FU902: Seminar 02
David Procházka
2023-10-25
1 Recap the R-Basics
2 Get familiar with the regression modelling in R
3 Learn (the regression modelling) by example
A. Download and import the datasheet
All files are available at this shared folder
For this Tutorial, download the file “FU902-dataset-01” to your local computer
Set a working directory using the command setwd(“C:/…/…/…/…”); where you have the downloaded file stored and where outputs will be exported (e.g., setwd(“C:/Users/MyPC/Documents/R/Paper01”)
Upload the download file from the working directory (for how to upload data in other formats, like txt, csv, please refer to the R-Basics)
library(readxl)
dataset <- as.data.frame(read_excel("FU902-dataset-01.xlsx"))
attach(dataset)
head(dataset)## Firm Year Industry Country Profit Revenue Orders ESG
## 1 1 2017 Services ESP 68761 435676 1.038 58
## 2 1 2018 Services ESP 27267 220696 0.976 39
## 3 1 2019 Services ESP 69729 255782 1.111 85
## 4 1 2020 Services ESP 87363 513659 1.055 63
## 5 1 2021 Services ESP 74637 615406 1.013 50
## 6 1 2022 Services ESP 139750 627756 1.112 85B. Descriptive statistics
- Calculate the descriptive statistics across countries
library(psych)
describeBy(dataset, Country)##
## Descriptive statistics by group
## group: CZE
## vars n mean sd median trimmed mad min
## Firm 1 60 38.80 12.10 42.00 41.75 5.19 5.00
## Year 2 60 2019.50 1.72 2019.50 2019.50 2.22 2017.00
## Industry* 3 60 3.00 1.28 3.00 3.00 1.48 1.00
## Country* 4 60 1.00 0.00 1.00 1.00 0.00 1.00
## Profit 5 60 46665.45 40407.52 34165.50 42318.92 27075.24 -20361.00
## Revenue 6 60 341549.33 153517.89 316265.00 333537.83 177058.76 118035.00
## Orders 7 60 0.99 0.03 0.99 0.99 0.04 0.92
## ESG 8 60 48.42 16.42 43.50 47.77 12.60 15.00
## max range skew kurtosis se
## Firm 49.00 44.00 -2.06 3.18 1.56
## Year 2022.00 5.00 0.00 -1.33 0.22
## Industry* 5.00 4.00 0.29 -1.04 0.16
## Country* 1.00 0.00 NaN NaN 0.00
## Profit 161901.00 182262.00 1.02 0.71 5216.59
## Revenue 727096.00 609061.00 0.43 -0.79 19819.07
## Orders 1.07 0.15 -0.03 -0.34 0.00
## ESG 85.00 70.00 0.36 -0.34 2.12
## ------------------------------------------------------------
## group: ESP
## vars n mean sd median trimmed mad min
## Firm 1 72 25.67 13.65 29.0 26.28 14.83 1.00
## Year 2 72 2019.50 1.72 2019.5 2019.50 2.22 2017.00
## Industry* 3 72 2.42 0.96 3.0 2.41 0.74 1.00
## Country* 4 72 1.00 0.00 1.0 1.00 0.00 1.00
## Profit 5 72 59288.17 41743.17 50939.5 54950.24 39711.44 -2351.00
## Revenue 6 72 391353.92 171825.62 402012.5 387911.74 230438.29 111562.00
## Orders 7 72 1.01 0.05 1.0 1.00 0.05 0.92
## ESG 8 72 50.86 14.77 49.0 49.95 12.60 17.00
## max range skew kurtosis se
## Firm 45.00 44.00 -0.38 -1.08 1.61
## Year 2022.00 5.00 0.00 -1.32 0.20
## Industry* 4.00 3.00 -0.33 -1.13 0.11
## Country* 1.00 0.00 NaN NaN 0.00
## Profit 195802.00 198153.00 0.98 0.89 4919.48
## Revenue 717552.00 605990.00 0.10 -1.27 20249.84
## Orders 1.21 0.29 0.96 1.10 0.01
## ESG 90.00 73.00 0.51 0.09 1.74
## ------------------------------------------------------------
## group: NED
## vars n mean sd median trimmed mad min
## Firm 1 108 21.50 10.91 21.50 20.86 10.38 3.00
## Year 2 108 2019.50 1.72 2019.50 2019.50 2.22 2017.00
## Industry* 3 108 3.33 1.21 3.50 3.41 0.74 1.00
## Country* 4 108 1.00 0.00 1.00 1.00 0.00 1.00
## Profit 5 108 55115.19 44107.13 44900.00 51342.93 40479.43 -17488.00
## Revenue 6 108 381606.18 171534.37 365409.50 379468.38 217206.09 