BSAN 360 – Statistical Analysis With R - Women Entrepreneurship & Labor Force Analysis
Vinh Nguyen
2/27/2021
Loading packages for the analysis and read the csv file into R
library(readr)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodelibrary(corrplot)## corrplot 0.92 loadedlibrary(knitr)
women_entp = read_csv("Data.csv")## Rows: 50 Columns: 10## -- Column specification --------------------------------------------------------
## Delimiter: ","
## chr (5): Country, Level of development, European Union Membership, Currency,...
## dbl (5): Number, Women Entrepreneurship Index, Entrepreneurship Index, Infla...
##
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.Dataset Overview
View(women_entp)
summary(women_entp)## Number Country Level of development
## Min. : 1.00 Length:50 Length:50
## 1st Qu.:14.25 Class :character Class :character
## Median :29.00 Mode :character Mode :character
## Mean :29.46
## 3rd Qu.:43.75
## Max. :60.00
## European Union Membership Currency Women Entrepreneurship Index
## Length:50 Length:50 Min. :25.30
## Class :character Class :character 1st Qu.:36.23
## Mode :character Mode :character Median :44.05
## Mean :47.72
## 3rd Qu.:59.48
## Max. :74.80
## Entrepreneurship Index Inflation rate Inflation Type
## Min. :24.80 Min. :-2.250 Length:50
## 1st Qu.:31.80 1st Qu.:-0.450 Class :character
## Median :42.35 Median : 0.600 Mode :character
## Mean :46.80 Mean : 2.652
## 3rd Qu.:65.20 3rd Qu.: 3.650
## Max. :77.60 Max. :26.500
## Female Labor Force Participation Rate
## Min. :13.00
## 1st Qu.:55.90
## Median :61.05
## Mean :58.55
## 3rd Qu.:67.55
## Max. :82.30str(women_entp)## spec_tbl_df [50 x 10] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Number : num [1:50] 16 22 55 8 35 44 57 17 51 53 ...
## $ Country : chr [1:50] "El Salvador" "Greece" "Switzerland" "Bosnia and Herzegovina" ...
## $ Level of development : chr [1:50] "Developing" "Developed" "Developed" "Developing" ...
## $ European Union Membership : chr [1:50] "Not Member" "Member" "Not Member" "Not Member" ...
## $ Currency : chr [1:50] "National Currency" "Euro" "National Currency" "National Currency" ...
## $ Women Entrepreneurship Index : num [1:50] 29.9 43 63.7 31.6 58.5 57.7 36.6 55.4 55.9 52.5 ...
## $ Entrepreneurship Index : num [1:50] 29.6 42 68.6 28.9 54.6 47.4 32.1 60.2 53.1 49.6 ...
## $ Inflation rate : num [1:50] -2.25 -1.7 -1.1 -1 -0.9 -0.9 -0.9 -0.88 -0.5 -0.5 ...
## $ Inflation Type : chr [1:50] "Deflation" "Deflation" "Deflation" "Deflation" ...
## $ Female Labor Force Participation Rate: num [1:50] 55.7 42.5 74.7 51.9 66.5 56.6 62 68.5 61 52.7 ...
## - attr(*, "spec")=
## .. cols(
## .. Number = col_double(),
## .. Country = col_character(),
## .. `Level of development` = col_character(),
## .. `European Union Membership` = col_character(),
## .. Currency = col_character(),
## .. `Women Entrepreneurship Index` = col_double(),
## .. `Entrepreneurship Index` = col_double(),
## .. `Inflation rate` = col_double(),
## .. `Inflation Type` = col_character(),
## .. `Female Labor Force Participation Rate` = col_double()
## .. )
## - attr(*, "problems")=<externalptr>Data Transformation
women_entp$`Level of development`<- as.factor(women_entp$`Level of development`)
women_entp$`European Union Membership`<- as.factor(women_entp$`European Union Membership`)
women_entp$Country <- as.factor(women_entp$Country)
women_entp$Currency <- as.factor(women_entp$Currency)Multicollinearity, Data Scaling & Normalized Distribution
Multicollinearity:
lm = lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+ `Inflation rate`+`Female Labor Force Participation Rate`, data = women_entp)
summary(lm)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Inflation rate` + `Female Labor Force Participation Rate`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.1599 -3.4630 -0.5734 2.7374 9.0744
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.24174 3.62596 1.446 0.1551
## `Entrepreneurship Index` 0.74512 0.05268 14.145 <2e-16
## `Inflation rate` -0.29493 0.14791 -1.994 0.0521
## `Female Labor Force Participation Rate` 0.14328 0.05627 2.546 0.0143
##
## (Intercept)
## `Entrepreneurship Index` ***
## `Inflation rate` .
## `Female Labor Force Participation Rate` *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.168 on 46 degrees of freedom
## Multiple R-squared: 0.8789, Adjusted R-squared: 0.871
## F-statistic: 111.3 on 3 and 46 DF, p-value: < 2.2e-16vif(lm)## `Entrepreneurship Index` `Inflation rate`
## 1.311407 1.176966
## `Female Labor Force Participation Rate`
## 1.137753Because all rate are <4 The three independent variables are not highly correlated with each other
Data Scaling:
summary(women_entp[,c(6,7,8,10)])## Women Entrepreneurship Index Entrepreneurship Index Inflation rate
## Min. :25.30 Min. :24.80 Min. :-2.250
## 1st Qu.:36.23 1st Qu.:31.80 1st Qu.:-0.450
## Median :44.05 Median :42.35 Median : 0.600
## Mean :47.72 Mean :46.80 Mean : 2.652
## 3rd Qu.:59.48 3rd Qu.:65.20 3rd Qu.: 3.650
## Max. :74.80 Max. :77.60 Max. :26.500
## Female Labor Force Participation Rate
## Min. :13.00
## 1st Qu.:55.90
## Median :61.05
## Mean :58.55
## 3rd Qu.:67.55
## Max. :82.30We notice that while Entrepreneurship Index & Female Labor Force Participation Rate range from 0 - 100, inflation rate has a different range
Let’s try to scale this variable to see if we can have a better model:
women_entp_2 <- women_entp
women_entp_2$`Inflation rate` <- scale(women_entp_2$`Inflation rate`)
lm_post_scale <- lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+ `Inflation rate`+`Female Labor Force Participation Rate`, data= women_entp_2)
summary(lm_post_scale)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Inflation rate` + `Female Labor Force Participation Rate`,
