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stats_analysis.py
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stats_analysis.py
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"""Module containing functions for statistical analysis."""
from typing import List, Tuple, Any
from math import ceil, sqrt
from pandas import DataFrame
from sklearn.linear_model import LinearRegression
class EmptyDatasetError(Exception):
"""Exception raised when calling statistical function on an empty data set."""
def __str__(self) -> str:
"""Return a string representation of this error."""
return 'function cannot be called on an empty dataset'
def median(values: List[float]) -> float:
"""Returns the mean of the data
Preconditions:
- len(values) != 0
>>> median([5.0, 7.0, 9.0, 11.0, 9.0])
9.0
>>> median([2.0, 2.0, 7.0, 4.0, 5.0, 1.0])
3.0
"""
global position
length = len(values)
sorted_list = sorted(values)
if length % 2 == 1:
position = ceil(length / 2)
return sorted_list[int(position) - 1]
elif length % 2 == 0 and length != 0:
position = length / 2
right_median = sorted_list[int(position)]
left_median = sorted_list[int(position) - 1]
return (right_median + left_median) / 2
elif length == 0:
raise EmptyDatasetError
def mode(values: List[float]) -> float:
"""Returns the mode of the data
Preconditions:
- len(values) != 0
>>> mode([2.0, 3.0, 6.0, 3.0, 7.0, 5.0, 1.0, 2.0, 3.0, 9.0])
3.0
>>> mode([13.0, 17.0, 20.0, 21.0, 23.0, 23.0, 26.0, 29.0, 30.0])
23.0
"""
empty_list = []
for num in values:
temp_list = [number for number in values if number == num]
list.append(empty_list, temp_list)
length = [len(numb) for numb in empty_list]
maximum = max(length)
index = length.index(maximum)
if len(values) != 0:
return empty_list[index][0]
else:
raise EmptyDatasetError
def mean(values: List[float]) -> float:
"""Returns the mean of the data
Preconditions:
- len(values) != 0
>>> mean([3.0, 4.0, 6.0, 6.0, 8.0, 9.0, 11.0])
6.714285714285714
"""
if len(values) != 0:
return sum(values) / len(values)
else:
raise EmptyDatasetError
def sample_standard_deviation(values: List[float]) -> float:
"""returns the measure of variability in the data
Preconditions:
- len(values) != 0"""
average = mean(values)
numerator1 = [num - average for num in values]
numerator2 = [number ** 2 for number in numerator1]
numerator3 = sum(numerator2)
denominator = len(values) - 1
final_value = sqrt(numerator3 / denominator)
if len(values) != 0:
return final_value
else:
raise EmptyDatasetError
def correlation(x_values: List[float], y_values: List[float]) -> float:
"""Returns the correlation between variables x and y
correlation: the measure of strength and direction between two quantitative variables
Preconditions:
- len(x_values) == len(y_values)
- len(x_values) != 0
- len(y_values) != 0
"""
average_of_x = mean(x_values)
average_of_y = mean(y_values)
standard_deviation_x = sample_standard_deviation(x_values)
standard_deviation_y = sample_standard_deviation(y_values)
x_difference = [num - average_of_x for num in x_values]
y_difference = [num - average_of_y for num in y_values]
empty_list = []
for i in range(0, len(x_difference)):
product = x_difference[i] * y_difference[i]
list.append(empty_list, product)
summation = sum(empty_list)
result = summation / (standard_deviation_x * standard_deviation_y)
return result / (len(x_difference) - 1)
def slope_of_best_fit(x_values: List[float], y_values: List[float]) -> float:
"""Return the slope of the line of best fit
Preconditions:
- len(x_values) == len(y_values)
- len(x_values) != 0
- len(y_values) != 0"""
deviation_of_x = sample_standard_deviation(x_values)
deviation_of_y = sample_standard_deviation(y_values)
r = correlation(x_values, y_values)
m = r * (deviation_of_y / deviation_of_x)
return m
def y_intercept_of_best_fit(x_values: List[float], y_values: List[float]) -> float:
"""returns the y-intercept of line of best fit
Preconditions:
- len(x_values) == len(y_values)
- len(x_values) != 0
- len(y_values) != 0
"""
m = slope_of_best_fit(x_values, y_values)
average_of_x = mean(x_values)
