Grande-MS,Brasil: RStudio/Rpubs, 2020. Disponível em http://rpubs.com/amrofi/exercicio_soja_apostila.

1 Exercício

Sabendo que a variável dependente Qsoja é a quantidade produzida de soja, a variável FERTILIZANTE é a quantidade utilizada de fertilizantes, a variável TRATOR é o número de horas-máquina utilizadas, e MO é a quantidade de mão-de-obra em número de pessoas.

Pede-se:

1. Quais os parâmetros significativos a 10% de significância? Explique e mostre seus valores.
   
2. Sabendo que o desejável numa função de produção é que o aumento no uso de insumos leve a uma produção maior, o resultado é coerente com a teoria econômica? Justifique sua resposta.
   
3. Qual a hipótese nula no teste de significância global do modelo? Qual a probabilidade de erro desse teste para essa regressão?

1.1 Chamando os dados de soja.

library(readxl)
# library(foreign)
dados <- read_excel("soja_apostila.xlsx", 
                    sheet = "dados")
# QSOJA = quantidade produzida de soja; 
# FERTILIZANTE = quantidade utilizada de fertilizantes, 
# TRATOR = número de horas-máquina utilizadas, e 
# MO = quantidade de mão-de-obra em número de pessoas 

1.2 Exibindo os dados

library(knitr)
kable(dados)

