'''simple docstring'''

import pandas as pd
from matplotlib import pyplot as plt
from sklearn.linear_model import LinearRegression

# Splitting the dataset into the Training set and Test set
from sklearn.model_selection import train_test_split

# Fitting Polynomial Regression to the dataset
from sklearn.preprocessing import PolynomialFeatures

# Importing the dataset
_A			:      Optional[Any]					      =				pd.read_csv(
    '''https://s3.us-west-2.amazonaws.com/public.gamelab.fun/dataset/'''
    '''position_salaries.csv'''
)
_A			:      str					      =				dataset.iloc[:, 1:2].values
_A			:      Tuple					      =				dataset.iloc[:, 2].values


_A      ,     _A      ,     _A      ,     _A			:      Optional[Any]					      =				train_test_split(X, y, test_size=0.2, random_state=0)


_A			:      Tuple					      =				PolynomialFeatures(degree=4)
_A			:      Union[str, Any]					      =				poly_reg.fit_transform(X)
_A			:      int					      =				LinearRegression()
pol_reg.fit(X_poly, y)







def      UpperCamelCase_						(					)					->     Dict:






 '''simple docstring'''

 plt.scatter(snake_case_						,		snake_case_						,		color="""red"""      )
 plt.plot(snake_case_						,		pol_reg.predict(poly_reg.fit_transform(snake_case_      )      )						,		color="""blue"""      )
 plt.title("""Truth or Bluff (Linear Regression)"""      )
 plt.xlabel("""Position level"""      )
 plt.ylabel("""Salary"""      )
 plt.show()


if __name__ == "__main__":
 viz_polymonial()

 # Predicting a new result with Polymonial Regression
 pol_reg.predict(poly_reg.fit_transform([[5.5]]))
 # output should be 132148.43750003







'''simple docstring'''

def      UpperCamelCase_						(					snake_case_       :       list[int]						,		snake_case_       :       list[int]      )					->     tuple[float, float]:






 '''simple docstring'''

 if not len(snake_case_      ) == len(snake_case_      ) == 3:
  raise ValueError("""Please enter a valid equation."""      )
 if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
  raise ValueError("""Both a & b of two equations can't be zero."""      )

 # Extract the coefficients
 __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						equationa
 __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						equationa

 # Calculate the determinants of the matrices
 __lowerCAmelCase											=						aa * ba - aa * ba
 __lowerCAmelCase											=						ca * ba - ca * ba
 __lowerCAmelCase											=						aa * ca - aa * ca

 # Check if the system of linear equations has a solution (using Cramer's rule)
 if determinant == 0:
  if determinant_x == determinant_y == 0:
   raise ValueError("""Infinite solutions. (Consistent system)"""      )
  else:
   raise ValueError("""No solution. (Inconsistent system)"""      )
 else:
  if determinant_x == determinant_y == 0:
   # Trivial solution (Inconsistent system)
   return (0.0, 0.0)
  else:
   __lowerCAmelCase											=						determinant_x / determinant
   __lowerCAmelCase											=						determinant_y / determinant
   # Non-Trivial Solution (Consistent system)
   return (x, y)