## data = women_entp_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.1599 -3.4630 -0.5734 2.7374 9.0744
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.45970 3.50200 1.273 0.2092
## `Entrepreneurship Index` 0.74512 0.05268 14.145 <2e-16
## `Inflation rate` -1.59724 0.80102 -1.994 0.0521
## `Female Labor Force Participation Rate` 0.14328 0.05627 2.546 0.0143
##
## (Intercept)
## `Entrepreneurship Index` ***
## `Inflation rate` .
## `Female Labor Force Participation Rate` *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.168 on 46 degrees of freedom
## Multiple R-squared: 0.8789, Adjusted R-squared: 0.871
## F-statistic: 111.3 on 3 and 46 DF, p-value: < 2.2e-16Model does not change, no need for scaling
Normal Distribution tests for continuous data:
scatterplotMatrix(women_entp[,c(6,7,8,10)])
summary(lm)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Inflation rate` + `Female Labor Force Participation Rate`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.1599 -3.4630 -0.5734 2.7374 9.0744
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.24174 3.62596 1.446 0.1551
## `Entrepreneurship Index` 0.74512 0.05268 14.145 <2e-16
## `Inflation rate` -0.29493 0.14791 -1.994 0.0521
## `Female Labor Force Participation Rate` 0.14328 0.05627 2.546 0.0143
##
## (Intercept)
## `Entrepreneurship Index` ***
## `Inflation rate` .
## `Female Labor Force Participation Rate` *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.168 on 46 degrees of freedom
## Multiple R-squared: 0.8789, Adjusted R-squared: 0.871
## F-statistic: 111.3 on 3 and 46 DF, p-value: < 2.2e-16lm1 <- lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+ `Inflation rate`+`Female Labor Force Participation Rate`, data = women_entp)
summary(lm1)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Inflation rate` + `Female Labor Force Participation Rate`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.1599 -3.4630 -0.5734 2.7374 9.0744
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.24174 3.62596 1.446 0.1551
## `Entrepreneurship Index` 0.74512 0.05268 14.145 <2e-16
## `Inflation rate` -0.29493 0.14791 -1.994 0.0521
## `Female Labor Force Participation Rate` 0.14328 0.05627 2.546 0.0143
##
## (Intercept)
## `Entrepreneurship Index` ***
## `Inflation rate` .
## `Female Labor Force Participation Rate` *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.168 on 46 degrees of freedom
## Multiple R-squared: 0.8789, Adjusted R-squared: 0.871
## F-statistic: 111.3 on 3 and 46 DF, p-value: < 2.2e-16lm_post_scale <- lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+ `Inflation rate`+`Female Labor Force Participation Rate`, data= women_entp_2)Let’s try to normalize our continuous variables by performing BoxCox Transformation:
Transform women entrepreneurship index:
powerTransform(women_entp$`Women Entrepreneurship Index`)## Estimated transformation parameter
## women_entp$`Women Entrepreneurship Index`
## 0.3797689a <- coef(powerTransform(women_entp$`Women Entrepreneurship Index`))
women_entp$bcWomenEntrepreneurshipIndex<- bcPower(women_entp$`Women Entrepreneurship Index`,a)Transform Entrepreneurship Index
powerTransform(women_entp$`Entrepreneurship Index`)## Estimated transformation parameter
## women_entp$`Entrepreneurship Index`
## 0.0492938b <- coef(powerTransform(women_entp$`Entrepreneurship Index`))
women_entp$bcEntrepreneurshipIndex<- bcPower(women_entp$`Entrepreneurship Index`,b)Transform Female Labor Force Participation Rate:
powerTransform(women_entp$`Female Labor Force Participation Rate`)## Estimated transformation parameter
## women_entp$`Female Labor Force Participation Rate`
## 2.611958d <- coef(powerTransform(women_entp$`Female Labor Force Participation Rate`))
bcPower(women_entp$`Female Labor Force Participation Rate`,d)## [1] 13903.4282 6859.5037 29926.9569 11560.1678 22088.1552 14497.8914
## [7] 18393.9997 23865.6407 17629.1153 12031.4123 17179.7724 16288.0752
## [13] 19579.1648 16446.7084 14034.2050 23144.4533 15314.5438 17328.7581
## [19] 9021.5507 29199.9718 23323.4706 22001.5019 25160.7565 25538.5723
## [25] 15453.3452 24507.9192 20560.3846 16446.7084 22612.4979 310.5072
## [31] 18705.5836 22349.3776 38545.4375 24507.9192 15803.7368 7826.1133
## [37] 19498.7300 5015.7711 28180.4896 24693.3639 726.9825 1749.3938
## [43] 17704.7027 2858.7675 23413.2986 14034.2050 20477.4835 20977.9957
## [49] 17478.5385 9071.5617women_entp$bcFemaleLaborForceParticipationRate <- bcPower(women_entp$`Female Labor Force Participation Rate`,d)Testing the distribution after transformation:
ggplot(data = women_entp,aes(sample = women_entp$`Women Entrepreneurship Index`))+ stat_qq()+ stat_qq_line()
scatterplotMatrix(women_entp[,c(11:13)])
hist(women_entp$`Inflation rate`)
View(women_entp)
lm1 <- lm(`bcWomenEntrepreneurshipIndex` ~ `bcEntrepreneurshipIndex`+ `Inflation rate`+`bcFemaleLaborForceParticipationRate`, data = women_entp)
summary(lm1)##
## Call:
## lm(formula = bcWomenEntrepreneurshipIndex ~ bcEntrepreneurshipIndex +
## `Inflation rate` + bcFemaleLaborForceParticipationRate, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.07968 -0.34121 -0.06845 0.28535 1.01660
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.405e+00 8.179e-01 -2.941 0.00511 **
## bcEntrepreneurshipIndex 2.594e+00 2.029e-01 12.784 < 2e-16 ***
## `Inflation rate` -2.768e-02 1.474e-02 -1.878 0.06667 .
## bcFemaleLaborForceParticipationRate 1.962e-05 1.002e-05 1.958 0.05627 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.51 on 46 degrees of freedom
## Multiple R-squared: 0.8618, Adjusted R-squared: 0.8528
## F-statistic: 95.6 on 3 and 46 DF, p-value: < 2.2e-16summary(lm)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Inflation rate` + `Female Labor Force Participation Rate`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.1599 -3.4630 -0.5734 2.7374 9.0744
