python_libraries/simple_linear_regration.py at master · parikh5555/python_libraries · GitHub

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## simple linear regression a single independent variable
## is used to predict the value of a dependent variable.
## 10 persons height and weight combinations are given
## Linear regration helps to predict 11th person weight from height
## Y = mX + C where m = Slope, C = Initial condition
## This formula is for understading the concepet
## let x1 = mean(x) = sum(x[i])/len(x) and y1 = mean(y) = sum(y[i])/len(y)
## Slope m = sum((x1-x[i])(y1-y[i])) /sum(x1-x[i])^2 For i in range (0,len(x))
## Initital condition C = y1 - m*x1

from sklearn import linear_model, metrics
import numpy as np
import matplotlib.pyplot as plt

def mean(numbers):
    return float(sum(abs(numbers))) / max(len(numbers), 1)


height = np.array([[4.0],[4.5],[5.0],[5.2],[5.4],[5.8],[6.1],[6.2],[6.4],[6.8]])
weight = np.array([42 ,  44 , 49, 55  , 53  , 58   , 60  , 64  ,  66 ,  69])

plt.scatter(height, weight) #scatter plot
plt.xlabel("height")
plt.ylabel("weight")
#plt.show()

# Create linear regression object
reg = linear_model.LinearRegression()

# Train the model using the training sets
reg.fit(height,weight)

mean_actual_height = mean(height)
mean_actual_weight = mean(weight)

##m1 =0
##for i in range (0,len(height)):
##    m1 = m1 + (abs(mean_actual_height - height[i][0])*abs((mean_actual_weight - weight[i])))/(sum((mean_actual_height - height)**2))
##print "calculated slope" ,m1
##c1 = mean_actual_weight - (m1 * mean_actual_height)
##print "calculated initial condition", c1


#the coefficients
m=reg.coef_[0] # Slope
c=reg.intercept_ #initial condition
print("slope=",m, "intercept=",c)

plt.scatter(height,weight,color='black')
predicted_values = [reg.coef_ * i + reg.intercept_ for i in height]
plt.plot(height, predicted_values, 'c') # linear plot
plt.xlabel("height")
plt.ylabel("weight")
plt.show()
#print len(predicted_values)

## Accuracy of the model
## Training accuracy : check y from few elements of x from the database
## Out of sample accuracy : Check y from out of dataset value of x -> should be high
## Model of evaluation
## 1. Test on the portion of dataset which is used to train it
## 2. Training and testing dataset should be mustually exclusive
## 2 -> gives better accuracy for real world problem

## Error = 1/n(Sum(Y(actual value) - Y1(Predicated values)

actual_weight = weight[-4:]
predicated_values_input_height = np.array([[6.1],[6.2],[6.4],[6.8]])
predicated_values_output_weight =  np.zeros(4)

predicted_values_output_weight = (m * predicated_values_input_height )+c
print "Prediction results", predicted_values_output_weight


## Mean absoulute error = Mean(abs(error))
## Mean Square error = Mean(square(error)) -> Increase exponantially
## so increse for larger error with respect to smaller once
## Root mean square error = Root(mean(square(error)))
## Relative absolute error = Sum(error)/sum(Y(predicted)-Y'(mean))
## Relative sqaure error = sum(squre(error))/sum(squre(Y(predicted)-Y'(mean)))
## R = root(1 - Relative sqaure error) -> gives how close data point to predicted value

def skikit_learn():

    MAE = metrics.mean_absolute_error(actual_weight,predicted_values_output_weight)
    print  MAE, "MAE"

    MSE = metrics.mean_squared_error(actual_weight,predicted_values_output_weight)
    print MSE, "MSE"

    RMSE = MSE**(0.5)
    print RMSE, "RMSE"

    RAE = metrics.median_absolute_error(actual_weight,predicted_values_output_weight)
    print RAE, "RMAE"


def pure_python():

    mean_predicted_weight = np.mean(predicted_values_output_weight)

    error_in_prediction = np.zeros(4)
    for i in range (0,len(predicted_values_output_weight)):
        error_in_prediction[i] = actual_weight[i]-predicted_values_output_weight[i][0]
    print "Error in prediction", error_in_prediction

    relative_diffrence = 0
    squared_relative_diffrence = 0
    for i in range (0,len(predicted_values_output_weight)):
        relative_diffrence = relative_diffrence + abs(predicted_values_output_weight[i][0] - mean_predicted_weight)
        squared_relative_diffrence = squared_relative_diffrence + ((predicted_values_output_weight[i][0] - mean_predicted_weight)**2)


    mean_abs_err = mean(error_in_prediction)
    print mean_abs_err, "MAE"

    mean_sqaure_error = mean(error_in_prediction * error_in_prediction)
    print mean_sqaure_error, "MSE"

    root_mean_square_error = mean_sqaure_error**(0.5)
    print root_mean_square_error, "RMSE"

    relative_absolute_error = sum(abs(error_in_prediction))/(relative_diffrence)
    print relative_absolute_error, "RAE"


    relative_squared_error = sum((error_in_prediction)**2)/(squared_relative_diffrence)
    print relative_squared_error, "RSE"

    relative_accuracy = 1 - relative_squared_error
    print relative_accuracy , "R"

pure_python()
skikit_learn()