107043.00
## Orders 7 108 1.02 0.06 1.02 1.02 0.06 0.87
## ESG 8 108 48.66 15.90 47.00 47.86 13.34 16.00
## max range skew kurtosis se
## Firm 48.00 45.00 0.50 0.05 1.05
## Year 2022.00 5.00 0.00 -1.30 0.17
## Industry* 5.00 4.00 -0.46 -0.65 0.12
## Country* 1.00 0.00 NaN NaN 0.00
## Profit 177800.00 195288.00 0.78 -0.05 4244.21
## Revenue 741595.00 634552.00 0.12 -1.23 16505.90
## Orders 1.14 0.26 0.08 -0.57 0.01
## ESG 95.00 79.00 0.46 0.20 1.53
## ------------------------------------------------------------
## group: SWE
## vars n mean sd median trimmed mad min
## Firm 1 66 22.09 16.95 16.0 21.11 17.79 2.00
## Year 2 66 2019.50 1.72 2019.5 2019.50 2.22 2017.00
## Industry* 3 66 2.45 1.17 2.0 2.33 1.48 1.00
## Country* 4 66 1.00 0.00 1.0 1.00 0.00 1.00
## Profit 5 66 52268.59 47728.59 41557.5 47235.26 44079.92 -41478.00
## Revenue 6 66 377650.41 160171.43 374480.5 375495.63 198617.25 122046.00
## Orders 7 66 1.01 0.06 1.0 1.00 0.05 0.89
## ESG 8 66 48.65 16.92 46.0 47.59 11.86 16.00
## max range skew kurtosis se
## Firm 51.00 49.00 0.56 -1.13 2.09
## Year 2022.00 5.00 0.00 -1.32 0.21
## Industry* 5.00 4.00 0.80 -0.19 0.14
## Country* 1.00 0.00 NaN NaN 0.00
## Profit 181660.00 223138.00 0.91 0.44 5874.98
## Revenue 704345.00 582299.00 0.10 -1.27 19715.74
## Orders 1.16 0.27 0.79 0.14 0.01
## ESG 97.00 81.00 0.67 0.40 2.08- Calculate the descriptive statistics across industries
describeBy(dataset, Industry)##
## Descriptive statistics by group
## group: ICT
## vars n mean sd median trimmed mad min
## Firm 1 30 31.80 16.47 38.0 32.88 19.27 4.00
## Year 2 30 2019.50 1.74 2019.5 2019.50 2.22 2017.00
## Industry* 3 30 1.00 0.00 1.0 1.00 0.00 1.00
## Country* 4 30 2.20 0.76 2.0 2.25 1.48 1.00
## Profit 5 30 46424.43 42346.68 32678.5 42482.00 39989.43 -17488.00
## Revenue 6 30 341190.07 139867.82 335716.0 340168.96 183136.68 122046.00
## Orders 7 30 1.00 0.04 1.0 0.99 0.04 0.94
## ESG 8 30 48.33 11.35 47.5 47.25 12.60 29.00
## max range skew kurtosis se
## Firm 51.00 47.00 -0.61 -0.98 3.01
## Year 2022.00 5.00 0.00 -1.38 0.32
## Industry* 1.00 0.00 NaN NaN 0.00
## Country* 3.00 2.00 -0.33 -1.27 0.14
## Profit 159744.00 177232.00 0.78 -0.09 7731.41
## Revenue 595021.00 472975.00 0.18 -1.35 25536.25
## Orders 1.12 0.18 0.81 0.03 0.01
## ESG 73.00 44.00 0.62 -0.38 2.07
## ------------------------------------------------------------
## group: Manufacturing
## vars n mean sd median trimmed mad min
## Firm 1 78 27.77 17.09 31.00 28.16 20.76 2.00
## Year 2 78 2019.50 1.72 2019.50 2019.50 2.22 2017.00
## Industry* 3 78 1.00 0.00 1.00 1.00 0.00 1.00
## Country* 4 78 2.69 1.21 3.00 2.73 1.48 1.00
## Profit 5 78 47364.54 42649.50 36107.50 42990.47 35153.93 -41478.00
## Revenue 6 78 368430.49 163544.62 355289.00 364098.42 208491.37 118035.00
## Orders 7 78 1.00 0.05 0.99 1.00 0.04 0.89
## ESG 8 78 47.90 17.08 44.00 46.86 14.83 15.00
## max range skew kurtosis se
## Firm 50.00 48.00 -0.31 -1.43 1.94
## Year 2022.00 5.00 0.00 -1.31 0.19
## Industry* 1.00 0.00 NaN NaN 0.00
## Country* 4.00 3.00 -0.19 -1.56 0.14
## Profit 181660.00 223138.00 1.00 0.94 4829.10
## Revenue 704345.00 586310.00 0.20 -1.24 18517.78
## Orders 1.15 0.26 0.96 0.90 0.01
## ESG 97.00 82.00 0.60 0.28 1.93
## ------------------------------------------------------------
## group: Mining
## vars n mean sd median trimmed mad min
## Firm 1 72 24.67 12.97 22.00 24.10 11.12 8.00
## Year 2 72 2019.50 1.72 2019.50 2019.50 2.22 2017.00
## Industry* 