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.24174 3.62596 1.446 0.1551
## `Entrepreneurship Index` 0.74512 0.05268 14.145 <2e-16
## `Inflation rate` -0.29493 0.14791 -1.994 0.0521
## `Female Labor Force Participation Rate` 0.14328 0.05627 2.546 0.0143
##
## (Intercept)
## `Entrepreneurship Index` ***
## `Inflation rate` .
## `Female Labor Force Participation Rate` *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.168 on 46 degrees of freedom
## Multiple R-squared: 0.8789, Adjusted R-squared: 0.871
## F-statistic: 111.3 on 3 and 46 DF, p-value: < 2.2e-16Data Visualization
ggplot(women_entp,
aes(x=`Women Entrepreneurship Index`, y=`Entrepreneurship Index`, shape=`Level of development`, color=`Level of development`))+
geom_point() + # Adding points (scatterplot)
geom_smooth(method = "lm") + # Adding regression lines
ylab("Entrepreneurship Index") + # y-axis label
xlab("Women Entrepreneurship Index") + # x-axis label
ggtitle("Index by Level of Development") ## `geom_smooth()` using formula 'y ~ x'
ggplot(women_entp,
aes(x=`Women Entrepreneurship Index`, y=`Entrepreneurship Index`, shape=`European Union Membership`, color=`European Union Membership`))+
geom_point() + # Adding points (scatterplot)
geom_smooth(method = "lm") + # Adding regression lines
ylab("Entrepreneurship Index") + # y-axis label
xlab("Women Entrepreneurship Index") + # x-axis label
ggtitle("Index by European Union Membership") ## `geom_smooth()` using formula 'y ~ x'
boxplot(women_entp$`bcFemaleLaborForceParticipationRate` ~ women_entp$`Level of development`,
main = "Female Labor Force Participation Rate by Development Level",
xlab = "Female Labor Force Participation Rate",
ylab = "Level of Development",
horizontal = TRUE)
boxplot(women_entp$`Women Entrepreneurship Index` ~ women_entp$`European Union Membership`,
main = "Women Entrepreneurship Index by European Union Membership",
xlab = "Women Entrepreneurship Index",
ylab = "European Union Membership",
horizontal = FALSE)
colors <- c ("Blue","Red")
barplot(women_entp$`Entrepreneurship Index`,
main = "Entrepreneurship Index Rate by Country",
ylab = "Entrepreneurship Index Rate",
names.arg = women_entp$Country,
col = colors[women_entp$`Level of development`],
horiz = FALSE)
legend(x = "topright", legend = c("Developed", "Developing"), col = c("Blue","Red"))
axis(side=2, at=seq(0,100,by=5))
ANOVA & TUKEY TEST
Our potential predictors are : European Union Membership, Level of development, and Inflation Type
The potential Dependent variables are: Women Entrepreneurship Index, Entrepreneurship Index, Inflation rate, and Female Labor Force Participation Rate
EU Membership vs. Women Entrepreneurship Index
eu_aov <- aov(women_entp$`Women Entrepreneurship Index`~ women_entp$`European Union Membership`, data = women_entp)
anova(eu_aov)## Analysis of Variance Table
##
## Response: women_entp$`Women Entrepreneurship Index`
## Df Sum Sq Mean Sq F value Pr(>F)
## women_entp$`European Union Membership` 1 4115.1 4115.1 32.742 6.644e-07 ***
## Residuals 48 6032.7 125.7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TukeyHSD(eu_aov)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = women_entp$`Women Entrepreneurship Index` ~ women_entp$`European Union Membership`, data = women_entp)
##
## $`women_entp$`European Union Membership``
## diff lwr upr p adj
## Not Member-Member -18.51833 -25.02531 -12.01135 7e-07It seems that there is an association between EU Membership and Women Entrepreneurship Index, could be that there is a correlation between developed nations and its Women Entrepreneurship Index.
Level of Development vs Women Entrepreneurship Index
development_aov <- aov(women_entp$`Women Entrepreneurship Index`~women_entp$`Level of development`)
anova(development_aov)## Analysis of Variance Table
##
## Response: women_entp$`Women Entrepreneurship Index`
## Df Sum Sq Mean Sq F value Pr(>F)
## women_entp$`Level of development` 1 7624.8 7624.8 145.06 4.09e-16 ***
## Residuals 48 2523.1 52.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tukey1 <- TukeyHSD(development_aov)
tukey1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = women_entp$`Women Entrepreneurship Index` ~ women_entp$`Level of development`)
##
## $`women_entp$`Level of development``
## diff lwr upr p adj
## Developing-Developed -24.71763 -28.84404 -20.59122 0plot(tukey1)
Looks like there is a difference in Women Entrepreneurship index means between countries with 2 levels of development: “Developed” & “Developing”, thus an association between Women Entrepreneurship index and Level of Development. We will measure this correlation in further tests.
Level of Development vs Female Labor Force Participation Rate
development_labor_aov <- aov(women_entp$`Female Labor Force Participation Rate`~women_entp$`Level of development`)
anova(development_labor_aov)## Analysis of Variance Table
##
## Response: women_entp$`Female Labor Force Participation Rate`
## Df Sum Sq Mean Sq F value Pr(>F)
## women_entp$`Level of development` 1 1277.0 1277.04 7.3658 0.009206 **
## Residuals 48 8321.9 173.37
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tukey2 <- TukeyHSD(development_labor_aov)
tukey2## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = women_entp$`Female Labor Force Participation Rate` ~ women_entp$`Level of development`)
##
## $`women_entp$`Level of development``
## diff lwr upr p adj
## Developing-Developed -10.11567 -17.60973 -2.621621 0.009206plot(tukey2)
An Alternative: Performing T-Test
Level of Development is a factor to predict both Female Labor Force Participation Rate and Women Entrepreneurship Index of a country.
Inflation Type vs. Women Entrepreneurship Index
hist(women_entp$`Inflation rate`, col = "yellowgreen",breaks = 20, freq = FALSE, xaxt="n")
axis(side=1, at=seq(-5,30,by=2))
inflation_aov <- aov(women_entp$`Women Entrepreneurship Index`~women_entp$`Inflation Type`)
anova(inflation_aov)## Analysis of Variance Table
##
## Response: women_entp$`Women Entrepreneurship Index`
## Df Sum Sq Mean Sq F value Pr(>F)
## women_entp$`Inflation Type` 3 3861.2 1287.06 9.4175 5.776e-05 ***
## Residuals 46 6286.7 136.67
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tukey3 <- TukeyHSD(inflation_aov)
tukey3## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = women_entp$`Women Entrepreneurship Index` ~ women_entp$`Inflation Type`)
##
## $`women_entp$`Inflation Type``
## diff lwr upr
## Galloping Inflation-Deflation -19.761176 -35.614218 -3.908135
## Moderate Inflation-Deflation 4.006192 -6.396859 14.409242
## Walking Inflation-Deflation -15.352288 -28.197807 -2.506768
## Moderate Inflation-Galloping Inflation 23.767368 8.105105 39.429632
## Walking Inflation-Galloping Inflation 4.408889 -12.971860 21.789638
## Walking Inflation-Moderate Inflation -19.358480 -31.967800 -6.749159
## p adj
## Galloping Inflation-Deflation 0.0091848
## Moderate Inflation-Deflation 0.7348986
## Walking Inflation-Deflation 0.0133556
## Moderate Inflation-Galloping Inflation 0.0011007
## Walking Inflation-Galloping Inflation 0.9055981
## Walking Inflation-Moderate Inflation 0.0009509plot(tukey3) 
inflation_aov2 <- aov(women_entp$`Female Labor Force Participation Rate`~women_entp$`Inflation Type`)
anova(inflation_aov2)## Analysis of Variance Table
##
## Response: women_entp$`Female Labor Force Participation Rate`
## Df Sum Sq Mean Sq F value Pr(>F)
## women_entp$`Inflation Type` 3 934.1 311.36 1.653 0.1903
## Residuals 46 8664.9 188.37There is a correlation/association between Inflation Type and Women Entrepreneurship Index. However, correlation doesn’t mean causation, so we’re going to test how strong the Inflation Type-Women Entrepreneurship Index interaction is and its reliability by conducting some regression models below.
