Multiple Linear Regression in R
Data called 50_Startups.csv
|
R&D Spend
|
Administration
|
Marketing Spend
|
State
|
Profit
|
|
165349.2
|
136897.8
|
471784.1
|
New York
|
192261.8
|
|
162597.7
|
151377.6
|
443898.5
|
California
|
191792.1
|
|
153441.5
|
101145.6
|
407934.5
|
Florida
|
191050.4
|
|
144372.4
|
118671.9
|
383199.6
|
New York
|
182902
|
|
142107.3
|
91391.77
|
366168.4
|
Florida
|
166187.9
|
|
131876.9
|
99814.71
|
362861.4
|
New York
|
156991.1
|
|
134615.5
|
147198.9
|
127716.8
|
California
|
156122.5
|
|
130298.1
|
145530.1
|
323876.7
|
Florida
|
155752.6
|
|
120542.5
|
148719
|
311613.3
|
New York
|
152211.8
|
|
123334.9
|
108679.2
|
304981.6
|
California
|
149760
|
|
101913.1
|
110594.1
|
229161
|
Florida
|
146122
|
|
100672
|
91790.61
|
249744.6
|
California
|
144259.4
|
|
93863.75
|
127320.4
|
249839.4
|
Florida
|
141585.5
|
|
91992.39
|
135495.1
|
252664.9
|
California
|
134307.4
|
|
119943.2
|
156547.4
|
256512.9
|
Florida
|
132602.7
|
|
114523.6
|
122616.8
|
261776.2
|
New York
|
129917
|
|
78013.11
|
121597.6
|
264346.1
|
California
|
126992.9
|
|
94657.16
|
145077.6
|
282574.3
|
New York
|
125370.4
|
|
91749.16
|
114175.8
|
294919.6
|
Florida
|
124266.9
|
|
86419.7
|
153514.1
|
0
|
New York
|
122776.9
|
|
76253.86
|
113867.3
|
298664.5
|
California
|
118474
|
|
78389.47
|
153773.4
|
299737.3
|
New York
|
111313
|
|
73994.56
|
122782.8
|
303319.3
|
Florida
|
110352.3
|
|
67532.53
|
105751
|
304768.7
|
Florida
|
108734
|
|
77044.01
|
99281.34
|
140574.8
|
New York
|
108552
|
|
64664.71
|
139553.2
|
137962.6
|
California
|
107404.3
|
|
75328.87
|
144136
|
134050.1
|
Florida
|
105733.5
|
|
72107.6
|
127864.6
|
353183.8
|
New York
|
105008.3
|
|
66051.52
|
182645.6
|
118148.2
|
Florida
|
103282.4
|
|
65605.48
|
153032.1
|
107138.4
|
New York
|
101004.6
|
|
61994.48
|
115641.3
|
91131.24
|
Florida
|
99937.59
|
|
61136.38
|
152701.9
|
88218.23
|
New York
|
97483.56
|
|
63408.86
|
129219.6
|
46085.25
|
California
|
97427.84
|
|
55493.95
|
103057.5
|
214634.8
|
Florida
|
96778.92
|
|
46426.07
|
157693.9
|
210797.7
|
California
|
96712.8
|
|
46014.02
|
85047.44
|
205517.6
|
New York
|
96479.51
|
|
28663.76
|
127056.2
|
201126.8
|
Florida
|
90708.19
|
|
44069.95
|
51283.14
|
197029.4
|
California
|
89949.14
|
|
20229.59
|
65947.93
|
185265.1
|
New York
|
81229.06
|
|
38558.51
|
82982.09
|
174999.3
|
California
|
81005.76
|
|
28754.33
|
118546.1
|
172795.7
|
California
|
78239.91
|
|
27892.92
|
84710.77
|
164470.7
|
Florida
|
77798.83
|
|
23640.93
|
96189.63
|
148001.1
|
California
|
71498.49
|
|
15505.73
|
127382.3
|
35534.17
|
New York
|
69758.98
|
|
22177.74
|
154806.1
|
28334.72
|
California
|
65200.33
|
|
1000.23
|
124153
|
1903.93
|
New York
|
64926.08
|
|
1315.46
|
115816.2
|
297114.5
|
Florida
|
49490.75
|
|
0
|
135426.9
|
0
|
California
|
42559.73
|
|
542.05
|
51743.15
|
0
|
New York
|
35673.41
|
|
0
|
116983.8
|
45173.06
|
California
|
14681.4
|
Step 1
#Import
dataset1 = read.csv('50_Startups.csv')
Step 2
# Encoding categorical data
Dataset1$State = factor(dataset1$State,
levels = c('New York', 'California', 'Florida'),
labels = c(1, 2, 3))
Step 3
# Fitting Multiple Linear Regression to the Training set
Regresor = lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend + State,
Data = training_set)
OR
regressor = lm(formula = Profit ~ .,
data = training_set)
summary(refressor)
Call:
lm(formula = Profit ~ ., data = training_set)
Residuals:
Min 1Q Median 3Q Max
-33128 -4865 5 6098 18065
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.965e+04 7.637e+03 6.501 1.94e-07 ***
R.D.Spend 7.986e-01 5.604e-02 14.251 6.70e-16 ***
Administration -2.942e-02 5.828e-02 -0.505 0.617
Marketing.Spend 3.268e-02 2.127e-02 1.537 0.134
State2 1.213e+02 3.751e+03 0.032 0.974
State3 2.376e+02 4.127e+03 0.058 0.954
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9908 on 34 degrees of freedom
Multiple R-squared: 0.9499, Adjusted R-squared: 0.9425