OBS	QSOJA	FERTILIZANTE	TRATOR	MO
1	436.6313	19.027154	3.171218	0.0680761
2	373.6483	17.896131	2.913073	0.0680761
3	394.4222	16.781633	2.796939	0.0680761
4	343.5695	13.490744	2.893457	0.0680761
5	303.7661	9.879220	3.098844	0.0715237
6	301.1642	9.475786	3.553420	0.0833560
7	288.9482	11.364279	3.977498	0.0985723
8	330.6534	15.127935	4.862550	0.1114103
9	312.7905	15.332867	5.270673	0.1144871
10	326.3374	12.851502	5.291795	0.1026860
11	393.9242	11.513764	4.386196	0.1213057
12	472.0955	12.855099	3.615497	0.1231947
13	506.5198	13.013046	3.180967	0.1133822
14	351.6223	13.455148	3.312036	0.0988436
15	381.6837	14.347826	3.586956	0.0807663
16	383.1624	13.446183	3.361546	0.0622686
17	411.0399	12.850584	2.793605	0.0838004
18	393.7213	11.878680	3.254433	0.0765244
19	434.5707	8.974284	2.692285	0.0574878
20	433.6160	11.285367	2.901951	0.0653656
21	397.5211	10.345953	2.955986	0.0725099
22	392.6673	10.167811	2.982558	0.0780549
23	388.1611	12.599515	3.239875	0.0806569
24	370.9625	18.063596	3.187693	0.0816669
25	392.9900	22.590552	3.804724	0.0822772
26	364.6083	27.078998	4.166000	0.0801052
27	346.4324	25.893400	4.256449	0.0750436
28	418.2499	24.670302	3.654860	0.0703104
29	406.4036	22.348288	3.428431	0.0796031
30	335.5657	23.066102	3.564761	0.0830485
31	372.3893	23.462026	4.105855	0.0935842
32	355.1380	23.374281	4.233765	0.1009140
33	350.3687	23.629311	4.219520	0.1086695
34	333.2291	21.508565	4.455346	0.1116064
35	331.4042	20.424435	4.221050	0.1188290
36	350.2156	18.864038	3.772808	0.1201338
37	347.9309	18.264942	4.058876	0.1182342
38	429.3538	16.125845	4.353978	0.1057403
39	312.6486	15.387261	3.718588	0.0934575
40	320.1290	15.747562	3.919400	0.0841935
41	367.6004	14.898356	3.862531	0.0798233
42	370.5812	18.571374	3.448969	0.0747408
43	318.2939	19.782503	3.406987	0.0708495
44	360.7165	19.933442	3.105908	0.0672991
45	344.1279	20.821774	3.407199	0.0611104
46	348.4604	20.266470	3.897398	0.0553948
47	339.9099	18.703933	3.587056	0.0660367
48	355.1158	16.939705	3.061392	0.0689438
49	333.9912	15.222441	2.563779	0.0669589
50	324.3522	15.390061	3.270388	0.0638619
51	326.3627	15.486698	3.613563	0.0596771
52	337.5229	14.188837	2.921231	0.0549264
53	326.4391	17.505796	3.728086	0.0734138
54	315.8837	18.449976	4.099995	0.0823331
55	309.3893	18.044338	4.009853	0.0834334
56	309.9922	18.765397	3.127566	0.0799067
57	294.8586	17.733992	3.665025	0.0716247
58	319.1269	14.470821	3.617705	0.0633701
59	321.0751	19.190613	2.741516	0.0934971
60	324.6171	23.610757	3.079664	0.1040755
61	326.4982	22.480939	2.248094	0.1008333
62	323.0241	19.962350	2.218039	0.0930098
63	306.6080	24.292193	3.238959	0.0813417
64	316.6854	23.777410	3.269394	0.0695737
65	306.6323	20.902855	2.717371	0.2104958
66	347.0512	17.613532	3.522706	0.2612609
67	281.0183	18.242280	2.634996	0.2587254
68	306.4382	18.496391	2.845599	0.2365993
69	310.1581	20.188705	3.028306	0.2068718
70	308.5547	17.216457	2.754633	0.1677468
71	317.9888	18.222855	3.796428	0.1263279
72	309.3025	17.634120	3.673775	0.1143292
73	301.9073	17.365134	4.341284	0.1047887
74	293.6960	21.165753	4.233151	0.0945763
75	286.2460	20.654657	5.507909	0.0848737
76	284.7420	20.538225	5.476860	0.0770183
77	281.5418	20.262582	5.403355	0.0741085
78	276.0765	20.031671	6.677224	0.0714092
79	225.2501	19.674789	6.558263	0.0683152
80	221.5791	19.232075	6.410692	0.0649973
81	222.8190	19.155695	6.385232	0.0629655
82	210.4651	18.665975	6.221992	0.0596274
83	204.5797	18.257353	6.085784	0.0578150
84	210.2081	18.025047	6.008349	0.0565786
85	214.6191	18.222036	6.074012	0.0566908
86	249.6837	18.180855	6.060285	0.0560576
87	234.0570	17.942735	5.980912	0.0548250
88	237.7827	17.893649	5.964550	0.0541780
89	247.7836	17.578291	5.859430	0.0539450
90	243.3269	17.445292	5.815097	0.0542532
91	250.5178	17.407543	5.802515	0.0548507
92	245.4773	17.287133	5.762378	0.0551812
93	242.5476	17.001003	5.667001	0.0549660
94	235.1395	16.795680	5.598560	0.0549919
95	246.0776	16.614144	5.538048	0.0547198
96	300.6604	16.613518	5.537839	0.0550400
97	311.5473	16.592259	5.530753	0.0552914
98	311.5925	22.074493	5.518623	0.0554913
99	311.6615	22.012328	5.503082	0.0556553
100	313.5211	21.820787	5.455197	0.0554884
101	324.6232	21.481866	5.370467	0.0541104
102	325.2196	21.391804	5.347951	0.0533696
103	316.0520	21.145550	5.286388	0.0522471
104	315.2351	21.021980	5.255495	0.0514367
105	313.0394	20.958717	5.239679	0.0507783
106	311.2563	20.813557	5.203389	0.0499265
107	314.7598	22.874988	5.198861	0.0499026
108	319.8599	22.885027	5.201142	0.0499440
109	315.8649	22.750874	5.170653	0.0496706
110	313.0671	22.673329	5.153029	0.0495206
111	305.2353	22.486607	5.110593	0.0491320
112	299.9114	22.332207	5.075502	0.0488136
113	292.8193	22.137539	6.037511	0.0483839
114	288.3748	22.133144	6.036312	0.0483701
115	282.5741	22.081594	6.022253	0.0482533
116	280.0402	22.111346	6.030367	0.0483141
117	272.0936	22.061101	6.016664	0.0482002

attach(dados)

1.3 RESET de Ramsey

1.3.1 Execucao manual do RESET de Ramsey para especificação

# PASSO 1: estimar o modelo

regressao1<-lm(QSOJA~FERTILIZANTE+TRATOR+MO)
summary(regressao1)