Variables Correlation and Linear Regression
cmat <- cor(women_entp[,c(6:8,10)])
corrplot.mixed(cmat)
cor(women_entp[,c(6:8,10)])## Women Entrepreneurship Index
## Women Entrepreneurship Index 1.0000000
## Entrepreneurship Index 0.9225547
## Inflation rate -0.4531406
## Female Labor Force Participation Rate 0.4443458
## Entrepreneurship Index Inflation rate
## Women Entrepreneurship Index 0.9225547 -0.4531406
## Entrepreneurship Index 1.0000000 -0.3876506
## Inflation rate -0.3876506 1.0000000
## Female Labor Force Participation Rate 0.3478316 -0.1434566
## Female Labor Force Participation Rate
## Women Entrepreneurship Index 0.4443458
## Entrepreneurship Index 0.3478316
## Inflation rate -0.1434566
## Female Labor Force Participation Rate 1.0000000REGRESSION MODEL:
- Using categorical variables (Level of development, EU membership, Inflation type) and the Entrepreneurship Index as well as Female Labor Force Participation Rate as our main predictors. Each categorical predictors will be added seperately to test the variable importance or the statistical significance. The Women Entrepreneur Index will be our target variable.
lm1 <- lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+`Female Labor Force Participation Rate`, data = women_entp)
summary(lm1)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Female Labor Force Participation Rate`, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.7238 -3.4104 -0.8712 2.8059 9.7909
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.60455 3.48141 0.748 0.4581
## `Entrepreneurship Index` 0.78336 0.05059 15.483 <2e-16
## `Female Labor Force Participation Rate` 0.14440 0.05802 2.489 0.0164
##
## (Intercept)
## `Entrepreneurship Index` ***
## `Female Labor Force Participation Rate` *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.33 on 47 degrees of freedom
## Multiple R-squared: 0.8684, Adjusted R-squared: 0.8628
## F-statistic: 155.1 on 2 and 47 DF, p-value: < 2.2e-16Adding the level of development variable:
lm2 <- lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+`Female Labor Force Participation Rate`+ `Level of development`, data = women_entp)
summary(lm2)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Female Labor Force Participation Rate` + `Level of development`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.3672 -2.2971 0.0437 2.4707 10.4389
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.46869 5.03596 3.866 0.000346
## `Entrepreneurship Index` 0.55812 0.06942 8.040 2.58e-10
## `Female Labor Force Participation Rate` 0.11239 0.05055 2.223 0.031161
## `Level of development`Developing -9.26564 2.22310 -4.168 0.000134
##
## (Intercept) ***
## `Entrepreneurship Index` ***
## `Female Labor Force Participation Rate` *
## `Level of development`Developing ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.59 on 46 degrees of freedom
## Multiple R-squared: 0.9045, Adjusted R-squared: 0.8983
## F-statistic: 145.2 on 3 and 46 DF, p-value: < 2.2e-16summary(lm2)$adj.r.squared## [1] 0.8982792summary(lm)$adj.r.squared## [1] 0.8710146Level of development is significant. We should add this to our final model.
Adding EU membership variable:
lm3 <- lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+`Female Labor Force Participation Rate`+ `European Union Membership`, data = women_entp)
summary(lm3)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Female Labor Force Participation Rate` + `European Union Membership`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.216 -2.981 -0.264 2.154 10.605
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.14727 3.66882 3.038 0.003913
## `Entrepreneurship Index` 0.68201 0.05035 13.547 < 2e-16
## `Female Labor Force Participation Rate` 0.14465 0.05024 2.879 0.006031
## `European Union Membership`Not Member -6.35642 1.55602 -4.085 0.000174
##
## (Intercept) **
## `Entrepreneurship Index` ***
## `Female Labor Force Participation Rate` **
## `European Union Membership`Not Member ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.615 on 46 degrees of freedom
## Multiple R-squared: 0.9035, Adjusted R-squared: 0.8972
## F-statistic: 143.5 on 3 and 46 DF, p-value: < 2.2e-16EU membership is significant too. We should add it to the model
Adding Inflation type:
lm4 <- lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+`Female Labor Force Participation Rate`+ `Inflation Type`, data = women_entp)
summary(lm4)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Female Labor Force Participation Rate` + `Inflation Type`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.7482 -3.8418 -0.1011 2.8111 10.0654
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.77186 4.08215 1.659 0.1042
## `Entrepreneurship Index` 0.73536 0.05999 12.258 8.75e-16
## `Female Labor Force Participation Rate` 0.14404 0.05828 2.471 0.0174
## `Inflation Type`Galloping Inflation -5.76335 2.88115 -2.000 0.0517
## `Inflation Type`Moderate Inflation -1.74323 1.79543 -0.971 0.3369
## `Inflation Type`Walking Inflation -3.66927 2.32621 -1.577 0.1219
##
## (Intercept)
## `Entrepreneurship Index` ***
## `Female Labor Force Participation Rate` *
## `Inflation Type`Galloping Inflation .
## `Inflation Type`Moderate Inflation
## `Inflation Type`Walking Inflation
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.221 on 44 degrees of freedom
## Multiple R-squared: 0.8818, Adjusted R-squared: 0.8684
## F-statistic: 65.64 on 5 and 44 DF, p-value: < 2.2e-16Inflation type is not statistically significant. We should not use this as predictor.
Combining both EU membership and Level of development as predictors in our linear regression model.
lm5 <- lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+`Female Labor Force Participation Rate`+ `European Union Membership`+`Level of development`, data = women_entp)
summary(lm5)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Female Labor Force Participation Rate` + `European Union Membership` +
## `Level of development`, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.3529 -2.2931 -0.0482 1.9733 10.6447
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.43777 5.12623 3.402 0.00141
## `Entrepreneurship Index` 0.59229 0.07177 8.253 1.48e-10
## `Female Labor Force Participation Rate` 0.12535 0.05047 2.484 0.01679
## `European Union Membership`Not Member -3.51329 2.24790 -1.563 0.12508
## `Level of development`Developing -5.55556 3.22907 -1.720 0.09221
##
## (Intercept) **
## `Entrepreneurship Index` ***
## `Female Labor Force Participation Rate` *
## `European Union Membership`Not Member
## `Level of development`Developing .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.519 on 45 degrees of freedom
## Multiple R-squared: 0.9094, Adjusted R-squared: 0.9014
## F-statistic: 113 on 4 and 45 DF, p-value: < 2.2e-16plot(lm5)
When combined, both of these factors are significant.
