Linear Regression (Salary Prediction)

Structure & Summary

My_data=Regression_Batch2
str(My_data)

Classes ‘tbl_df’, ‘tbl’ and 'data.frame':   40 obs. of  5 variables:
 $ Student       : num  1 2 3 4 5 6 7 8 9 10 ...
 $ School_Ranking: num  78 56 23 67 56 78 68 89 37 67 ...
 $ GPA           : num  2.92 3.84 3.04 3.2 3.61 2.99 3.78 3.2 3.42 3.05 ...
 $ Experience    : num  3 9 6 6 7 5 8 5 7 5 ...
 $ Salary        : num  73590 87000 76970 79320 79530 ...

summary(My_data)

    Student      School_Ranking       GPA          Experience   
 Min.   : 1.00   Min.   :15.00   Min.   :2.760   Min.   :2.000  
 1st Qu.:10.75   1st Qu.:45.75   1st Qu.:3.033   1st Qu.:5.000  
 Median :20.50   Median :67.00   Median :3.155   Median :6.000  
 Mean   :20.50   Mean   :59.88   Mean   :3.233   Mean   :5.975  
 3rd Qu.:30.25   3rd Qu.:76.50   3rd Qu.:3.350   3rd Qu.:7.000  
 Max.   :40.00   Max.   :89.00   Max.   :3.850   Max.   :9.000  
     Salary     
 Min.   :71040  
 1st Qu.:76913  
 Median :78670  
 Mean   :78721  
 3rd Qu.:80600  
 Max.   :87000  

Correlation

cor(My_data)

                   Student School_Ranking        GPA Experience      Salary
Student         1.00000000      0.0582101 -0.1262402 0.04395596 -0.00261919
School_Ranking  0.05821010      1.0000000  0.2051312 0.20250931  0.23429048
GPA            -0.12624017      0.2051312  1.0000000 0.65904413  0.73788910
Experience      0.04395596      0.2025093  0.6590441 1.00000000  0.78580114
Salary         -0.00261919      0.2342905  0.7378891 0.78580114  1.00000000

Scatterplot & Boxplot Analysis

par(mfrow=c(1,2))
scatter.smooth(My_data$Experience,col="Red",main="Scatterplot Analysis")
boxplot(My_data$GPA,col="Blue",main="Boxplot Analysis")

Corplot Analysis

library(corrplot)
corr_anlysis=cor(My_data)
corrplot(corr_anlysis,main="Corrplot Analysis")

Setting First Linear Model Equation

My_L_Reg_Eq=lm(Salary~.,data=My_data)
summary(My_L_Reg_Eq)

Call:
lm(formula = Salary ~ ., data = My_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-6359.4  -736.0   306.7  1392.8  4440.1 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    52751.870   4928.281  10.704 1.39e-12 ***
Student            7.064     31.929   0.221 0.826188    
School_Ranking     9.442     18.450   0.512 0.612031    
GPA             5534.006   1785.345   3.100 0.003811 ** 
Experience      1232.513    294.651   4.183 0.000183 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2273 on 35 degrees of freedom
Multiple R-squared:  0.7058,    Adjusted R-squared:  0.6722 
F-statistic: 20.99 on 4 and 35 DF,  p-value: 6.703e-09

Setting Final Linear Model Equation Based On Pivot Value

My_L_Reg_Eq_AP=lm(Salary~GPA+Experience,data=My_data)
summary(My_L_Reg_Eq_AP)

Call:
lm(formula = Salary ~ GPA + Experience, data = My_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-6147.5  -830.1   379.3  1481.8  4767.5 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  53295.4     4566.5  11.671 5.78e-14 ***
GPA           5539.8     1696.5   3.265  0.00236 ** 
Experience    1257.3      282.8   4.445 7.71e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2221 on 37 degrees of freedom
Multiple R-squared:  0.7031,    Adjusted R-squared:  0.687 
F-statistic:  43.8 on 2 and 37 DF,  p-value: 1.756e-10

Salary Prediction

My_Prediction=data.frame(GPA=3,Experience=7)
My_Prediction_Result=predict(My_L_Reg_Eq_AP,My_Prediction)
My_Prediction_Result

       1 
78715.65