## 
## Call:
## lm(formula = QSOJA ~ FERTILIZANTE + TRATOR + MO)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -66.714 -33.171   1.768  24.894 149.637 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   494.9657    25.5723  19.356  < 2e-16 ***
## FERTILIZANTE   -0.5535     1.0589  -0.523   0.6022    
## TRATOR        -33.6899     3.7410  -9.006 6.09e-15 ***
## MO           -209.1407   107.8926  -1.938   0.0551 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 41.51 on 113 degrees of freedom
## Multiple R-squared:  0.4651, Adjusted R-squared:  0.4509 
## F-statistic: 32.75 on 3 and 113 DF,  p-value: 2.608e-15

library(stargazer)

## 
## Please cite as:

##  Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.

##  R package version 5.2.2. https://CRAN.R-project.org/package=stargazer

stargazer(list(regressao1),type="text",style="all" )

## 
## =======================================================
##                             Dependent variable:        
##                     -----------------------------------
##                                    QSOJA               
## -------------------------------------------------------
## FERTILIZANTE                      -0.554               
##                                   (1.059)              
##                                 t = -0.523             
##                                  p = 0.603             
## TRATOR                          -33.690***             
##                                   (3.741)              
##                                 t = -9.006             
##                                  p = 0.000             
## MO                               -209.141*             
##                                  (107.893)             
##                                 t = -1.938             
##                                  p = 0.056             
## Constant                        494.966***             
##                                  (25.572)              
##                                 t = 19.356             
##                                  p = 0.000             
## -------------------------------------------------------
## Observations                        117                
## R2                                 0.465               
## Adjusted R2                        0.451               
## Residual Std. Error          41.506 (df = 113)         
## F Statistic         32.753*** (df = 3; 113) (p = 0.000)
## =======================================================
## Note:                       *p<0.1; **p<0.05; ***p<0.01

#PASSO 2: obtencao dos valores ajustados 
# utilizaremos o recurso I(fitted(regressao1)) para gerar automaticamente e já estimar a regressão de teste

#PASSO 3: colocar valores ajustados ao quadrado e ao cubo e a quarta potencias
#PASSO 4: estimar regressão de teste

reg_RESET_3<-lm(QSOJA~FERTILIZANTE+TRATOR+MO+I(fitted(regressao1)^2)+
                  I(fitted(regressao1)^3)+I(fitted(regressao1)^4),data=dados)

reg_RESET<-lm(QSOJA~FERTILIZANTE+TRATOR+MO+
                I(fitted(regressao1)^2)+I(fitted(regressao1)^3),data=dados)
results<-stargazer(list(regressao1,reg_RESET_3),type="text",style="all" )

## 
## ==============================================================================================
##                                                  Dependent variable:                          
##                        -----------------------------------------------------------------------
##                                                         QSOJA                                 
##                                        (1)                                 (2)                
## ----------------------------------------------------------------------------------------------
## FERTILIZANTE                         -0.554                             304.130**             
##                                      (1.059)                            (135.047)             
##                                    t = -0.523                           t = 2.252             
##                                     p = 0.603                           p = 0.027             
## TRATOR                             -33.690***                         18,591.290**            
##                                      (3.741)                           (8,231.767)            
##                                    t = -9.006                           t = 2.258             
##                                     p = 0.000                           p = 0.026             
## MO                                  -209.141*                         115,237.700**           
##                                     (107.893)                         (51,069.360)            
##                                    t = -1.938                           t = 2.256             
##                                     p = 0.056                           p = 0.027             
## I(fitted(regressao1)2)                                                   2.665**              
##                                                                          (1.165)              
##                                                                         t = 2.287             
##                                                                         p = 0.025             
## I(fitted(regressao1)3)                                                  -0.006**              
##                                                                          (0.002)              
##                                                                        t = -2.300             
##                                                                         p = 0.024             
## I(fitted(regressao1)4)                                                  0.00000**             
##                                                                         (0.00000)             
##                                                                         t = 2.303             
##                                                                         p = 0.024             
## Constant                           494.966***                        -230,604.700**           
##                                     (25.572)                          (101,861.300)           
##                                    t = 19.356                          t = -2.264             
##                                     p = 0.000                           p = 0.026             
## ----------------------------------------------------------------------------------------------
## Observations                           117                                 117                
## R2                                    0.465                               0.532               
## Adjusted R2                           0.451                               0.507               
## Residual Std. Error             41.506 (df = 113)                   39.331 (df = 110)         
## F Statistic            32.753*** (df = 3; 113) (p = 0.000) 20.879*** (df = 6; 110) (p = 0.000)
## ==============================================================================================
## Note:                                                              *p<0.1; **p<0.05; ***p<0.01

