2.8 Application

In R:

In this real example, We want to regress the annual Gross domestic product of Algeria (which is a country oil) gdp variable on the annual oil price oilprice3.

library(tidyverse)
# load the data
mydata <-
  read_delim(
    "alger.csv",
    delim = ";", locale = locale(decimal_mark = ','))
# display first few rows
head(mydata)
Table 2.11: the first rows of the data in R
years gdp oilprice gexp inv
80 143343 36.83 44016 54880
81 169035 35.93 57655 63044
82 181076 32.97 72445 71487
83 203580 29.55 84825 80319
84 231010 28.78 91598 87482
85 252863 27.56 99841 92765

Note: We used the locale = locale(decimal_mark = ',') to convert the decimal mark in my data from ‘,’ to ‘.’.

Since the dgp variable has larger values than the oilprice variable, we log transform the former before fitting the model.

mydata$gdp <- log(mydata$gdp) 
mod <- lm(gdp ~ oilprice, data = mydata)
tidy(mod)
Table 2.12: Estimation with one regressor in R
term estimate std.error statistic p.value
(Intercept) 12.9374632 0.3727419 34.708903 0.00000
oilprice 0.0348542 0.0086450 4.031697 0.00035

Since the p-value of the slope is very tiny 2e-16, we can say that the oilprice variable is highly significant to explain the response gdp. the intercept is also highly significant with p-value 0.00035. If we want to drop insignificant constant from the model, we can simply add -1 to the right hand side of ~ .

It is a good practice to visualize the results, if possible, to get a better insight into what is happening.

library(ggplot2)
ggplot(mydata, aes(oilprice, gdp)) +
  geom_point() +
  geom_smooth(method = "lm",
    color = "red"
  ) +
  theme_classic()
#> `geom_smooth()` using formula = 'y ~ x'

If you have noticed, we have many issues about this regression, such as the points that are not displayed randomly around the fitted line. We will discuss them in detail in the following chapters.

In Python:

We first read the data.

import pandas as pd
# we read the data
data_p = pd.read_csv(
"alger.csv",  
sep=';',  decimal=',')

# display the first 5 rows
data_p.head()
Table 2.13: The first rows of the data in Python
years gdp oilprice gexp inv
80 143343 36.83 44016 54880
81 169035 35.93 57655 63044
82 181076 32.97 72445 71487
83 203580 29.55 84825 80319
84 231010 28.78 91598 87482

Then fit the model and display the results.

import numpy as np
from statsmodels.formula.api import ols  
import pybroom as br
data_p['gdp']=np.log(data_p['gdp'])
m_p = ols('gdp ~ oilprice', data=data_p).fit() 
m_p = m_p.summary2().tables[1]
m_p
Table 2.14: Estimation with one regressor in Python
Coef. Std.Err. t P>|t| [0.025 ]
Intercept 12.9374632 0.3727419 34.708903 0.00000 12.1762227 13.6987038
oilprice 0.0348542 0.0086450 4.031697 0.00035 0.0171987 0.0525097 

fig = plt.figure(figsize=(5,5))
g = sns.lmplot(x='oilprice', y='gdp', data=data_p)
plt.show()
Linear regression with python

Figure 2.10: Linear regression with python

  1. https://github.com/Metalesaek/econometric_data/blob/main/alger.csv↩︎