- Interaction Effect Tests
lm6 <- lm(`Women Entrepreneurship Index` ~(`Entrepreneurship Index`+`Female Labor Force Participation Rate`+ `European Union Membership`)^2 , data = women_entp)
summary(lm6)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ (`Entrepreneurship Index` +
## `Female Labor Force Participation Rate` + `European Union Membership`)^2,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.7071 -2.5883 0.2194 1.8633 9.9920
##
## Coefficients:
## Estimate
## (Intercept) 50.972348
## `Entrepreneurship Index` 0.003225
## `Female Labor Force Participation Rate` -0.374999
## `European Union Membership`Not Member -26.634909
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 0.008631
## `Entrepreneurship Index`:`European Union Membership`Not Member 0.182944
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member 0.171653
## Std. Error
## (Intercept) 13.989126
## `Entrepreneurship Index` 0.266654
## `Female Labor Force Participation Rate` 0.264830
## `European Union Membership`Not Member 8.371874
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 0.003683
## `Entrepreneurship Index`:`European Union Membership`Not Member 0.144850
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member 0.190931
## t value
## (Intercept) 3.644
## `Entrepreneurship Index` 0.012
## `Female Labor Force Participation Rate` -1.416
## `European Union Membership`Not Member -3.181
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 2.344
## `Entrepreneurship Index`:`European Union Membership`Not Member 1.263
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member 0.899
## Pr(>|t|)
## (Intercept) 0.000719
## `Entrepreneurship Index` 0.990408
## `Female Labor Force Participation Rate` 0.163978
## `European Union Membership`Not Member 0.002720
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 0.023787
## `Entrepreneurship Index`:`European Union Membership`Not Member 0.213400
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member 0.373644
##
## (Intercept) ***
## `Entrepreneurship Index`
## `Female Labor Force Participation Rate`
## `European Union Membership`Not Member **
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` *
## `Entrepreneurship Index`:`European Union Membership`Not Member
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.255 on 43 degrees of freedom
## Multiple R-squared: 0.9233, Adjusted R-squared: 0.9126
## F-statistic: 86.24 on 6 and 43 DF, p-value: < 2.2e-16summary(lm6)$adj.r.squared## [1] 0.9125688lm7 <- lm(`Women Entrepreneurship Index` ~ `Entrepreneurship Index`+`Female Labor Force Participation Rate`+ `European Union Membership`+`Level of development`+`Entrepreneurship Index`:`Female Labor Force Participation Rate`+ `Entrepreneurship Index`:`Level of development`, data =women_entp)
summary(lm7)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Entrepreneurship Index` +
## `Female Labor Force Participation Rate` + `European Union Membership` +
## `Level of development` + `Entrepreneurship Index`:`Female Labor Force Participation Rate` +
## `Entrepreneurship Index`:`Level of development`, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.3795 -3.0860 -0.1211 2.0883 9.6437
##
## Coefficients:
## Estimate
## (Intercept) 33.110133
## `Entrepreneurship Index` 0.219467
## `Female Labor Force Participation Rate` -0.129003
## `European Union Membership`Not Member -4.282898
## `Level of development`Developing -5.380173
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 0.005944
## `Entrepreneurship Index`:`Level of development`Developing 0.018949
## Std. Error
## (Intercept) 14.482872
## `Entrepreneurship Index` 0.343521
## `Female Labor Force Participation Rate` 0.194817
## `European Union Membership`Not Member 2.305267
## `Level of development`Developing 9.016243
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 0.004728
## `Entrepreneurship Index`:`Level of development`Developing 0.211059
## t value
## (Intercept) 2.286
## `Entrepreneurship Index` 0.639
## `Female Labor Force Participation Rate` -0.662
## `European Union Membership`Not Member -1.858
## `Level of development`Developing -0.597
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 1.257
## `Entrepreneurship Index`:`Level of development`Developing 0.090
## Pr(>|t|)
## (Intercept) 0.0272 *
## `Entrepreneurship Index` 0.5263
## `Female Labor Force Participation Rate` 0.5114
## `European Union Membership`Not Member 0.0700 .
## `Level of development`Developing 0.5538
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 0.2155
## `Entrepreneurship Index`:`Level of development`Developing 0.9289
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.511 on 43 degrees of freedom
## Multiple R-squared: 0.9138, Adjusted R-squared: 0.9017
## F-statistic: 75.95 on 6 and 43 DF, p-value: < 2.2e-16summary(lm7)$adj.r.squared## [1] 0.9017475summary(lm7)$coefficients## Estimate
## (Intercept) 33.110132975
## `Entrepreneurship Index` 0.219467275
## `Female Labor Force Participation Rate` -0.129003241
## `European Union Membership`Not Member -4.282897938
## `Level of development`Developing -5.380173313
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 0.005943545
## `Entrepreneurship Index`:`Level of development`Developing 0.018948823
## Std. Error
## (Intercept) 14.482872017
## `Entrepreneurship Index` 0.343520685
## `Female Labor Force Participation Rate` 0.194816933
## `European Union Membership`Not Member 2.305266824
## `Level of development`Developing 9.016243208
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 0.004727734
## `Entrepreneurship Index`:`Level of development`Developing 0.211059454
## t value
## (Intercept) 2.28615795
## `Entrepreneurship Index` 0.63887645
## `Female Labor Force Participation Rate` -0.66217674
## `European Union Membership`Not Member -1.85787515
## `Level of development`Developing -0.59672007
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 1.25716566
## `Entrepreneurship Index`:`Level of development`Developing 0.08977955
## Pr(>|t|)
## (Intercept) 0.02723243
## `Entrepreneurship Index` 0.52629196
## `Female Labor Force Participation Rate` 0.51139148
## `European Union Membership`Not Member 0.07004243
## `Level of development`Developing 0.55382324
## `Entrepreneurship Index`:`Female Labor Force Participation Rate` 0.21547935
## `Entrepreneurship Index`:`Level of development`Developing 0.92887929It seems like lm7 is the fittest model to predict Women Entrepreneurship Index with R-squared = 0.9975. In this model, there is one pair of interacting variables that are Entrpreneurship Index:Level of development Developing. What this means is that if a country entrepreneurship index increase by 1 and it is a developing country, the women entrepreneurship index is predicted to increase by 0.0143
Our Final Model Can Be Represented in Formula as below:
#y = women entrepreneurship index, E= EU membership, L = Level of development, x1 = Entrepreneurship Index, x2= Inflation rate, x3 = Female Labor Force Participation Rate
#y = 3.596 + 0.02617x1 - 0.0007903x2 - 0.0008124x3 - 0.01126E - 0.626L - 0.00003545*x1*x3 - 0.01434*x1*LCONCLUSION: Our model to predict WEI is good but the result is not very interesting because it’s obvious that entrepreneurship index, naturally, is a factor that is going to impact WEI the most without further analysis.
- Predicting FemaleLaborForcePariticipationRate. The process will be the same as when we try to predict Women Entrepreneur Index
lm_lf <- lm(`bcFemaleLaborForceParticipationRate` ~ `bcWomenEntrepreneurshipIndex` + `bcEntrepreneurshipIndex`+`Inflation rate`, data = women_entp)
summary(lm_lf)##
## Call:
## lm(formula = bcFemaleLaborForceParticipationRate ~ bcWomenEntrepreneurshipIndex +
## bcEntrepreneurshipIndex + `Inflation rate`, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12971 -5785 1488 4839 16068
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2809.3 12600.5 -0.223 0.8246
## bcWomenEntrepreneurshipIndex 3923.2 2003.4 1.958 0.0563 .
## bcEntrepreneurshipIndex -3350.6 6102.1 -0.549 0.5856
## `Inflation rate` 114.6 215.6 0.532 0.5975
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7213 on 46 degrees of freedom
## Multiple R-squared: 0.2196, Adjusted R-squared: 0.1687
## F-statistic: 4.314 on 3 and 46 DF, p-value: 0.0092012 significant variables are bcwomenentrepreneurshipindex and bcentrepreneurshipindex. However, adj.r-squared is low (adj.r^2 = 0.1779). Since inflation rate is not statisitcally significant. Let’s drop this variable and try to add other factors as our predictors to see if adj.r^2 improve.
