SalaryHike

Simple Linear Regression

library(e1071)

## Warning: package 'e1071' was built under R version 3.5.1

Salary_Data <- read.csv("E:\\Data Science\\data science\\assignments\\Simple Linear Regression\\Salary_Data.csv")

attach(Salary_Data)

# First Moment Business Decision
summary(Salary_Data)

##  YearsExperience      Salary      
##  Min.   : 1.100   Min.   : 37731  
##  1st Qu.: 3.200   1st Qu.: 56721  
##  Median : 4.700   Median : 65237  
##  Mean   : 5.313   Mean   : 76003  
##  3rd Qu.: 7.700   3rd Qu.:100545  
##  Max.   :10.500   Max.   :122391

# Second Moment Business Decision
var(Salary)

## [1] 751550960

var(YearsExperience)

## [1] 8.053609

sd(Salary)

## [1] 27414.43

sd(YearsExperience)

## [1] 2.837888

#Third Moment Business Decision
skewness(Salary)

## [1] 0.3194946

skewness(YearsExperience)

## [1] 0.3424477

# Fourth Moment Business Decision
kurtosis(Salary)

## [1] -1.395477

kurtosis(YearsExperience)

## [1] -1.17293

plot(Salary, YearsExperience, col = "blue")

# correlation coeffeicient 
cor(Salary, YearsExperience)

## [1] 0.9782416

model1 <- lm(YearsExperience~Salary)
summary(model1)

## 
## Call:
## lm(formula = YearsExperience ~ Salary)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.12974 -0.46457  0.04105  0.54311  0.79669 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.383e+00  3.273e-01  -7.281  6.3e-08 ***
## Salary       1.013e-04  4.059e-06  24.950  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5992 on 28 degrees of freedom
## Multiple R-squared:  0.957,  Adjusted R-squared:  0.9554 
## F-statistic: 622.5 on 1 and 28 DF,  p-value: < 2.2e-16

confint(model1, level = 0.95)

##                     2.5 %        97.5 %
## (Intercept) -3.053603e+00 -1.7127178614
## Salary       9.295173e-05  0.0001095796

predict(model1, interval = "predict")

## Warning in predict.lm(model1, interval = "predict"): predictions on current data refer to _future_ responses

##          fit       lwr       upr
## 1   1.600934 0.3165619  2.885307
## 2   2.295819 1.0237773  3.567861
## 3   1.437694 0.1500755  2.725313
## 4   2.024427 0.7478589  3.300996
## 5   1.656428 0.3731291  2.939727
## 6   3.352729 2.0947042  4.610754
## 7   3.707969 2.4533424  4.962595
## 8   3.130248 1.8697562  4.390740
## 9   4.142905 2.8915256  5.394284
## 10  3.408121 2.1506703  4.665572
## 11  4.018652 2.7664480  5.270856
## 12  3.266856 2.0079094  4.525802
## 13  3.384628 2.1269353  4.642320
## 14  3.397185 2.1396216  4.654747
## 15  3.805285 2.5514728  5.059097
## 16  4.496626 3.2471410  5.746111
## 17  4.303310 3.0528728  5.553747
## 18  6.030801 4.7817265  7.279875
## 19  5.856117 4.6076374  7.104597
## 20  7.129735 5.8731707  8.386300
## 21  6.906748 5.6522247  8.161272
## 22  7.568520 6.3071722  8.829867
## 23  7.875253 6.6099641  9.140542
## 24  9.142087 7.8554139 10.428759
## 25  8.698442 7.4201795  9.976704
## 26  8.308670 7.0369817  9.580359
## 27  9.461782 8.1684469 10.755118
## 28  9.022897 7.7385799 10.307214
## 29 10.010845 8.7049141 11.316775
## 30  9.958288 8.6536250 11.262951

# R-squared value for the above model is 0.957 hence the above model is good.