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"Talented people will find a way to make a living.

How can you be certain it's with you and your company?"

 Attrition of employees has become a critical concern for a company's competitive edge. Finding, hiring, and training new employees is quite costly. It is more cost-effective for a corporation to maintain its current staff. To keep its staff for a longer amount of time, a corporation must maintain a nice working environment.

Whether an employee will stay or quit a firm, his or her response is just binary, i.e., "YES" or "NO." A link between predictor variables and a categorical response variable is analyzed using logistic regression. It's a technique for analyzing a data set with a dependent variable and one or more independent variables in order to predict the result of a binary variable, which means there are only two possibilities. The sigmoid function, also known as the logistic function, produces a 'S' shaped curve that may be used to transfer any real-valued integer to a value between 0 and 1.

p = 1 / 1 + e-y

e - y = (p / p – 1)

y = log (p / p – 1)

log (p / p – 1) = β0 + β1X1 + β2X2 + … + βnXn

Here employee attrition will be the dependent categorical variable so we are using logistic regression to predict and analyze the employee attrition.

I'll show you how to utilize R software to assess employee attrition in five simple stages.

·         Exploration of data set

·         Data pre-processing

·         Dividing the data into two parts "training" and "testing"

·         Use the "training data set" to build the model.

·         Use the "testing data set" to conduce the accuracy test.

Exploration of Data set

This data set was collected using Kaggle. There are 14999 observations and 10 variables in this dataset. "Attrition(left)" is the dependent variable among ten variables.

Data pre processing

1.      Detecting the variable names in the data set

#Variable names in the data set

variable.names(HR)

2.      Detecting the summary of all variables in the data set

#Summary of all the variables in the data set (5point summary)

summary(HR)

3.      Detect the missing values

Let check whether there is any missing values in the dataset.

missmap(HR,main ="Missing values vs observed")

Result: No missing value was observed

4.      Changing data types

To build a good model, we must first change the data type of the character variables to factor.

Department and pay are the two-character variables. 8 and 9 are the column numbers, respectively.

#Converting the data of department and salary into factor to analyse the data

HR [, c (8,9)] =lapply (HR [, c (8,9)], as. factor)

Dividing the data into "training" and "testing"

In every regression analysis, the dataset must be divided into two parts:

·         Data set for Training

·         Data set for Testing

First, we’ll develop our model with the Training Data set and then verify its accuracy with the Testing Data set.

# Splitting of data set as training data and testing data to analyse further

ran=sample(x=c("Training","Testing"),size=nrow(HR),replace=T,prob=c(0.8,0.2))

TrainingData1=HR[ran=="Training",] #training data set

TestingData1=HR[ran=="Testing",] #testing data set

#no. of rows presents in the training data set

nrow(TrainingData1)

#no. of rows presents in the testing data set

nrow (TestingData1)

Building up the model

We'll next build the model together in a few simple steps, as follows:

·         Identify the variables that are independent.

·         Build the model by incorporating TRAINING data into the equation.

#Dependent variable is attrition (left)

independent variables=colnames(HR[,1:9])

#Display of all the independent variables in the data set

independent variables

Then, using the "glm" function, we'll add "Training Data" to the equation and create a logistic regression model.

#Incorporation of training data to build the logistic regression model

#Using glm function

model1=glm(HR$left~HR$satisfaction_level+HR$last_evaluation+HR$number_project+HR$average_montly_hours+HR$time_spend_company+HR$Work_accident+HR$promotion_last_5years+HR$Department+HR$salary,data=TrainingData1,family=binomial(link='logit'))

#Summary of the logistic regression model

summary(model1)

As we can see from the table above, employee satisfaction, last evaluation, number of projects, average monthly hours, time spent in the company, work accident, promotion in the last five years, and salary are all crucial factors in influencing employee attrition. There will be less chances of losing an employee if the organisation focuses on these areas.

Confusion Matrix

# Run the test data through the model

res1<-predict (model1,TestingData1, type = "response")

res1

#validate the model - confusion matrix

confusionMatrix<-table(Actual_value=HR$left,predicted_value = res1 >0.5)

confusionMatrix

Interpretation

Our logistic regression model works quite well. This method can be used to analyse any dataset of employee attrition facts, helping the company to gain a competitive edge and effectively manage its resources.

Course: Master of Business Administration

Amrita School of Business, Coimbatore

Amrita Vishwa Vidyapeetham.

Forecasting of monthly turnover of BSE using AR model

One of the approaches used for time-series analysis is autoregressive (AR) modelling. AR models are a useful tool in time series research since they allow us to estimate the future using previous data. AR models may be used to represent anything that has some degree of autocorrelation, which indicates that data at adjacent time steps have a connection. This form of modelling is most commonly used with stock market prices, where the price today (t) is highly associated with the price one day ago (t-1).

yt = c + φ1yt−1 + φ2yt−2 + · · · + φp yt−p + εt, where εt is white noise. This is a multiple regression with lagged values of yt as predictors.

I'll show you how to utilise R software to assess forecasting in the following stages.

·         Exploration of data set

·         Data pre-processing and converting into time series data

·         Testing for stationarity

·         Predicting the model and lag using ACF and PACF

·         Predicting the Model for better results

·         Forecasting the next period of data

Exploration of Data set

This data set was collected from RBI website.