#PASSOS 4 A 6: calcular estatisticas de teste
# RESET: H0: o modelo esta bem especificado, ou H0: COEFICIENTES incluindo "fitted" sao nulos
library(car)

## Loading required package: carData

# RESETH0<-c("I(fitted(regressao1)^2)","I(fitted(regressao1)^3)",
#         "I(fitted(regressao1)^4)")
RESETH0<-c("I(fitted(regressao1)^2)","I(fitted(regressao1)^3)")
Tabela_RESET<-linearHypothesis(reg_RESET,RESETH0)
# outra alternativa é usar a linha abaixo com o matchCoefs
#Tabela_RESET<-linearHypothesis(reg_RESET, matchCoefs(reg_RESET,"fitted"))
Tabela_RESET

1.3.2 RESET pelo comando resettest da library(lmtest)

library(lmtest)

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

TesteRESET<-resettest(regressao1, power = 2:3) # default é power = 2:3
TesteRESET

## 
##  RESET test
## 
## data:  regressao1
## RESET = 5.0746, df1 = 2, df2 = 111, p-value = 0.007783

#alterando as potencias
TesteRESET.power<-resettest(regressao1, power = 2:4)
TesteRESET.power

## 
##  RESET test
## 
## data:  regressao1
## RESET = 5.2816, df1 = 3, df2 = 110, p-value = 0.001932

1.3.3 fazendo os criterios de informacao de Akaike e Schwarz

regressao1$AIC <- AIC(regressao1)
regressao1$BIC <- BIC(regressao1)


#mostrando os valores de AIC e SIC
library(stargazer)
star.1 <- stargazer(regressao1,
                    title="Título: Resultado da Regressão",
                    align=TRUE,
                    type = "text", style = "all",
                    keep.stat=c("aic","bic","rsq", "adj.rsq","n")
)

## 
## Título: Resultado da Regressão
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                QSOJA           
## -----------------------------------------------
## FERTILIZANTE                  -0.554           
##                               (1.059)          
##                             t = -0.523         
##                              p = 0.603         
## TRATOR                      -33.690***         
##                               (3.741)          
##                             t = -9.006         
##                              p = 0.000         
## MO                           -209.141*         
##                              (107.893)         
##                             t = -1.938         
##                              p = 0.056         
## Constant                    494.966***         
##                              (25.572)          
##                             t = 19.356         
##                              p = 0.000         
## -----------------------------------------------
## Observations                    117            
## R2                             0.465           
## Adjusted R2                    0.451           
## Akaike Inf. Crit.            1,209.807         
## Bayesian Inf. Crit.          1,223.617         
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

1.3.4 Regressão log-log

reg.loglog<-lm(log(QSOJA)~log(FERTILIZANTE)+log(TRATOR)+log(MO))
reg.loglog$AIC <- AIC(reg.loglog)
reg.loglog$BIC <- BIC(reg.loglog)
summary(reg.loglog)

## 
## Call:
## lm(formula = log(QSOJA) ~ log(FERTILIZANTE) + log(TRATOR) + log(MO))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.28745 -0.11478  0.01292  0.09072  0.35834 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        6.36829    0.17474  36.445  < 2e-16 ***
## log(FERTILIZANTE) -0.03156    0.05807  -0.543    0.588    
## log(TRATOR)       -0.41543    0.05420  -7.664 6.74e-12 ***
## log(MO)           -0.02877    0.03960  -0.727    0.469    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1351 on 113 degrees of freedom
## Multiple R-squared:  0.4275, Adjusted R-squared:  0.4123 
## F-statistic: 28.13 on 3 and 113 DF,  p-value: 1.162e-13

library(stargazer)
stargazer(regressao1,reg.loglog,
          type="text",style="all",
          keep.stat=c("aic","bic","rsq", "adj.rsq","n"))