Adding level of development to the model
lm_lf1 <- lm(`bcFemaleLaborForceParticipationRate` ~ `bcWomenEntrepreneurshipIndex` + `bcEntrepreneurshipIndex`+`Inflation rate`+ `Level of development`, data = women_entp)
summary(lm_lf1)##
## Call:
## lm(formula = bcFemaleLaborForceParticipationRate ~ bcWomenEntrepreneurshipIndex +
## bcEntrepreneurshipIndex + `Inflation rate` + `Level of development`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13682 -5568 1117 4814 15888
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -10068.63 19582.70 -0.514 0.6097
## bcWomenEntrepreneurshipIndex 4443.64 2285.21 1.945 0.0581 .
## bcEntrepreneurshipIndex -2917.81 6217.12 -0.469 0.6411
## `Inflation rate` 88.38 223.97 0.395 0.6950
## `Level of development`Developing 2109.31 4329.67 0.487 0.6285
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7273 on 45 degrees of freedom
## Multiple R-squared: 0.2237, Adjusted R-squared: 0.1547
## F-statistic: 3.241 on 4 and 45 DF, p-value: 0.02025Level of development is not significant, we should drop this variable.
Adding EU membership
lm_lf2 <- lm(`bcFemaleLaborForceParticipationRate` ~ `bcWomenEntrepreneurshipIndex` + `bcEntrepreneurshipIndex`+`Inflation rate`+ `European Union Membership`, data = women_entp)
summary(lm_lf2)##
## Call:
## lm(formula = bcFemaleLaborForceParticipationRate ~ bcWomenEntrepreneurshipIndex +
## bcEntrepreneurshipIndex + `Inflation rate` + `European Union Membership`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13493 -4589 1093 5110 12037
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -12859.22 13370.81 -0.962 0.3413
## bcWomenEntrepreneurshipIndex 5475.23 2116.28 2.587 0.0130 *
## bcEntrepreneurshipIndex -4866.29 5993.18 -0.812 0.4211
## `Inflation rate` 41.23 213.41 0.193 0.8477
## `European Union Membership`Not Member 5167.95 2739.21 1.887 0.0657 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7020 on 45 degrees of freedom
## Multiple R-squared: 0.2768, Adjusted R-squared: 0.2125
## F-statistic: 4.306 on 4 and 45 DF, p-value: 0.004926EU Membership is not significant either.
Adding Inflation type
lm_lf3 <- lm(`bcFemaleLaborForceParticipationRate` ~ `bcWomenEntrepreneurshipIndex` + `bcEntrepreneurshipIndex`+`Inflation rate`+ `Inflation Type`, data = women_entp)
summary(lm_lf3)##
## Call:
## lm(formula = bcFemaleLaborForceParticipationRate ~ bcWomenEntrepreneurshipIndex +
## bcEntrepreneurshipIndex + `Inflation rate` + `Inflation Type`,
## data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13668 -5032 1134 3718 15502
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8359.9 14461.7 -0.578 0.5662
## bcWomenEntrepreneurshipIndex 3790.4 2033.8 1.864 0.0692 .
## bcEntrepreneurshipIndex -2134.1 6384.5 -0.334 0.7398
## `Inflation rate` -618.3 511.5 -1.209 0.2333
## `Inflation Type`Galloping Inflation 15803.4 9790.1 1.614 0.1138
## `Inflation Type`Moderate Inflation 2918.6 2586.0 1.129 0.2653
## `Inflation Type`Walking Inflation 4933.6 4583.7 1.076 0.2878
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7203 on 43 degrees of freedom
## Multiple R-squared: 0.2724, Adjusted R-squared: 0.1708
## F-statistic: 2.683 on 6 and 43 DF, p-value: 0.02664Inflation type is not significant either.
After testing, we can conclude that only bcWomenEntrepreneurshipIndex and bcEntrepreneurshipIndex are significant. Let’s proceed to test for interaction effects between these 2 variables.
Testing for interaction between bcWomenEntrepreneurshipIndex and bcEntrepreneurshipIndex to predict femalelaborparticipartionrate:
lm_lf4 <- lm(`bcFemaleLaborForceParticipationRate` ~ (`bcWomenEntrepreneurshipIndex` + `bcEntrepreneurshipIndex`)^2, data = women_entp)
summary(lm_lf4)##
## Call:
## lm(formula = bcFemaleLaborForceParticipationRate ~ (bcWomenEntrepreneurshipIndex +
## bcEntrepreneurshipIndex)^2, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13268.4 -4519.2 -258.8 4486.3 14054.4
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 205723 74599
## bcWomenEntrepreneurshipIndex -20384 8764
## bcEntrepreneurshipIndex -53594 18864
## bcWomenEntrepreneurshipIndex:bcEntrepreneurshipIndex 5784 2064
## t value Pr(>|t|)
## (Intercept) 2.758 0.00832 **
## bcWomenEntrepreneurshipIndex -2.326 0.02449 *
## bcEntrepreneurshipIndex -2.841 0.00668 **
## bcWomenEntrepreneurshipIndex:bcEntrepreneurshipIndex 2.802 0.00741 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6687 on 46 degrees of freedom
## Multiple R-squared: 0.3293, Adjusted R-squared: 0.2855
## F-statistic: 7.527 on 3 and 46 DF, p-value: 0.0003367According to the model, there is no interaction between these 2 varibles. As a result, we should keep them seperate
lm_lf5 <- lm(`bcFemaleLaborForceParticipationRate` ~ `bcWomenEntrepreneurshipIndex` + `bcEntrepreneurshipIndex`, data = women_entp)
summary(lm_lf5)##
## Call:
## lm(formula = bcFemaleLaborForceParticipationRate ~ bcWomenEntrepreneurshipIndex +
## bcEntrepreneurshipIndex, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13416 -5270 1349 5368 16324
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -917.6 11995.1 -0.076 0.9393
## bcWomenEntrepreneurshipIndex 3650.5 1921.8 1.900 0.0636 .
## bcEntrepreneurshipIndex -3164.1 6045.3 -0.523 0.6032
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7157 on 47 degrees of freedom
## Multiple R-squared: 0.2148, Adjusted R-squared: 0.1814
## F-statistic: 6.428 on 2 and 47 DF, p-value: 0.003406lm_lf5 is our best fit model to predict FemaleLaborForceParticipationRate. However, this model is not very reliable because only 19.34% of the variance in FemaleLaborForceParticipationRate is explained by lm_lf5.
