Simple-Linear-Regression-using-statsmodel

Predicting employee salary based on their experience using linear regression.

SIMPLE LINEAR REGRESSION

# Import th relevant libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import statsmodels.api as sm
import seaborn as snb
snb.set()

Load the dataset

data=pd.read_csv("Salary_Data.csv")

data

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	YearsExperience	Salary
0	1.1	39343.0
1	1.3	46205.0
2	1.5	37731.0
3	2.0	43525.0
4	2.2	39891.0
5	2.9	56642.0
6	3.0	60150.0
7	3.2	54445.0
8	3.2	64445.0
9	3.7	57189.0
10	3.9	63218.0
11	4.0	55794.0
12	4.0	56957.0
13	4.1	57081.0
14	4.5	61111.0
15	4.9	67938.0
16	5.1	66029.0
17	5.3	83088.0
18	5.9	81363.0
19	6.0	93940.0
20	6.8	91738.0
21	7.1	98273.0
22	7.9	101302.0
23	8.2	113812.0
24	8.7	109431.0
25	9.0	105582.0
26	9.5	116969.0
27	9.6	112635.0
28	10.3	122391.0
29	10.5	121872.0

data.describe()

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	YearsExperience	Salary
count	30.000000	30.000000
mean	5.313333	76003.000000
std	2.837888	27414.429785
min	1.100000	37731.000000
25%	3.200000	56720.750000
50%	4.700000	65237.000000
75%	7.700000	100544.750000
max	10.500000	122391.000000

Create regression

spliting the data into independent variable x and dependent y.

X=data['YearsExperience']
y=data['Salary']

X

0      1.1
1      1.3
2      1.5
3      2.0
4      2.2
5      2.9
6      3.0
7      3.2
8      3.2
9      3.7
10     3.9
11     4.0
12     4.0
13     4.1
14     4.5
15     4.9
16     5.1
17     5.3
18     5.9
19     6.0
20     6.8
21     7.1
22     7.9
23     8.2
24     8.7
25     9.0
26     9.5
27     9.6
28    10.3
29    10.5
Name: YearsExperience, dtype: float64

y

0      39343.0
1      46205.0
2      37731.0
3      43525.0
4      39891.0
5      56642.0
6      60150.0
7      54445.0
8      64445.0
9      57189.0
10     63218.0
11     55794.0
12     56957.0
13     57081.0
14     61111.0
15     67938.0
16     66029.0
17     83088.0
18     81363.0
19     93940.0
20     91738.0
21     98273.0
22    101302.0
23    113812.0
24    109431.0
25    105582.0
26    116969.0
27    112635.0
28    122391.0
29    121872.0
Name: Salary, dtype: float64

Explor the data

plt.scatter(X,y,color="blue")
plt.xlabel("YEAR OF EXPERERIENCE", fontsize=20,color="blue")
plt.ylabel("SALARY",fontsize=20,color="blue")
plt.show()

Creating the regresion with statsmodel

x=sm.add_constant(X)
results=sm.OLS(y,x).fit()
results.summary()

OLS Regression Results

Dep. Variable:	Salary	R-squared:	0.957
Model:	OLS	Adj. R-squared:	0.955
Method:	Least Squares	F-statistic:	622.5
Date:	Thu, 12 Nov 2020	Prob (F-statistic):	1.14e-20
Time:	17:21:23	Log-Likelihood:	-301.44
No. Observations:	30	AIC:	606.9
Df Residuals:	28	BIC:	609.7
Df Model:	1
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	2.579e+04	2273.053	11.347	0.000	2.11e+04	3.04e+04
YearsExperience	9449.9623	378.755	24.950	0.000	8674.119	1.02e+04

Omnibus:	2.140	Durbin-Watson:	1.648
Prob(Omnibus):	0.343	Jarque-Bera (JB):	1.569
Skew:	0.363	Prob(JB):	0.456
Kurtosis:	2.147	Cond. No.	13.2

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

plot the regresion

plt.scatter(X,y ,color="red")
y_pred=2.579e+04+X*9449.9623
fig=plt.plot(X,y_pred,color="black")
plt.xlabel("YEAR EXPERIENCE",fontsize="20")
plt.ylabel("SALARY",fontsize="20")
plt.show()