DA_DIS#14_Multi-Linear_Model
Pin Lyu
2023-12-07
1. Data Preparation
# Load data (panel data)
data('RiceFarms', package = 'plm')
stargazer(RiceFarms, type = 'text', title = ' Table 1: Data Summary Statistics')##
## Table 1: Data Summary Statistics
## ========================================================
## Statistic N Mean St. Dev. Min Max
## --------------------------------------------------------
## id 1,026 374,954.100 164,378.900 101,001 609,245
## size 1,026 0.432 0.547 0.010 5.322
## seed 1,026 18.206 45.251 1 1,250
## urea 1,026 95.441 127.149 1 1,250
## phosphate 1,026 33.728 47.588 0 700
## pesticide 1,026 595.005 2,927.581 0 62,600
## pseed 1,026 112.072 64.280 40.000 375.000
## purea 1,026 78.980 8.674 50.000 100.000
## pphosph 1,026 79.568 9.272 60.000 120.000
## hiredlabor 1,026 237.023 422.233 1 4,536
## famlabor 1,026 151.470 148.116 1 1,526
## totlabor 1,026 388.447 484.204 17 4,774
## wage 1,026 80.423 42.189 30.000 175.350
## goutput 1,026 1,405.167 1,921.757 42 20,960
## noutput 1,026 1,240.920 1,638.983 42 17,610
## price 1,026 90.961 37.495 50.000 190.000
## --------------------------------------------------------Comments: Data contains no missing values. However, it may suffer from outliers in some variables.
2. Multi-Linear Regression
Objective:
- Aim to uncover the relationship that land, labor inputs, and other chemicals used inputs during the production of rice with one farm’s total output capacity.
Regression Equation:
- \[ \widehat{Yield} = \beta_0 + \beta_1\ PO_4level + \beta_2\ PricePO_4\ + \beta_3\ Farmsize + \beta_4\ Seed + \beta_5\ Variety + \beta_6 \ Wage + \beta_7 Laborhours + \beta_8 \ Region + \epsilon \]
# Multi-linear Model
mlr <- lm(goutput ~ phosphate +
pphosph+
size +
seed +
varieties +
wage +
totlabor +
factor(region),
data = RiceFarms
)
stargazer(mlr, type = 'text')##
## =====================================================
## Dependent variable:
## ---------------------------
## goutput
## -----------------------------------------------------
## phosphate 10.296***
## (0.612)
##
## pphosph 1.841
## (3.791)
##
## size 1,714.079***
## (109.906)
##
## seed 0.930
## (0.594)
##
## varietieshigh 203.785***
## (77.325)
##
## varietiesmixed -109.855
## (104.478)
##
## wage 2.498***
## (0.849)
##
## totlabor 0.981***
## (0.110)
##
## factor(region)langan 141.568*
## (84.964)
##
## factor(region)gunungwangi -45.203
## (102.699)
##
## factor(region)malausma -52.304
## (104.870)
##
## factor(region)sukaambit 11.254
## (99.470)
##
## factor(region)ciwangi 127.068
## (105.914)
##
## Constant -508.665**
## (257.105)
##
## -----------------------------------------------------
## Observations 1,026
## R2 0.878
## Adjusted R2 0.877
## Residual Std. Error 674.987 (df = 1012)
## F Statistic 561.280*** (df = 13; 1012)
## =====================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Comments: Interpretation of the coefficients are the following and only coefficients that are statistically significant will be interpreted.
- Increase in One kilogram of phosphate used in production, will lead to 10 kilograms of increase in gross rice output.
- Each increase in hectare of the farm, will increase the gross rice output by 1714 kilograms
- On average, high yielding variaty will increase the gross rice output by 203.7 kilograms comparing to traditional variety.
- One Rupiah increase in wage will increase the gross rice output by 2.49 kilograms
- Each hour increase in total labor hours hired will increase the output by 0.98 kilograms.
- Comparing to Wargabinangun, region Langan will have a higher gross output by 141.5 kilograms.
3. Residual Analysis
# plot residual graphs
par(mfrow = c(2, 2))
plot(mlr)
Comments:
- Residual vs. Fitted:
- Residuals show a sign of fanning out which can suggest heteroskedasticity exist in our model. The fitted line also concaved up which suggests that the variance of the residuals are not constant.
- Normal Q-Q:
- Majority of the residual dots located on the dashed line are within the -/+2 standard deviation unit which means that 95% of residuals are on the line. This can allow us to conclude that the distribution of the residual are either normal or close enough to be normally distributed.
- Scale-Location:
- Quite a lot residual dots are scattered above the threshold of 1 standard deviation away from the mean. This is an signal of influence from outliers.
- Residuals vs. Leverage:
- There are 5 large influential residual points in this graph that are causing the mean line of standard deviation to deviate from the center of 0. The data entries that corresponds to these residual points need to be removed in order to reduce bias in this model.
4. Gauss-Markov Assumptions
Linearity: the parameters we are estimating using the OLS method must be themselves linear.
- Satisfied: Parameters are linear in this regression
Random: our data must have been randomly sampled from the population.
- Satisfied: The data is sampled randomly from the population in Indonesia,
Non-Collinearity: the regressors being calculated aren’t perfectly correlated with each other.
- Unsatisfied: Several regressors included in the model share high positive correlation between each other.
- Exogeneity: the regressors aren’t correlated with the error term.
Homoscedasticity: no matter what the values of our regressors might be, the error of the variance is constant.
- Unsatisfied: As pointed out earlier in the report, the model suffers a small level of heteroskedasticity due to several large outliers in the data set.