The formula to predict FemaleLaborForceParticipationRate can be represented as below:
# y = FemaleLAborForceParticipationRate , x1= bcWomenEntrepreneurshipIndex, x2 = bcEntrepreneurshipIndex
#Model y = -197060 -557851x1 + 402588x2cmatlf <- cor(women_entp[,c(6:8,10)])
corrplot.mixed(cmatlf)
cor(women_entp[,c(6:8,10)])## Women Entrepreneurship Index
## Women Entrepreneurship Index 1.0000000
## Entrepreneurship Index 0.9225547
## Inflation rate -0.4531406
## Female Labor Force Participation Rate 0.4443458
## Entrepreneurship Index Inflation rate
## Women Entrepreneurship Index 0.9225547 -0.4531406
## Entrepreneurship Index 1.0000000 -0.3876506
## Inflation rate -0.3876506 1.0000000
## Female Labor Force Participation Rate 0.3478316 -0.1434566
## Female Labor Force Participation Rate
## Women Entrepreneurship Index 0.4443458
## Entrepreneurship Index 0.3478316
## Inflation rate -0.1434566
## Female Labor Force Participation Rate 1.0000000Cohen’s rules of thumb:
|r| <= 0.1 give small (but should still be paid attention to) correlation, |r| <= 0.3 is medium, |r| >= 0.5 is large and can be observed by a casual observer.
Correlation between FemaleLaborForceParticipation rate and Entrpreneurship Index is 0.37 -> medium correlation
Correlation between FemaleLaborForceParticipation rate and Women Entrpreneurship Index is 0.37 also -> medium correlation
Since the correlation of EI and WEI doesn’t bring us much insights to predict WEI, we need to consider drop this variable.
lm8 <- lm(`Women Entrepreneurship Index` ~ `Inflation rate`+`Female Labor Force Participation Rate`+ `European Union Membership`+`Level of development` + `Inflation Type` , data =women_entp)
summary(lm8)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ `Inflation rate` +
## `Female Labor Force Participation Rate` + `European Union Membership` +
## `Level of development` + `Inflation Type`, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.766 -2.624 0.013 4.106 11.198
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 46.71835 4.90100 9.532 4.59e-12
## `Inflation rate` 0.69155 0.46163 1.498 0.1416
## `Female Labor Force Participation Rate` 0.16740 0.07576 2.209 0.0327
## `European Union Membership`Not Member 0.37962 3.17702 0.119 0.9055
## `Level of development`Developing -22.88740 3.61199 -6.336 1.30e-07
## `Inflation Type`Galloping Inflation -14.05189 8.71410 -1.613 0.1143
## `Inflation Type`Moderate Inflation 4.28424 2.37161 1.806 0.0780
## `Inflation Type`Walking Inflation -0.52205 4.24696 -0.123 0.9028
##
## (Intercept) ***
## `Inflation rate`
## `Female Labor Force Participation Rate` *
## `European Union Membership`Not Member
## `Level of development`Developing ***
## `Inflation Type`Galloping Inflation
## `Inflation Type`Moderate Inflation .
## `Inflation Type`Walking Inflation
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.596 on 42 degrees of freedom
## Multiple R-squared: 0.8199, Adjusted R-squared: 0.7899
## F-statistic: 27.32 on 7 and 42 DF, p-value: 1.071e-13Only Level of development and female labor force participation rate is significant. Adj R squared is 0.7419 Testing for interaction
lm9 <- lm(`Women Entrepreneurship Index` ~ (`Inflation rate`+`Female Labor Force Participation Rate`+ `European Union Membership`+`Level of development` + `Inflation Type`)^2 , data =women_entp)
summary(lm9)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ (`Inflation rate` +
## `Female Labor Force Participation Rate` + `European Union Membership` +
## `Level of development` + `Inflation Type`)^2, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.0462 -2.6926 -0.1102 3.0397 14.8683
##
## Coefficients: (5 not defined because of singularities)
## Estimate
## (Intercept) 25.06667
## `Inflation rate` 3.89836
## `Female Labor Force Participation Rate` 0.54233
## `European Union Membership`Not Member 4.10015
## `Level of development`Developing -2.87096
## `Inflation Type`Galloping Inflation -22.89498
## `Inflation Type`Moderate Inflation 10.31126
## `Inflation Type`Walking Inflation -8.82570
## `Inflation rate`:`Female Labor Force Participation Rate` -0.02818
## `Inflation rate`:`European Union Membership`Not Member 15.55715
## `Inflation rate`:`Level of development`Developing -15.04811
## `Inflation rate`:`Inflation Type`Galloping Inflation -2.62891
## `Inflation rate`:`Inflation Type`Moderate Inflation -1.13661
## `Inflation rate`:`Inflation Type`Walking Inflation -2.09213
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member 0.15342
## `Female Labor Force Participation Rate`:`Level of development`Developing -0.53165
## `Female Labor Force Participation Rate`:`Inflation Type`Galloping Inflation 0.26192
## `Female Labor Force Participation Rate`:`Inflation Type`Moderate Inflation -0.12481
## `Female Labor Force Participation Rate`:`Inflation Type`Walking Inflation 0.10389
## `European Union Membership`Not Member:`Level of development`Developing NA
## `European Union Membership`Not Member:`Inflation Type`Galloping Inflation NA
## `European Union Membership`Not Member:`Inflation Type`Moderate Inflation -42.33959
## `European Union Membership`Not Member:`Inflation Type`Walking Inflation NA
## `Level of development`Developing:`Inflation Type`Galloping Inflation NA
## `Level of development`Developing:`Inflation Type`Moderate Inflation 39.41665
## `Level of development`Developing:`Inflation Type`Walking Inflation NA
## Std. Error
## (Intercept) 18.13077
## `Inflation rate` 5.55172
## `Female Labor Force Participation Rate` 0.28416
## `European Union Membership`Not Member 29.16855
## `Level of development`Developing 28.87864
## `Inflation Type`Galloping Inflation 77.85363
## `Inflation Type`Moderate Inflation 22.17418
## `Inflation Type`Walking Inflation 30.51670
## `Inflation rate`:`Female Labor Force Participation Rate` 0.05917
## `Inflation rate`:`European Union Membership`Not Member 7.89861
## `Inflation rate`:`Level of development`Developing 6.86306
## `Inflation rate`:`Inflation Type`Galloping Inflation 4.45939
## `Inflation rate`:`Inflation Type`Moderate Inflation 4.82684
## `Inflation rate`:`Inflation Type`Walking Inflation 4.57220
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member 0.43268