## 
## ================================================
##                         Dependent variable:     
##                     ----------------------------
##                         QSOJA       log(QSOJA)  
##                          (1)            (2)     
## ------------------------------------------------
## FERTILIZANTE            -0.554                  
##                        (1.059)                  
##                       t = -0.523                
##                       p = 0.603                 
## TRATOR                -33.690***                
##                        (3.741)                  
##                       t = -9.006                
##                       p = 0.000                 
## MO                    -209.141*                 
##                       (107.893)                 
##                       t = -1.938                
##                       p = 0.056                 
## log(FERTILIZANTE)                     -0.032    
##                                       (0.058)   
##                                     t = -0.543  
##                                      p = 0.588  
## log(TRATOR)                          -0.415***  
##                                       (0.054)   
##                                     t = -7.664  
##                                      p = 0.000  
## log(MO)                               -0.029    
##                                       (0.040)   
##                                     t = -0.727  
##                                      p = 0.470  
## Constant              494.966***     6.368***   
##                        (25.572)       (0.175)   
##                       t = 19.356    t = 36.445  
##                       p = 0.000      p = 0.000  
## ------------------------------------------------
## Observations             117            117     
## R2                      0.465          0.428    
## Adjusted R2             0.451          0.412    
## Akaike Inf. Crit.     1,209.807      -130.503   
## Bayesian Inf. Crit.   1,223.617      -116.692   
## ================================================
## Note:                *p<0.1; **p<0.05; ***p<0.01

1.3.5 Será que tenho outliers?

outlierTest(reg.loglog)

## No Studentized residuals with Bonferroni p < 0.05
## Largest |rstudent|:
##    rstudent unadjusted p-value Bonferroni p
## 13 2.777133          0.0064307      0.75239

outlierTest(regressao1)

##    rstudent unadjusted p-value Bonferroni p
## 13 3.882668         0.00017511     0.020487

1.3.6 Testes de Heterocedasticidade

1.3.6.1 Teste de Breusch-Pagan - bptest simples

library(AER)

## Loading required package: sandwich

## Loading required package: survival

bp.het<-bptest(regressao1, studentize = TRUE)
bp.het

## 
##  studentized Breusch-Pagan test
## 
## data:  regressao1
## BP = 10.087, df = 3, p-value = 0.01784

1.3.6.2 Teste de White sem termos cruzados

# regressao1<-lm(QSOJA~FERTILIZANTE+TRATOR+MO)
m <- regressao1
data <- dados
#rotina do teste com base em m e data
u2 <- m$residuals^2
#sem termos cruzados, no cross-terms
reg.auxiliar <- lm(u2 ~ FERTILIZANTE+TRATOR+MO+
                     I(FERTILIZANTE^2)+I(TRATOR^2)+I(MO^2))  
summary(reg.auxiliar)

## 
## Call:
## lm(formula = u2 ~ FERTILIZANTE + TRATOR + MO + I(FERTILIZANTE^2) + 
##     I(TRATOR^2) + I(MO^2))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3451.5 -1319.0  -345.4   365.3 18550.3 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)  
## (Intercept)          9516.00    6550.45   1.453   0.1491  
## FERTILIZANTE         -810.45     551.79  -1.469   0.1448  
## TRATOR              -2061.75    2106.30  -0.979   0.3298  
## MO                  76907.49   29850.12   2.576   0.0113 *
## I(FERTILIZANTE^2)      18.85      15.37   1.226   0.2227  
## I(TRATOR^2)           245.72     236.74   1.038   0.3016  
## I(MO^2)           -230942.82  103719.00  -2.227   0.0280 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2805 on 110 degrees of freedom
## Multiple R-squared:  0.1389, Adjusted R-squared:  0.09188 
## F-statistic: 2.956 on 6 and 110 DF,  p-value: 0.0103

Ru2<- summary(reg.auxiliar)$r.squared
LM <- nrow(data)*Ru2
#obtendo o numero de regressores menos o intercepto
k <- length(coefficients(reg.auxiliar))-1
k

## [1] 6

p.value <- 1-pchisq(LM, k) # O TESTE TEM k TERMOS REGRESSORES EM reg.auxiliar
#c("LM","p.value")
c(LM, p.value)