3 72 1.00 0.00 1.00 1.00 0.00 1.00
## Country* 4 72 2.50 1.05 3.00 2.50 1.48 1.00
## Profit 5 72 59115.46 48335.25 48511.00 54980.86 43935.37 -20361.00
## Revenue 6 72 407734.46 173533.15 433565.00 406913.71 209018.43 111562.00
## Orders 7 72 1.02 0.06 1.02 1.02 0.05 0.89
## ESG 8 72 54.04 16.83 50.50 53.47 15.57 18.00
## max range skew kurtosis se
## Firm 46.00 38.00 0.47 -1.19 1.53
## Year 2022.00 5.00 0.00 -1.32 0.20
## Industry* 1.00 0.00 NaN NaN 0.00
## Country* 4.00 3.00 -0.22 -1.22 0.12
## Profit 177800.00 198161.00 0.72 -0.40 5696.36
## Revenue 741595.00 630033.00 -0.01 -1.17 20451.08
## Orders 1.14 0.25 0.28 -0.54 0.01
## ESG 95.00 77.00 0.30 -0.36 1.98
## ------------------------------------------------------------
## group: Services
## vars n mean sd median trimmed mad min
## Firm 1 84 26.64 13.74 26.50 26.88 16.31 1.00
## Year 2 84 2019.50 1.72 2019.50 2019.50 2.22 2017.00
## Industry* 3 84 1.00 0.00 1.00 1.00 0.00 1.00
## Country* 4 84 2.50 0.74 2.50 2.50 0.74 1.00
## Profit 5 84 57867.13 42439.02 53417.50 53974.62 38295.56 -14025.00
## Revenue 6 84 365588.99 172529.43 362280.50 359109.51 208808.64 107043.00
## Orders 7 84 1.01 0.06 1.01 1.01 0.06 0.87
## ESG 8 84 46.93 13.33 44.50 46.50 14.08 16.00
## max range skew kurtosis se
## Firm 48.00 47.00 -0.07 -0.98 1.50
## Year 2022.00 5.00 0.00 -1.31 0.19
## Industry* 1.00 0.00 NaN NaN 0.00
## Country* 4.00 3.00 0.00 -0.36 0.08
## Profit 195802.00 209827.00 0.93 0.83 4630.48
## Revenue 717552.00 610509.00 0.30 -1.16 18824.50
## Orders 1.21 0.34 0.59 0.44 0.01
## ESG 85.00 69.00 0.39 0.47 1.45
## ------------------------------------------------------------
## group: Utility
## vars n mean sd median trimmed mad min
## Firm 1 42 19.57 11.22 19.00 19.47 17.79 5.00
## Year 2 42 2019.50 1.73 2019.50 2019.50 2.22 2017.00
## Industry* 3 42 1.00 0.00 1.00 1.00 0.00 1.00
## Country* 4 42 2.43 1.06 3.00 2.41 1.48 1.00
## Profit 5 42 53964.83 40160.99 43756.50 49955.68 32646.11 -9245.00
## Revenue 6 42 375457.14 158993.22 358653.50 376042.12 195319.95 123638.00
## Orders 7 42 1.01 0.05 1.01 1.01 0.04 0.92
## ESG 8 42 47.95 18.44 47.50 47.35 12.60 15.00
## max range skew kurtosis se
## Firm 35.00 30.00 0.15 -1.46 1.73
## Year 2022.00 5.00 0.00 -1.35 0.27
## Industry* 1.00 0.00 NaN NaN 0.00
## Country* 4.00 3.00 -0.18 -1.34 0.16
## Profit 179293.00 188538.00 1.00 0.74 6196.98
## Revenue 632005.00 508367.00 0.03 -1.35 24533.19
## Orders 1.16 0.24 0.74 0.50 0.01
## ESG 89.00 74.00 0.39 -0.54 2.85C. Inspect correlations
- What is the correlation coefficient between Profits and ESG Score?
cor(Profit, ESG, method = "pearson")## [1] 0.308978- Is the correlation between Profits and ESG Score statistically significant?
cor.test(Profit, ESG, method = "pearson")##
## Pearson's product-moment correlation
##
## data: Profit and ESG
## t = 5.6644, df = 304, p-value = 3.421e-08
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2039190 0.4070015
## sample estimates:
## cor
## 0.308978- Alternatively, rcorr() function from the Hmisc package can be applied both for the correlation and test
library(Hmisc)
rcorr(Profit, ESG, type="pearson")## x y
## x 1.00 0.31
## y 0.31 1.00
##
## n= 306
##
##
## P
## x y
## x 0
## y 0- Calculate correlation coefficient for all variables
- Please note that the “dataset” includes two non-numeric variables (Industry & Country), therefore the codes cor(dataset) or rcorr(dataset) cannot calculate the correlation matrix (try it)