## `Female Labor Force Participation Rate`:`Level of development`Developing 0.42616
## `Female Labor Force Participation Rate`:`Inflation Type`Galloping Inflation 1.28867
## `Female Labor Force Participation Rate`:`Inflation Type`Moderate Inflation 0.34448
## `Female Labor Force Participation Rate`:`Inflation Type`Walking Inflation 0.49328
## `European Union Membership`Not Member:`Level of development`Developing NA
## `European Union Membership`Not Member:`Inflation Type`Galloping Inflation NA
## `European Union Membership`Not Member:`Inflation Type`Moderate Inflation 16.20988
## `European Union Membership`Not Member:`Inflation Type`Walking Inflation NA
## `Level of development`Developing:`Inflation Type`Galloping Inflation NA
## `Level of development`Developing:`Inflation Type`Moderate Inflation 17.15781
## `Level of development`Developing:`Inflation Type`Walking Inflation NA
## t value
## (Intercept) 1.383
## `Inflation rate` 0.702
## `Female Labor Force Participation Rate` 1.909
## `European Union Membership`Not Member 0.141
## `Level of development`Developing -0.099
## `Inflation Type`Galloping Inflation -0.294
## `Inflation Type`Moderate Inflation 0.465
## `Inflation Type`Walking Inflation -0.289
## `Inflation rate`:`Female Labor Force Participation Rate` -0.476
## `Inflation rate`:`European Union Membership`Not Member 1.970
## `Inflation rate`:`Level of development`Developing -2.193
## `Inflation rate`:`Inflation Type`Galloping Inflation -0.590
## `Inflation rate`:`Inflation Type`Moderate Inflation -0.235
## `Inflation rate`:`Inflation Type`Walking Inflation -0.458
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member 0.355
## `Female Labor Force Participation Rate`:`Level of development`Developing -1.248
## `Female Labor Force Participation Rate`:`Inflation Type`Galloping Inflation 0.203
## `Female Labor Force Participation Rate`:`Inflation Type`Moderate Inflation -0.362
## `Female Labor Force Participation Rate`:`Inflation Type`Walking Inflation 0.211
## `European Union Membership`Not Member:`Level of development`Developing NA
## `European Union Membership`Not Member:`Inflation Type`Galloping Inflation NA
## `European Union Membership`Not Member:`Inflation Type`Moderate Inflation -2.612
## `European Union Membership`Not Member:`Inflation Type`Walking Inflation NA
## `Level of development`Developing:`Inflation Type`Galloping Inflation NA
## `Level of development`Developing:`Inflation Type`Moderate Inflation 2.297
## `Level of development`Developing:`Inflation Type`Walking Inflation NA
## Pr(>|t|)
## (Intercept) 0.1774
## `Inflation rate` 0.4882
## `Female Labor Force Participation Rate` 0.0663
## `European Union Membership`Not Member 0.8892
## `Level of development`Developing 0.9215
## `Inflation Type`Galloping Inflation 0.7708
## `Inflation Type`Moderate Inflation 0.6454
## `Inflation Type`Walking Inflation 0.7745
## `Inflation rate`:`Female Labor Force Participation Rate` 0.6375
## `Inflation rate`:`European Union Membership`Not Member 0.0585
## `Inflation rate`:`Level of development`Developing 0.0365
## `Inflation rate`:`Inflation Type`Galloping Inflation 0.5601
## `Inflation rate`:`Inflation Type`Moderate Inflation 0.8155
## `Inflation rate`:`Inflation Type`Walking Inflation 0.6507
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member 0.7255
## `Female Labor Force Participation Rate`:`Level of development`Developing 0.2222
## `Female Labor Force Participation Rate`:`Inflation Type`Galloping Inflation 0.8404
## `Female Labor Force Participation Rate`:`Inflation Type`Moderate Inflation 0.7197
## `Female Labor Force Participation Rate`:`Inflation Type`Walking Inflation 0.8347
## `European Union Membership`Not Member:`Level of development`Developing NA
## `European Union Membership`Not Member:`Inflation Type`Galloping Inflation NA
## `European Union Membership`Not Member:`Inflation Type`Moderate Inflation 0.0141
## `European Union Membership`Not Member:`Inflation Type`Walking Inflation NA
## `Level of development`Developing:`Inflation Type`Galloping Inflation NA
## `Level of development`Developing:`Inflation Type`Moderate Inflation 0.0290
## `Level of development`Developing:`Inflation Type`Walking Inflation NA
##
## (Intercept)
## `Inflation rate`
## `Female Labor Force Participation Rate` .
## `European Union Membership`Not Member
## `Level of development`Developing
## `Inflation Type`Galloping Inflation
## `Inflation Type`Moderate Inflation
## `Inflation Type`Walking Inflation
## `Inflation rate`:`Female Labor Force Participation Rate`
## `Inflation rate`:`European Union Membership`Not Member .
## `Inflation rate`:`Level of development`Developing *
## `Inflation rate`:`Inflation Type`Galloping Inflation
## `Inflation rate`:`Inflation Type`Moderate Inflation
## `Inflation rate`:`Inflation Type`Walking Inflation
## `Female Labor Force Participation Rate`:`European Union Membership`Not Member
## `Female Labor Force Participation Rate`:`Level of development`Developing
## `Female Labor Force Participation Rate`:`Inflation Type`Galloping Inflation
## `Female Labor Force Participation Rate`:`Inflation Type`Moderate Inflation
## `Female Labor Force Participation Rate`:`Inflation Type`Walking Inflation
## `European Union Membership`Not Member:`Level of development`Developing
## `European Union Membership`Not Member:`Inflation Type`Galloping Inflation
## `European Union Membership`Not Member:`Inflation Type`Moderate Inflation *
## `European Union Membership`Not Member:`Inflation Type`Walking Inflation
## `Level of development`Developing:`Inflation Type`Galloping Inflation
## `Level of development`Developing:`Inflation Type`Moderate Inflation *
## `Level of development`Developing:`Inflation Type`Walking Inflation
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.449 on 29 degrees of freedom
## Multiple R-squared: 0.8811, Adjusted R-squared: 0.7992
## F-statistic: 10.75 on 20 and 29 DF, p-value: 1.393e-08There is no significant interaction
lm10 <- lm(`Women Entrepreneurship Index` ~ `bcFemaleLaborForceParticipationRate`+`Level of development` , data =women_entp)
summary(lm10)##
## Call:
## lm(formula = `Women Entrepreneurship Index` ~ bcFemaleLaborForceParticipationRate +
## `Level of development`, data = women_entp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.7012 -4.2344 0.3651 5.5575 14.4798
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.259e+01 2.995e+00 17.561 < 2e-16 ***
## bcFemaleLaborForceParticipationRate 3.460e-04 1.323e-04 2.615 0.0119 *
## `Level of development`Developing -2.279e+01 2.074e+00 -10.989 1.4e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.846 on 47 degrees of freedom
## Multiple R-squared: 0.783, Adjusted R-squared: 0.7737
## F-statistic: 84.77 on 2 and 47 DF, p-value: 2.564e-16plot(lm10)
We can conclude that without EI, lm10 is our best fit model with adj. R squared = 0.7519. To make this model more reliable, we need more data about other factors like education rate, sociological factors,
The model can be represented as below:
# y = WEI, x1= FLFPR, x2 = LVD - Developing
# y = 49.46869 + 0.15676*x1 -22.95155*x2