## [1] 16.24547461  0.01249533

Agora com o bptest para reproduzir White. Pelo pacote lmtest, o bptest dará o mesmo resultado, desde que especifique a mesma regressão auxiliar usada no White acima.

bptest(regressao1,
       ~ FERTILIZANTE+TRATOR+MO+
         I(FERTILIZANTE^2)+I(TRATOR^2)+I(MO^2))

## 
##  studentized Breusch-Pagan test
## 
## data:  regressao1
## BP = 16.245, df = 6, p-value = 0.0125

1.3.6.3 White com termos cruzados - com cross-terms

reg.auxiliar <- lm(u2 ~ FERTILIZANTE+I(FERTILIZANTE*FERTILIZANTE)+
                     I(FERTILIZANTE*TRATOR)+I(FERTILIZANTE*MO)+
                     TRATOR+I(TRATOR*TRATOR)+I(TRATOR*MO)+
                     MO+I(MO*MO))
summary(reg.auxiliar)

## 
## Call:
## lm(formula = u2 ~ FERTILIZANTE + I(FERTILIZANTE * FERTILIZANTE) + 
##     I(FERTILIZANTE * TRATOR) + I(FERTILIZANTE * MO) + TRATOR + 
##     I(TRATOR * TRATOR) + I(TRATOR * MO) + MO + I(MO * MO))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4733.0 -1149.1  -261.6   588.4 15712.6 
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     -20557.49    9888.59  -2.079  0.04002 *  
## FERTILIZANTE                       445.35     600.72   0.741  0.46010    
## I(FERTILIZANTE * FERTILIZANTE)      25.27      15.81   1.599  0.11283    
## I(FERTILIZANTE * TRATOR)          -120.17      87.70  -1.370  0.17349    
## I(FERTILIZANTE * MO)            -13077.63    3137.31  -4.168 6.24e-05 ***
## TRATOR                             864.94    3116.37   0.278  0.78190    
## I(TRATOR * TRATOR)                 309.35     253.61   1.220  0.22522    
## I(TRATOR * MO)                  -22449.97   12081.31  -1.858  0.06588 .  
## MO                              426443.96   90390.39   4.718 7.24e-06 ***
## I(MO * MO)                     -365960.48  130236.21  -2.810  0.00589 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2600 on 107 degrees of freedom
## Multiple R-squared:  0.2806, Adjusted R-squared:  0.2201 
## F-statistic: 4.638 on 9 and 107 DF,  p-value: 3.426e-05

Ru2<- summary(reg.auxiliar)$r.squared
LM <- nrow(data)*Ru2
#obtendo o numero de regressores menos o intercepto
k <- length(coefficients(reg.auxiliar))-1
k

## [1] 9

p.value <- 1-pchisq(LM, k) # O TESTE TEM k TERMOS REGRESSORES EM reg.auxiliar
c(LM, p.value)

## [1] 3.283525e+01 1.426649e-04

Novamente, pelo bptest:

library(lmtest)
# reg.auxiliar <- lm(u2 ~ FERTILIZANTE+I(FERTILIZANTE*FERTILIZANTE)+
#                     I(FERTILIZANTE*TRATOR)+I(FERTILIZANTE*MO)+
#                     TRATOR+I(TRATOR*TRATOR)+I(TRATOR*MO)+
#                     MO+I(MO*MO))
bptest(regressao1,
       ~ FERTILIZANTE+I(FERTILIZANTE*FERTILIZANTE)+
         I(FERTILIZANTE*TRATOR)+I(FERTILIZANTE*MO)+
         TRATOR+I(TRATOR*TRATOR)+I(TRATOR*MO)+
         MO+I(MO*MO))

## 
##  studentized Breusch-Pagan test
## 
## data:  regressao1
## BP = 32.835, df = 9, p-value = 0.0001427

1.3.6.4 Correção de Var-cov conforme White (hc1)

#regressao1<-lm(QSOJA~FERTILIZANTE+TRATOR+MO)
#library(car) 
#possibilidades: hccm(regressao1,type=c("hc0","hc1","hc2","hc3","hc4"))
vcov.white0<-hccm(regressao1,type=c("hc1"))
#
coeftest(regressao1,vcov.white0)