sapply(dataset, class)## Firm Year Industry Country Profit Revenue
## "numeric" "numeric" "character" "character" "numeric" "numeric"
## Orders ESG
## "numeric" "numeric"- How to fix it? Put the character variables as factors!
cor(cbind(Firm, Year, as.factor(Industry), as.factor(Country), Profit, Revenue, Orders, ESG), method = "pearson")## Firm Year Profit
## Firm 1.00000000 0.000000000 -0.17853656 -0.38065308 -0.03008774
## Year 0.00000000 1.000000000 0.00000000 0.00000000 0.05853613
## -0.17853656 0.000000000 1.00000000 -0.14050003 0.08055415
## -0.38065308 0.000000000 -0.14050003 1.00000000 0.02636924
## Profit -0.03008774 0.058536131 0.08055415 0.02636924 1.00000000
## Revenue -0.03718055 -0.005873849 0.02910782 0.05802155 0.67161871
## Orders -0.32345668 0.001889944 0.07354719 0.14154164 0.52607706
## ESG -0.03896236 0.051334904 -0.02377912 -0.01412567 0.30897803
## Revenue Orders ESG
## Firm -0.037180546 -0.323456682 -0.03896236
## Year -0.005873849 0.001889944 0.05133490
## 0.029107819 0.073547190 -0.02377912
## 0.058021554 0.141541636 -0.01412567
## Profit 0.671618714 0.526077060 0.30897803
## Revenue 1.000000000 0.204336248 0.14630965
## Orders 0.204336248 1.000000000 0.30523890
## ESG 0.146309651 0.305238901 1.00000000rcorr(cbind(Firm, Year, as.factor(Industry), as.factor(Country), Profit, Revenue, Orders, ESG), type="pearson")## Firm Year Profit Revenue Orders ESG
## Firm 1.00 0.00 -0.18 -0.38 -0.03 -0.04 -0.32 -0.04
## Year 0.00 1.00 0.00 0.00 0.06 -0.01 0.00 0.05
## -0.18 0.00 1.00 -0.14 0.08 0.03 0.07 -0.02
## -0.38 0.00 -0.14 1.00 0.03 0.06 0.14 -0.01
## Profit -0.03 0.06 0.08 0.03 1.00 0.67 0.53 0.31
## Revenue -0.04 -0.01 0.03 0.06 0.67 1.00 0.20 0.15
## Orders -0.32 0.00 0.07 0.14 0.53 0.20 1.00 0.31
## ESG -0.04 0.05 -0.02 -0.01 0.31 0.15 0.31 1.00
##
## n= 306
##
##
## P
## Firm Year Profit Revenue Orders ESG
## Firm 1.0000 0.0017 0.0000 0.6001 0.5170 0.0000 0.4971
## Year 1.0000 1.0000 1.0000 0.3074 0.9185 0.9737 0.3708
## 0.0017 1.0000 0.0139 0.1598 0.6120 0.1995 0.6786
## 0.0000 1.0000 0.0139 0.6459 0.3117 0.0132 0.8056
## Profit 0.6001 0.3074 0.1598 0.6459 0.0000 0.0000 0.0000
## Revenue 0.5170 0.9185 0.6120 0.3117 0.0000 0.0003 0.0104
## Orders 0.0000 0.9737 0.1995 0.0132 0.0000 0.0003 0.0000
## ESG 0.4971 0.3708 0.6786 0.8056 0.0000 0.0104 0.0000Please note that Industry and Country variable names are not printed (their printing would require creating another dataset in which those two variables are transformed to numeric ones)
An additional option to calculate the correlation matrix is offered by the package “corrr” (but Industry & Country would not be included in the output)
library(corrr)
correlate(dataset, method = "pearson", diagonal = 1)## Non-numeric variables removed from input: `Industry`, and `Country`
## Correlation computed with
## • Method: 'pearson'
## • Missing treated using: 'pairwise.complete.obs'## # A tibble: 6 × 7
## term Firm Year Profit Revenue Orders ESG
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Firm 1 0 -0.0301 -0.0372 -0.323 -0.0390
## 2 Year 0 1 0.0585 -0.00587 0.00189 0.0513
## 3 Profit -0.0301 0.0585 1 0.672 0.526 0.309
## 4 Revenue -0.0372 -0.00587 0.672 1 0.204 0.146
## 5 Orders -0.323 0.00189 0.526 0.204 1 0.305
## 6 ESG -0.0390 0.0513 0.309 0.146 0.305 1- Finally, the package “correlation” can do everything (even factors). The output is not so handsome, but it provides the confidence intervals in addition to the previous methods
library(correlation)
correlation(dataset, include_factors = TRUE, method = "pearson")## # Correlation Matrix (pearson-method)
