Python Machine Learning Multiple Regression

Multiple regression is like linear regression, but with more than one 
independent value, meaning that we try to predict a value based on two 
or more variables.
Take a look at the data set below, it contains some information about cars.
We can predict the CO2 emission of a car based on 
the size of the engine, but with multiple regression we can throw in more 
variables, like the weight of the car, to make the prediction more accurate.
In Python we have modules that will do the work for us. Start by importing 
the Pandas module.
import pandas 
Learn about the Pandas module in our Pandas Tutorial.
The Pandas module allows us to read csv files and return a DataFrame object.
The file is meant for testing purposes only, you can download it here: cars.csv
df = pandas.read_csv("cars.csv") 
Then make a list of the independent values and call this 
variable X. 
Put the dependent values in a variable called y.
X = df[['Weight', 'Volume']]
y = df['CO2'] 
Tip:  It is common to name the list of independent values with a upper 
case X, and the list of dependent values with a lower case y.
We will use some methods from the sklearn module, so we will have to import that module as well:
from sklearn import linear_model 
From the sklearn module we will use the LinearRegression() method 
to create a linear regression object.
This object has a method called fit() that takes 
the independent and dependent values as parameters and fills the regression object with data that describes the relationship:
regr = linear_model.LinearRegression()
regr.fit(X, y) 
Now we have a regression object that are ready to predict CO2 values based on 
a car's weight and volume:
#predict the CO2 emission of a car where the weight 
  is 2300kg, and the volume is 1300cm3:
  predictedCO2 = regr.predict([[2300, 1300]]) 
See the whole example in action:
[107.2087328]

Run example »

We have predicted that a car with 1.3 liter engine, and a weight of 2300 kg, will release approximately 107 grams of CO2 for every 
kilometer it drives.
The coefficient is a factor that describes the relationship 
with an unknown variable.
Example: if x is a variable, then
2x is x two 
times. x is the unknown variable, and the 
number 2 is the coefficient.
In this case, we can ask for the coefficient value of weight against CO2, and 
for volume against CO2. The answer(s) we get tells us what would happen if we 
increase, or decrease, one of the independent values.
Print the coefficient values of the regression object:
[0.00755095 0.00780526]

Run example »

The result array represents the coefficient values of weight and volume.
Weight: 0.00755095
Volume: 0.00780526
These values tell us that if the weight increase by 1kg, the CO2 
emission increases by 0.00755095g.
And if the engine size (Volume) increases by 1 cm3, the CO2 emission 
increases by 0.00780526 g.
I think that is a fair guess, but let test it!
We have already predicted that if a car with a 1300cm3 engine weighs 2300kg, the CO2 emission will be approximately 107g.
What if we increase the weight with 1000kg?
Copy the example from before, but change the weight from 2300 to 3300:
[114.75968007]

Run example »


We have predicted that a car with 1.3 liter engine, and a weight of 
3300 kg, will release approximately 115 grams of CO2 for every kilometer it drives.

Which shows that the coefficient of 0.00755095 is correct:

107.2087328 + (1000 * 0.00755095) = 114.75968
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