(https://dbie.rbi.org.in/DBIE/dbie.rbi?site=publications)

The data contains the monthly turnover of BSE from 1990 to 2021. For forecasting we will be taking a time period from 2005 to 2021 to forecast the future prediction.

library(readxl)

HBS_Table_No_183_Monthly_Turnover_at_BSE <- read_excel("C:/Users/jeeva nave/Downloads/HBS_Table_No._183___Monthly_Turnover_at_BSE.xlsx",

                                                        +     sheet = "Sheet1")

View(HBS_Table_No_183_Monthly_Turnover_at_BSE)

data<-HBS_Table_No_183_Monthly_Turnover_at_BSE

Data pre processing and converting into time series data

1.      Detecting the summary of all variables in the data set

#Summary of all the variables in the data set

summary(data) 

2.      Converting the data into time series

We are converting the data set into time series before building the model for forecasting. Since we are predicting the monthly turnover first, we will remove the annual data from the dataset. Once the data is converted, we will plot the graph to check the presence of outliers.

data<-data[-13,]

View(data)

data1<-c(data$`2005-06`,data$`2006-07`,data$`2007-08`,data$`2008-09`,data$`2009-10`,data$`2010-11`,data$`2011-12`,

        data$`2012-13`,data$`2013-14`,data$`2014-15`,data$`2015-16`,data$`2016-17`,data$`2017-18`,data$`2018-19`,data$`2019-20`,data$`2020-21`)

data1<-as.numeric(data1)

View(data1)

m<-data1

data1<-matrix(data1,nrow=length(data1),ncol=1)

m<-data1[1:190]

View(m)

library(tseries)

# converting the data set into time series

x<-ts(m,start=c(2005,1),end=c(2021,1),frequency=12)

summary(x)

#plotting the series to find the presence of outlier.

plot(x)

boxplot(x[1:190])

boxplot.stats(x)

From the plot we can identify the presence of outlier in the dataset. We need to remove the outlier in order to proceed with the prediction.

We are identifying the outlier and removing it

#Identify(x)

#  Identifying the outliers

x[c(which(x>150000))] # identifying the outliers

outliers1<-which(x>150000) # identifying the outliers

which(x>150000) # identifying the outliers

x1<-x # making a duplicate

x1[2]<-x[1] # replacing the outliers with previous period value

for (i in 1:6) { x1[outliers1[i]]<-x1[(outliers1[i])-1]}

x1

plot(x1, col="red”, type="l")

lines(x1, type='p',col='blue')

boxplot(x1)

boxplot.stats(x1)

The outlier is removed by making a duplicate of the dataset and then the outlier are replaced by the previous lowest value. The boxplot represents the removal of outlier from the dataset.

Test for stationarity

In the field of time series analysis, stationarity is a key concept that has a big impact on how data is interpreted and projected. Most time series models presume that each point is independent of the others for forecasting or predicting the future. When the dataset of previous cases is steady, this is the best indicator. The statistical features of a system must not vary over time for data to be stationary. This does not imply that the values for each data point must be same, but the data's overall behaviour should be consistent.

The ADF (Augmented Dickey-Fuller) test is a statistical significance test that provides findings for null and alternative hypotheses in hypothesis testing. As a consequence, we will get a p-value from which we will need to interpret whether the time series is stationary or not.

The following assumptions are used in the ADF test.

·         The Null Hypothesis (HO) states that the series is non-stationary or has a unit root.

·         Alternative Hypothesis (HA): The series is stationary or there is no unit root in the series.

#dicky fuller test for checking unit root

adf.test(x1)

# series is not stationary so we will go for differencing the series

dx<-diff(x1,1)

plot(dx)

adf.test(dx) 

#adf test says differenced  series is stationary

By doing adf test it was found that the time series is not stationary the p value is founded to greater than 0.05. In order to make the series stationary first we will be differentiating the series. We will differentiate the series once. After differentiating we again perform adf test to check the stationarity.

ADF test showed that the series is now stationary and the p value is found to be less than 0.05 so we reject null hypothesis. The plot shows the differentiate time series data.  

Predicting the model and lag using ACF and PACF

ACF stands for auto-correlation function, and it returns the auto-correlation values of any series with its lagged values. Trend, seasonality, cyclic, and residual components can all be found in a time series. Because ACF incorporates all of these factors while determining correlations, it is known as a 'full auto-correlation plot.'

The partial auto-correlation function (PACF) is a type of auto-correlation function. Essentially, instead of identifying connections between present and lags as ACF does, it looks for correlations between residuals and the next lag value.

#modelling the series

#we have to find the pattern so we will use autocorelation fun

acf(x1,lag.max = 100)

#acf pattern (exponential decay to zero)indicate AR process

#inorder to know the order of the process we have to use pacf

pacf(x1)

The ACF plot represents positive and negative strikes decaying to zero which indicates AR model. In order to identify the lag values, we perform PACF and the plot shows the lag value exists at 1,2 and 14.

Predicting the Model for better results

# pacf suggest 1 or 2 lag

result<-arima(x1,c(1,1,0))

result

result1<-arima(x1,c(2,1,0))

result1

# we get better result in ar2

predict(result1,10)

The predict results shows the forecast values of next 10 periods.

Forecasting the next period of data

We have predicted the next 10 forecast data of monthly turnover of BSE. Let’s plot the original, data used for estimation, the forecasted data together to visualize the changes in single plot. First, we will convert the predicted values also into a time series data.

x[195:205]

z<-c(x,53120.98, 54962.34, 54330.06, 54547.17, 54472.62, 54498.22, 54489.43, 54492.45 ,54491.41 ,54491.76)

plot(z,type = 'l')

a<-ts(z,start = c(2005,1),frequency = 12,end = c(2021,1))

View(a)

m1<-a

a<-matrix(a,nrow=length(data1),ncol=1)

m1<-a[1:205]

View(m1)

c<-cbind(a,z,x1)

plot(c,main="Timeseries")

The plot represents the time series dataset along with predicted values.

Here x represents the original data, x1 represents the data used for estimation of forecast and z1 represents the forecasted data of next 10 months of the time series data.

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Course: Master of Business Administration

Amrita School of Business, Coimbatore

Amrita Vishwa Vidyapeetham.