##
## Parameter1 | Parameter2 | r | 95% CI | t(304) | p
## -------------------------------------------------------------------------------------------------
## Firm | Year | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Firm | Industry.ICT | 0.13 | [ 0.02, 0.24] | 2.28 | > .999
## Firm | Industry.Manufacturing | 0.07 | [-0.04, 0.18] | 1.23 | > .999
## Firm | Industry.Mining | -0.05 | [-0.16, 0.06] | -0.88 | > .999
## Firm | Industry.Services | 0.03 | [-0.09, 0.14] | 0.47 | > .999
## Firm | Industry.Utility | -0.17 | [-0.28, -0.06] | -3.08 | 0.167
## Firm | Country.CZE | 0.43 | [ 0.33, 0.52] | 8.29 | < .001***
## Firm | Country.ESP | -0.01 | [-0.12, 0.10] | -0.22 | > .999
## Firm | Country.NED | -0.23 | [-0.33, -0.12] | -4.04 | 0.006**
## Firm | Country.SWE | -0.14 | [-0.25, -0.03] | -2.45 | > .999
## Firm | Profit | -0.03 | [-0.14, 0.08] | -0.52 | > .999
## Firm | Revenue | -0.04 | [-0.15, 0.08] | -0.65 | > .999
## Firm | Orders | -0.32 | [-0.42, -0.22] | -5.96 | < .001***
## Firm | ESG | -0.04 | [-0.15, 0.07] | -0.68 | > .999
## Year | Industry.ICT | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Year | Industry.Manufacturing | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Year | Industry.Mining | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Year | Industry.Services | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Year | Industry.Utility | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Year | Country.CZE | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Year | Country.ESP | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Year | Country.NED | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Year | Country.SWE | 0.00 | [-0.11, 0.11] | 0.00 | > .999
## Year | Profit | 0.06 | [-0.05, 0.17] | 1.02 | > .999
## Year | Revenue | -5.87e-03 | [-0.12, 0.11] | -0.10 | > .999
## Year | Orders | 1.89e-03 | [-0.11, 0.11] | 0.03 | > .999
## Year | ESG | 0.05 | [-0.06, 0.16] | 0.90 | > .999
## Industry.ICT | Industry.Manufacturing | -0.19 | [-0.30, -0.08] | -3.43 | 0.055
## Industry.ICT | Industry.Mining | -0.18 | [-0.29, -0.07] | -3.24 | 0.101
## Industry.ICT | Industry.Services | -0.20 | [-0.31, -0.09] | -3.61 | 0.029*
## Industry.ICT | Industry.Utility | -0.13 | [-0.24, -0.02] | -2.31 | > .999
## Industry.ICT | Country.CZE | 3.26e-03 | [-0.11, 0.12] | 0.06 | > .999
## Industry.ICT | Country.ESP | -0.18 | [-0.29, -0.07] | -3.24 | 0.101
## Industry.ICT | Country.NED | 0.03 | [-0.08, 0.14] | 0.57 | > .999
## Industry.ICT | Country.SWE | 0.15 | [ 0.04, 0.26] | 2.60 | 0.695
## Industry.ICT | Profit | -0.06 | [-0.17, 0.06] | -0.98 | > .999
## Industry.ICT | Revenue | -0.07 | [-0.18, 0.04] | -1.18 | > .999
## Industry.ICT | Orders | -0.07 | [-0.18, 0.05] | -1.18 | > .999
## Industry.ICT | ESG | -0.02 | [-0.13, 0.10] | -0.29 | > .999
## Industry.Manufacturing | Industry.Mining | -0.32 | [-0.42, -0.22] | -5.98 | < .001***
## Industry.Manufacturing | Industry.Services | -0.36 | [-0.45, -0.26] | -6.72 | < .001***
## Industry.Manufacturing | Industry.Utility | -0.23 | [-0.34, -0.12] | -4.18 | 0.003**
## Industry.Manufacturing | Country.CZE | 0.05 | [-0.06, 0.16] | 0.89 | > .999
## Industry.Manufacturing | Country.ESP | -6.24e-03 | [-0.12, 0.11] | -0.11 | > .999
## Industry.Manufacturing | Country.NED | -0.24 | [-0.35, -0.14] | -4.38 | 0.001**
## Industry.Manufacturing | Country.SWE | 0.24 | [ 0.13, 0.34] | 4.31 | 0.002**
## Industry.Manufacturing | Profit | -0.09 | [-0.20, 0.03] | -1.52 | > .999
## Industry.Manufacturing | Revenue | -0.02 | [-0.14, 0.09] | -0.42 | > .999
## Industry.Manufacturing | Orders | -0.07 | [-0.18, 0.04] | -1.30 | > .999
## Industry.Manufacturing | ESG | -0.05 | [-0.16, 0.07] | -0.79 | > .999
## Industry.Mining | Industry.Services | -0.34 | [-0.44, -0.24] | -6.33 | < .001***
## Industry.Mining | Industry.Utility | -0.22 | [-0.33, -0.11] | -3.96 | 0.008**
## Industry.Mining | Country.CZE | 0.08 | [-0.04, 0.19] | 1.32 | > .999
## Industry.Mining | Country.ESP | -0.09 | [-0.20, 0.02] | -1.57 | > .999
## Industry.Mining | Country.NED | 0.07 | [-0.04, 0.18] | 1.29 | > .999
## Industry.Mining | Country.SWE | -0.07 | [-0.18, 0.05] | -1.16 | > .999
## Industry.Mining | Profit | 0.07 | [-0.05, 0.18] | 1.18 | > .999
## Industry.Mining | Revenue | 0.11 | [ 0.00, 0.22] | 1.91 | > .999
## Industry.Mining | Orders | 0.10 | [-0.01, 0.21] | 1.76 | > .999
## Industry.Mining | ESG | 0.17 | [ 0.06, 0.28] | 3.03 | 0.194
## Industry.Services | Industry.Utility | -0.25 | [-0.35, -0.14] | -4.41 | 0.001**
## Industry.Services | Country.CZE | -0.19 | [-0.30, -0.08] | -3.43 | 0.055
## Industry.Services | Country.ESP | 0.28 | [ 0.17, 0.38] | 5.09 | < .001***
## Industry.Services | Country.NED | 0.10 | [-0.01, 0.21] | 1.71 | > .999
## Industry.Services | Country.SWE | -0.22 | [-0.32, -0.11] | -3.85 | 0.012*
## Industry.Services | Profit | 0.06 | [-0.06, 0.17] | 1.00 | > .999
## Industry.Services | Revenue | -0.04 | [-0.15, 0.08] | -0.62 | > .999
## Industry.Services | Orders | 6.75e-03 | [-0.11, 0.12] | 0.12 | > .999
## Industry.Services | ESG | -0.09 | [-0.20, 0.03] | -1.49 | > .999
## Industry.Utility | Country.CZE | 0.09 | [-0.02, 0.20] | 1.58 | > .999
## Industry.Utility | Country.ESP | -0.09 | [-0.20, 0.03] | -1.52 | > .999
## Industry.Utility | Country.NED | 0.06 | [-0.05, 0.17] | 1.10 | > .999
## Industry.Utility | Country.SWE | -0.07 | [-0.18, 0.04] | -1.23 | > .999
## Industry.Utility | Profit | 1.27e-03 | [-0.11, 0.11] | 0.02 | > .999
## Industry.Utility | Revenue | 6.38e-04 | [-0.11, 0.11] | 0.01 | > .999
## Industry.Utility | Orders | 0.02 | [-0.09, 0.13] | 0.34 | > .999
## Industry.Utility | ESG | -0.03 | [-0.14, 0.08] | -0.51 | > .999
## Country.CZE | Country.ESP | -0.27 | [-0.37, -0.17] | -4.97 | < .001***
## Country.CZE | Country.NED | -0.36 | [-0.46, -0.26] | -6.83 | < .001***
## Country.CZE | Country.SWE | -0.26 | [-0.36, -0.15] | -4.68 | < .001***
## Country.CZE | Profit | -0.08 | [-0.19, 0.03] | -1.42 | > .999
## Country.CZE | Revenue | -0.10 | [-0.21, 0.01] | -1.76 | > .999
## Country.CZE | Orders | -0.18 | [-0.29, -0.07] | -3.28 | 0.090
## Country.CZE | ESG | -0.02 | [-0.13, 0.09] | -0.39 | > .999
## Country.ESP | Country.NED | -0.41 | [-0.50, -0.31] | -7.83 | < .001***
## Country.ESP | Country.SWE | -0.29 | [-0.39, -0.18] | -5.30 | < .001***
## Country.ESP | Profit | 0.07 | [-0.04, 0.18] | 1.21 | > .999
## Country.ESP | Revenue | 0.05 | [-0.06, 0.17] | 0.95 | > .999
## Country.ESP | Orders | -4.75e-03 | [-0.12, 0.11] | -0.08 | > .999
## Country.ESP | ESG | 0.06 | [-0.05, 0.17] | 1.06 | > .999
## Country.NED | Country.SWE | -0.39 | [-0.48, -0.29] | -7.32 | < .001***
## Country.NED | Profit | 0.02 | [-0.09, 0.13] | 0.38 | > .999
## Country.NED | Revenue | 0.03 | [-0.08, 0.14] | 0.50 | > .999
## Country.NED | Orders | 0.16 | [ 0.05, 0.27] | 2.89 | 0.301
## Country.NED | ESG | -0.02 | [-0.13, 0.09] | -0.38 | > .999
## Country.SWE | Profit | -0.02 | [-0.13, 0.09] | -0.33 | > .999
## Country.SWE | Revenue | 7.78e-03 | [-0.10, 0.12] | 0.14 | > .999
## Country.SWE | Orders | -6.63e-03 | [-0.12, 0.11] | -0.12 | > .999
## Country.SWE | ESG | -0.02 | [-0.13, 0.10] | -0.27 | > .999
## Profit | Revenue | 0.67 | [ 0.61, 0.73] | 15.81 | < .001***
## Profit | Orders | 0.53 | [ 0.44, 0.60] | 10.79 | < .001***
## Profit | ESG | 0.31 | [ 0.20, 0.41] | 5.66 | < .001***
## Revenue | Orders | 0.20 | [ 0.09, 0.31] | 3.64 | 0.026*
## Revenue | ESG | 0.15 | [ 0.03, 0.25] | 2.58 | 0.737
## Orders | ESG | 0.31 | [ 0.20, 0.40] | 5.59 | < .001***
##
## p-value adjustment method: Holm (1979)
## Observations: 306- Visualise the correlogram for the quantitative variables with underlying data
library(GGally)## Loading required package: ggplot2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alpha## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2ggpairs(dataset[, c("Revenue", "Profit", "Orders", "ESG")]) +
theme(axis.line=element_blank(),
axis.text=element_blank(),
axis.ticks=element_blank())
D. Run the regression models
- Construct a simple linear model for Profit (dependent variable) and ESG Score (explanatory variable)
OLS.M1 <- lm(Profit ~ ESG, dataset)