## 
## t test of coefficients:
## 
##                Estimate Std. Error t value  Pr(>|t|)    
## (Intercept)   494.96573   26.46010 18.7061 < 2.2e-16 ***
## FERTILIZANTE   -0.55354    1.27243 -0.4350   0.66437    
## TRATOR        -33.68994    3.79488 -8.8777 1.198e-14 ***
## MO           -209.14074  115.17696 -1.8158   0.07205 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2 Usando o estimatr

library(estimatr)
library(car)

# Erros padrões robustos HC1 - padrão do Stata
model <- lm_robust(QSOJA~FERTILIZANTE+TRATOR+MO, 
                   data = dados,
                   se_type = "stata")
summary(model)

## 
## Call:
## lm_robust(formula = QSOJA ~ FERTILIZANTE + TRATOR + MO, data = dados, 
##     se_type = "stata")
## 
## Standard error type:  HC1 
## 
## Coefficients:
##               Estimate Std. Error t value  Pr(>|t|) CI Lower CI Upper  DF
## (Intercept)   494.9657     26.460  18.706 2.147e-36  442.543  547.388 113
## FERTILIZANTE   -0.5535      1.272  -0.435 6.644e-01   -3.074    1.967 113
## TRATOR        -33.6899      3.795  -8.878 1.198e-14  -41.208  -26.172 113
## MO           -209.1407    115.177  -1.816 7.205e-02 -437.327   19.046 113
## 
## Multiple R-squared:  0.4651 ,    Adjusted R-squared:  0.4509 
## F-statistic: 33.94 on 3 and 113 DF,  p-value: 1.021e-15

stargazer(regressao1,
          se = starprep(regressao1,se_type = "HC1"),
          p = starprep(regressao1,se_type = "HC1", stat = "p.value"),
          type="text",style="all",
          omit.stat = "f")

## 
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                QSOJA           
## -----------------------------------------------
## FERTILIZANTE                  -0.554           
##                               (1.272)          
##                             t = -0.435         
##                              p = 0.665         
## TRATOR                      -33.690***         
##                               (3.795)          
##                             t = -8.878         
##                              p = 0.000         
## MO                           -209.141*         
##                              (115.177)         
##                             t = -1.816         
##                              p = 0.073         
## Constant                    494.966***         
##                              (26.460)          
##                             t = 18.706         
##                              p = 0.000         
## -----------------------------------------------
## Observations                    117            
## R2                             0.465           
## Adjusted R2                    0.451           
## Residual Std. Error      41.506 (df = 113)     
## Akaike Inf. Crit.            1,209.807         
## Bayesian Inf. Crit.          1,223.617         
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

2.1 Agora com HC3

# alternativa HC3 - padrão do R
model.hc3 <- lm_robust(QSOJA~FERTILIZANTE+TRATOR+MO, 
                   data = dados,
                   se_type = "HC3")
summary(model.hc3)

## 
## Call:
## lm_robust(formula = QSOJA ~ FERTILIZANTE + TRATOR + MO, data = dados, 
##     se_type = "HC3")
## 
## Standard error type:  HC3 
## 
## Coefficients:
##               Estimate Std. Error t value  Pr(>|t|) CI Lower CI Upper  DF
## (Intercept)   494.9657     27.746 17.8390 1.194e-34  439.995  549.936 113
## FERTILIZANTE   -0.5535      1.308 -0.4233 6.729e-01   -3.144    2.037 113
## TRATOR        -33.6899      3.896 -8.6463 4.069e-14  -41.410  -25.970 113
## MO           -209.1407    129.250 -1.6181 1.084e-01 -465.208   46.927 113
## 
## Multiple R-squared:  0.4651 ,    Adjusted R-squared:  0.4509 
## F-statistic: 32.44 on 3 and 113 DF,  p-value: 3.334e-15

3 Referências

HEISS, Florian. Using R for Introductory Econometrics. 2.ed. Florian Heiss, 2020. Recurso online. Disponível em: http://www.urfie.net/.

WOOLDRIDGE, J.M. Introdução à Econometria: uma abordagem moderna. São Paulo: Pioneira Thomson Learning, 2006.(tradução da segunda edição americana).