F-statistic: 129 on 5 and 34 DF, p-value: < 2.2e-16
# Predicting the Test set results
y_pred = predict(regressor, newdata = test_set)
Step 4
# Building the optimal model using Backward Elimination
regressor = lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend + State,
data = dataset1)
summary(regressor)
Call:
lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend +
State, data = dataset1)
Residuals:
Min 1Q Median 3Q Max
-33504 -4736 90 6672 17338
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.008e+04 6.953e+03 7.204 5.76e-09 ***
R.D.Spend 8.060e-01 4.641e-02 17.369 < 2e-16 ***
Administration -2.700e-02 5.223e-02 -0.517 0.608
Marketing.Spend 2.698e-02 1.714e-02 1.574 0.123
State2 4.189e+01 3.256e+03 0.013 0.990
State3 2.407e+02 3.339e+03 0.072 0.943
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9439 on 44 degrees of freedom
Multiple R-squared: 0.9508, Adjusted R-squared: 0.9452
F-statistic: 169.9 on 5 and 44 DF, p-value: < 2.2e-16
State is not significant so removing
Step 5
regressor = lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend,
data = dataset1)
summary(regressor)
Call:
lm(formula = Profit ~ R.D.Spend + Administration + Marketing.Spend,
data = dataset1)
Residuals:
Min 1Q Median 3Q Max
-33534 -4795 63 6606 17275
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.012e+04 6.572e+03 7.626 1.06e-09 ***
R.D.Spend 8.057e-01 4.515e-02 17.846 < 2e-16 ***
Administration -2.682e-02 5.103e-02 -0.526 0.602
Marketing.Spend 2.723e-02 1.645e-02 1.655 0.105
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9232 on 46 degrees of freedom
Multiple R-squared: 0.9507, Adjusted R-squared: 0.9475
F-statistic: 296 on 3 and 46 DF, p-value: < 2.2e-16
Administration is not significant so removing
Step 6
regressor = lm(formula = Profit ~ R.D.Spend + Marketing.Spend,
data = dataset1)
summary(regressor)
Call:
lm(formula = Profit ~ R.D.Spend + Marketing.Spend, data = dataset1)
Residuals:
Min 1Q Median 3Q Max
-33645 -4632 -414 6484 17097
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.698e+04 2.690e+03 17.464 <2e-16 ***
R.D.Spend 7.966e-01 4.135e-02 19.266 <2e-16 ***
Marketing.Spend 2.991e-02 1.552e-02 1.927 0.06 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9161 on 47 degrees of freedom
Multiple R-squared: 0.9505, Adjusted R-squared: 0.9483
F-statistic: 450.8 on 2 and 47 DF, p-value: < 2.2e-16
Marketing.Spend is not significant so removing.
Step 7
regressor = lm(formula = Profit ~ R.D.Spend,
data = dataset1)
summary(regressor)
Call:
lm(formula = Profit ~ R.D.Spend, data = dataset1)
Residuals:
Min 1Q Median 3Q Max
-34351 -4626 -375 6249 17188
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.903e+04 2.538e+03 19.32 <2e-16 ***
R.D.Spend 8.543e-01 2.931e-02 29.15 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9416 on 48 degrees of freedom
Multiple R-squared: 0.9465, Adjusted R-squared: 0.9454
F-statistic: 849.8 on 1 and 48 DF, p-value: < 2.2e-16
Step 8
y_pred = predict(regressor, newdata = test_set)
y_pred
step 9
#visualising the training set results
#load ggplot2 library
ggplot()+
geom_point(aes(x=training_set$R.D.Spend, y=training_set$Profit),
color = 'red')+
geom_line(aes(x=training_set$R.D.Spend, y=predict(regressor ,newdata = training_set)),
color = 'blue')+
ggtitle('Profit vs R.D.Spend(training_set)')+
xlab("R.D.Spend")+
ylab("Profit")
#plot interpretation
red points are real
the blue line is our linear regression model
#visualising the test set results
#load ggplot2 library
ggplot()+
geom_point(aes(x=test_set$YearsExperience, y=test_set$Salary),
color = 'red')+
geom_line(aes(x=training_set$YearsExperience, y=predict(regressor ,newdata = training_set)),
color = 'blue')+
ggtitle('salary vs experience(test_set)')+
xlab("years of experience")+
ylab("salary")
#plot interpretation
red points are real
the blue line is our linear regression model, these are very much near to predicted values.
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