summary(OLS.M1)##
## Call:
## lm(formula = Profit ~ ESG, data = dataset)
##
## Residuals:
## Min 1Q Median 3Q Max
## -78834 -28182 -9087 20803 148659
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12191.7 7725.5 1.578 0.116
## ESG 847.5 149.6 5.664 3.42e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 41610 on 304 degrees of freedom
## Multiple R-squared: 0.09547, Adjusted R-squared: 0.09249
## F-statistic: 32.09 on 1 and 304 DF, p-value: 3.421e-08- How to visualise the results graphically?
plot(Profit ~ ESG, xlab = "ESG", ylab ="Profit", col = "#b10061")
abline(OLS.M1, col = "#00A5EB")
8. Construct a multiple linear model for Profit (dependent
variable) and Revenue, Orders, ESG Score, Country and Industry
(explanatory variables)
Model2 <- Profit ~ Revenue + Orders + ESG + Country + Industry- For Model2, calculate the OLS regression (pooling) and panel data regression (Fixed Effects individual, Fixed Effects time, Fixed Effects both individual and time; Random Effects)
library(plm)
OLS.M2 <- plm(Model2, dataset, model= "pooling")
summary(OLS.M2)## Pooling Model
##
## Call:
## plm(formula = Model2, data = dataset, model = "pooling")
##
## Balanced Panel: n = 51, T = 6, N = 306
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -88486.6 -14695.4 -2275.6 13367.7 94979.8
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) -3.3183e+05 2.9728e+04 -11.1620 < 2.2e-16 ***
## Revenue 1.5502e-01 9.5737e-03 16.1927 < 2.2e-16 ***
## Orders 3.1748e+05 3.1267e+04 10.1538 < 2.2e-16 ***
## ESG 3.1594e+02 1.0346e+02 3.0538 0.002466 **
## CountryESP -5.5548e+03 4.9960e+03 -1.1118 0.267108
## CountryNED -1.0497e+04 4.5408e+03 -2.3117 0.021482 *
## CountrySWE -6.3042e+03 4.9215e+03 -1.2809 0.201219
## IndustryManufacturing -5.8661e+03 5.8599e+03 -1.0011 0.317621
## IndustryMining -6.3739e+03 5.9799e+03 -1.0659 0.287341
## IndustryServices 5.0419e+03 6.0439e+03 0.8342 0.404841
## IndustryUtility -2.4968e+03 6.5247e+03 -0.3827 0.702246
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 5.8185e+11
## Residual Sum of Squares: 2.1222e+11
## R-Squared: 0.63526
## Adj. R-Squared: 0.6229
## F-statistic: 51.3795 on 10 and 295 DF, p-value: < 2.22e-16FEind.M2 <- plm(Model2, dataset, model= "within", effect="individual")
summary(FEind.M2)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = Model2, data = dataset, effect = "individual",
## model = "within")
##
## Balanced Panel: n = 51, T = 6, N = 306
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -91945.1 -13063.3 -740.1 12378.6 93192.2
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## Revenue 1.5556e-01 1.0229e-02 15.2072 <2e-16 ***
## Orders 3.6064e+05 3.4608e+04 10.4209 <2e-16 ***
## ESG 2.4956e+02 1.0845e+02 2.3012 0.0222 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 4.8233e+11
## Residual Sum of Squares: 1.6469e+11
## R-Squared: 0.65856
## Adj. R-Squared: 0.58675
## F-statistic: 162.015 on 3 and 252 DF, p-value: < 2.22e-16FEtime.M2 <- plm(Model2, dataset, model= "within", effect="time")
summary(FEtime.M2)## Oneway (time) effect Within Model
##
## Call:
## plm(formula = Model2, data = dataset, effect = "time", model = "within")
##
## Balanced Panel: n = 51, T = 6, N = 306
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -90545.7 -15017.3 -1974.1 11569.4 93372.2
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## Revenue 1.5575e-01 9.5797e-03 16.2582 < 2.2e-16 ***
## Orders 3.1879e+05 3.1096e+04 10.2517 < 2.2e-16 ***
## ESG 3.0097e+02 1.0381e+02 2.8993 0.004025 **
## CountryESP -5.5633e+03 4.9654e+03 -1.1204 0.263469
## CountryNED -1.0560e+04 4.5131e+03 -2.3399 0.019968 *
## CountrySWE -6.3519e+03 4.8914e+03 -1.2986 0.195115
## IndustryManufacturing -5.9121e+03 5.8240e+03 -1.0151 0.310891
## IndustryMining -6.3726e+03 5.9433e+03 -1.0722 0.284504
## IndustryServices 4.9777e+03 6.0070e+03 0.8287 0.407979
## IndustryUtility -2.5544e+03 6.4848e+03 -0.3939 0.693935
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 5.7564e+11
## Residual Sum of Squares: 2.0607e+11
## R-Squared: 0.64202
## Adj. R-Squared: 0.6235
## F-statistic: 52.0094 on 10 and 290 DF, p-value: < 2.22e-16FE.M2 <- plm(Model2, dataset, model= "within", effect="twoways")
summary(FE.M2)## Twoways effects Within Model
##
## Call:
## plm(formula = Model2, data = dataset, effect = "twoways", model = "within")
##
## Balanced Panel: n = 51, T = 6, N = 306
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -89370.09 -11924.44 485.24 11791.01 91388.61
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## Revenue 1.5645e-01 1.0216e-02 15.3136 < 2e-16 ***
