# Introduction

• Work experience is an important factor that usually affect employee salary. Employers usually consider experience as a predictive measure of performance for the employee role in the company. Thus, it is anticipated that an employee experience will be an essentail factor that affects the ability of individuals to get a job, affects their starting salary, and plays a role in determining increments and promotions. (Dash et.al, 2017)

• There is a typical fact that, the more experience someone has specific to the job he/she is starting, the more he/she'll know about the position, making that person more valuable to the company.

• This report intends to analyse how this relationship behaves and how to measure it statistically. In this analysis, the author attempt to cover these areas with a well known statistical method.

# Problem statement

• In this analysis, the author tried to answer the question:

    Is there a significant relationship between employee salary and employee years of experience?

• The analysis is done in 2 steps:
• First step is to check whether there is a considerable relationship between the two variables.
• Then the data is fitted into a simple linear regression model.
• Linear Regression algorithm works on the basis of Least Square Method in Statistics. Basically it takes one more independent variables(X) and find the relationship on scalar response variable(Y).

• A simple linear regression equation will be as: \[y= \beta_0 + \beta_1x \]

• Where \(\beta_0\) is the intercept and \(\beta_1\) is the coefficient of independent variable}

# Data

• The data source used for the analysis is available at https://www.kaggle.com/rsadiq/salary
• This data set is a sample data set provided for beginners to learn data analysis and apply some basic principles on a simple dataset.
• The dataset consists of salary and years of experience of 35 jobholders.
• First few rows of data:

There are two columns YearsExperience and Salary

# Descriptive Statistics

Data Summary

##  YearsExperience      Salary      
##  Min.   : 1.100   Min.   : 37731  
##  1st Qu.: 3.450   1st Qu.: 57019  
##  Median : 5.300   Median : 81363  
##  Mean   : 6.309   Mean   : 83946  
##  3rd Qu.: 9.250   3rd Qu.:113224  
##  Max.   :13.500   Max.   :139465

# Histogram of Salary and Years of Experience

# Data cleansing - Checking for outliers and missing values

• Checking for outliers

There are no outliers in the dataset

• Checking for missing values

any(is.na(data))

## [1] FALSE

There are no missing vaues in the dataset

# Scatter plot of salary and years of experience

• Here we can see a strong possitive relationship between the salary and years of experience"

# Correlation between salary and years of experience

• \(H0\) (Null hypothesis)= There is no significant correlation between salary and years of experience
• \(H1\) (Alternative hypothesis)= There is a significant correlation between salary and years of experience

## 
##  Pearson's product-moment correlation
## 
## data:  data$YearsExperience and data$Salary
## t = 30.237, df = 33, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.9651673 0.9911731
## sample estimates:
##       cor 
## 0.9824273

• The correlation between salary and years of experience is 0.98 which concludes a very strong possitive relationship
• p value of the Pearson's test is defined as P < 0.05 which indicates a statistical significance and leads to the rejection of null hypothesis (\(H0\) is rejected).
• Therefore we can conclude that there is a significant statistical correlation between salary and years of experience with a 0.02 level of significance.

# Splitting the dataset

For further analysis of the data, the dataset is splited into two sets a training set and a test set.

The first few rows of the each set are as follows:

• training_set
• test_set

# Fitting a simple regression model

• The independent variable is the years of experience and the dependent variable is salary
• The fitted simple regression model:

## 
## Call:
## lm(formula = Salary ~ YearsExperience, data = training_set)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##  -8470  -4293    244   3200  12700 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      28864.3     2349.0   12.29 2.47e-12 ***
## YearsExperience   8810.6      343.2   25.67  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6235 on 26 degrees of freedom
## Multiple R-squared:  0.9621, Adjusted R-squared:  0.9606 
## F-statistic: 659.1 on 1 and 26 DF,  p-value: < 2.2e-16

• p value of the F statistic is less than 0.02 leads to model significance.
• p value of the coefficient is less than 0.02 leads to coefficient significance.
• R-squared: 0.9621 concludes that 96.2% of varience in salary can be explained by the years of experience

# Check for heteroscedasticity

Breusch-Pagan test to check for heteroscedasticity

• \(H0\) (Null hypothesis) = variance of the residuals is constant
• \(Ha\) (Alternative hypothesis) = variance of the residuals is not constant

## 
##  studentized Breusch-Pagan test
## 
## data:  lm1
## BP = 0.37999, df = 1, p-value = 0.5376

• p value of the Breusch-Pagan test is very high (more than 0.05) leads to the acceptance of null hypothesis
• Therefore we can conclude that the variance of the residuals is constant at 0.02 level of significance

# Regression line for the training and test datasets

# Regression line for the full dataset

# Evaluation

##  Mean Absolute Error: 5151.473 
##  Mean Square Error: 32305371 
##  Root Mean Square Error: 5683.781 
##  R-squared: 0.9692507

• There is a strong possitive relationship between the salary and years of experience.
• The fitted model can explain above 95% of salary variation by the number of years of experience.

# Discussion

• Since the data set used for this analysis is very simple and and the sample is small in size, it is advised that this analysis is repeated with a larger dataset in order to achieve more practical results.
• An important limitation for this analysis in practice is that there are multiple confinding factors which may impact salary in addition to years of experience.
• Therefore it is recommended to use a dataset that can represent other factors and apply multiple linear regression to make a salary prediction model.

# References

• Mihir Dash & Suprabha Bakshi & Aarushi Chugh, 2017. "The Relationship Between Work Experience and Employee Compensation: A Case Study of the Indian IT Industry," Journal of Applied Management and Investments, Department of Business Administration and Corporate Security, International Humanitarian University, vol. 6(1), pages 5-10, February.

• https://support.rstudio.com/hc/en-us/articles/200486468-Authoring-R-Presentations#:~:text=%20Authoring%20Content%20%201%20Formatted%20Text.%20Content,you%20want%20to%20float%20an%20image...%20More%20

• https://work.chron.com/factors-affect-starting-salary-8712.html