## Orders 3.6231e+05 3.4316e+04 10.5582 < 2e-16 ***
## ESG 2.3090e+02 1.0859e+02 2.1263 0.03447 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 4.7611e+11
## Residual Sum of Squares: 1.5837e+11
## R-Squared: 0.66737
## Adj. R-Squared: 0.58927
## F-statistic: 165.192 on 3 and 247 DF, p-value: < 2.22e-16RE.M2 <- plm(Model2, dataset, model= "random")
summary(RE.M2)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = Model2, data = dataset, model = "random")
##
## Balanced Panel: n = 51, T = 6, N = 306
##
## Effects:
## var std.dev share
## idiosyncratic 653516609 25564 0.906
## individual 67715703 8229 0.094
## theta: 0.2147
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -89614.6 -14539.1 -1417.7 12778.1 90330.6
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) -3.4431e+05 3.0157e+04 -11.4172 < 2.2e-16 ***
## Revenue 1.5541e-01 9.5362e-03 16.2972 < 2.2e-16 ***
## Orders 3.3121e+05 3.1508e+04 10.5120 < 2.2e-16 ***
## ESG 2.9422e+02 1.0242e+02 2.8726 0.004071 **
## CountryESP -5.7778e+03 6.0613e+03 -0.9532 0.340472
## CountryNED -1.0941e+04 5.4872e+03 -1.9939 0.046163 *
## CountrySWE -6.6115e+03 5.9738e+03 -1.1067 0.268403
## IndustryManufacturing -6.0059e+03 7.1354e+03 -0.8417 0.399956
## IndustryMining -6.5874e+03 7.2596e+03 -0.9074 0.364194
## IndustryServices 4.8504e+03 7.3567e+03 0.6593 0.509692
## IndustryUtility -2.7396e+03 7.9397e+03 -0.3450 0.730059
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 5.4369e+11
## Residual Sum of Squares: 1.9429e+11
## R-Squared: 0.64265
## Adj. R-Squared: 0.63054
## Chisq: 530.525 on 10 DF, p-value: < 2.22e-16library(stargazer)
stargazer(OLS.M2, FE.M2, RE.M2, type = "text", model.names = TRUE, column.labels = c("OLS", "FE.BOTH", "RE"))##
## =======================================================================================
## Dependent variable:
## -----------------------------------------------------------------
## Profit
## panel
## linear
## OLS FE.BOTH RE
## (1) (2) (3)
## ---------------------------------------------------------------------------------------
## Revenue 0.155*** 0.156*** 0.155***
## (0.010) (0.010) (0.010)
##
## Orders 317,476.300*** 362,311.700*** 331,206.600***
## (31,266.600) (34,315.640) (31,507.580)
##
## ESG 315.936*** 230.900** 294.225***
## (103.456) (108.593) (102.424)
##
## CountryESP -5,554.804 -5,777.823
## (4,996.004) (6,061.291)
##
## CountryNED -10,497.050** -10,940.970**
## (4,540.797) (5,487.217)
##
## CountrySWE -6,304.210 -6,611.534
## (4,921.527) (5,973.835)
##
## IndustryManufacturing -5,866.106 -6,005.856
## (5,859.931) (7,135.382)
##
## IndustryMining -6,373.948 -6,587.362
## (5,979.876) (7,259.582)
##
## IndustryServices 5,041.865 4,850.397
## (6,043.922) (7,356.687)
##
## IndustryUtility -2,496.770 -2,739.561
## (6,524.737) (7,939.674)
##
## Constant -331,827.600*** -344,311.700***
## (29,728.270) (30,157.350)
##
## ---------------------------------------------------------------------------------------
## Observations 306 306 306
## R2 0.635 0.667 0.643
## Adjusted R2 0.623 0.589 0.631
## F Statistic 51.380*** (df = 10; 295) 165.192*** (df = 3; 247) 530.525***
## =======================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01- Inspect the Gauss-Markov assumptions
library(lmtest)
# Heterescedasticity
bptest(Model2, data = dataset)##
## studentized Breusch-Pagan test
##
## data: Model2
## BP = 52.173, df = 10, p-value = 1.06e-07# Auto (serial) correlation
dwtest(Model2, data = dataset)##
## Durbin-Watson test
##
## data: Model2
## DW = 1.7761, p-value = 0.009831
## alternative hypothesis: true autocorrelation is greater than 0# Cross-sectional dependance
pcdtest(Model2, dataset, index = c("Firm", "Year"))##
## Pesaran CD test for cross-sectional dependence in panels
##
## data: Profit ~ Revenue + Orders + ESG + Country + Industry
## z = 3.5003, p-value = 0.0004647
## alternative hypothesis: cross-sectional dependence# Multicolinearity (VIF analysis)
car::vif(OLS.M2)## GVIF Df GVIF^(1/(2*Df))
## Revenue 1.069475 1 1.034154
## Orders 1.197391 1 1.094254
## ESG 1.150658 1 1.072687
## Country 1.364049 3 1.053105
## Industry 1.349843 4 1.038211- How to select among OLS, Fixed Effects, Random Effects
# OLS vs FE
pFtest (OLS.M2, FE.M2) ## Warning in pf(stat, df1, df2, lower.tail = FALSE): NaNs produced##
## F test for individual effects
##
## data: Model2
## F = 1.5596, df1 = -48, df2 = 295, p-value = NA
## alternative hypothesis: significant effects# OLS vs RE
plmtest(OLS.M2, effect = "individual", type = "bp") ##
## Lagrange Multiplier Test - (Breusch-Pagan)
##
## data: Model2
## chisq = 2.9882, df = 1, p-value = 0.08388
## alternative hypothesis: significant effects# FE vs RE
phtest(FE.M2, RE.M2) ##
## Hausman Test
##
## data: Model2
## chisq = 8.2053, df = 3, p-value = 0.04195
## alternative hypothesis: one model is inconsistent