average_of_y = mean(y_values)
b = average_of_y - (m * average_of_x)
return b
def best_fit_regression_equation(x_values: List[float], y_values: List[float]) -> str:
"""Return equation of line of best fit
Preconditions:
- len(x_values) == len(y_values)
- len(x_values) != 0
- len(y_values) != 0
"""
slope = slope_of_best_fit(x_values, y_values)
y_intercept = y_intercept_of_best_fit(x_values, y_values)
return 'y = ' + str(slope) + 'x + ' + str(y_intercept)
def interpolation(x_value: float, x_values: List[float], y_values: List[float]) -> float:
"""Return value of y using line of best fit
Preconditions:
- x_value in range(round(int(sorted(x_values)[0])), round(int(sorted(x_values)[-1])))
- len(x_values) == len(y_values)
- len(x_values) != 0
- len(y_values) != 0
>>> x = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]
>>> y = [5.0, 7.0, 9.0, 11.0, 13.0, 15.0, 17.0 , 19.0, 21.0, 23.0, 25.0]
>>> interpolation(1.5, x, y)
8.0
"""
m = slope_of_best_fit(x_values, y_values)
b = y_intercept_of_best_fit(x_values, y_values)
y_value = m * x_value + b
return y_value
def extrapolation(start_point: int, end_point: int, x_values: List[float],
y_values: List[float]) -> List[float]:
"""Predict the value of the dependent variable for the independent variable that is outside
the range of our data
Preconditions:
- x_value not in range(round(int(sorted(x_values)[0])), round(int(sorted(x_values)[-1])))
- start_point < end_point
- len(x_values) == len(y_values)
- len(x_values) != 0
- len(y_values) != 0
>>> x_list = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]
>>> y_list = [5.0, 7.0, 9.0, 11.0, 13.0, 15.0, 17.0 , 19.0, 21.0, 23.0, 25.0]
>>> extrapolation(15, 20, x_list, y_list)
[35.0, 37.0, 39.0, 41.0, 43.0, 45.0]
"""
m = slope_of_best_fit(x_values, y_values)
b = y_intercept_of_best_fit(x_values, y_values)
empty_list = []
for x in range(start_point, end_point + 1):
y_value = m * x + b
list.append(empty_list, y_value)
return empty_list
def r_squared(x_values: List[float], y_values: List[float]) -> float:
"""Calculates the coefficient of determination
Preconditions:
- len(x_values) == len(y_values)
- len(x_values) != 0
- len(y_values) != 0
"""
r_r = correlation(x_values, y_values)
r_r_2 = r_r ** 2
return r_r_2
def variance(values: List[float]) -> float:
"""Calculate the variance of the data. A way to measure the spread of a distribution of
numerical data
Preconditions:
- len(values) != 0
"""
s = sample_standard_deviation(values)
return s ** 2
def root_mean_squared_error(start_point: int, end_point: int, x_values: List[float],
y_values: List[float]) -> float:
"""Calculates the RMSE. Measures the prediction error for predictions from a linear
regression model
Precondition:
- start_point < end_point
- len(x_values) == len(y_values)
- len(x_values) != 0
- len(y_values) != 0
"""
predicted_values = extrapolation(start_point, end_point, x_values, y_values)
empty_list = []
for value in predicted_values:
for y in y_values:
difference = (y - value) ** 2
list.append(empty_list, difference)
summation = sum(empty_list)
denominator = len(x_values) - 1
root = sqrt(summation / denominator)
return root
def multiple_lin_reg(df1: DataFrame, df2: DataFrame, df3: DataFrame) -> Tuple[Any, Any, Any]:
""" Perform multiple linear regression on the given data
and return coefficients, intercept, and summary of results.
"""
data = df1.merge(df2).merge(df3)
# separating features and target
y = data[df1.columns[1]]
x = data[[df1.columns[0], df2.columns[0], df3.columns[0]]]
# defining the multiple linear regression model
lin_reg = LinearRegression()
# 'training' the model
model = lin_reg.fit(x, y)
return (model.coef_, model.intercept_, model.score(x, y))
if __name__ == '__main__':
# When you are ready to check your work with python_ta, uncomment the following lines.
# (Delete the "#" and space before each line.)
# IMPORTANT: keep this code indented inside the "if __name__ == '__main__'" block
# Leave this code uncommented when you submit your files.
import python_ta
python_ta.check_all(config={
'allowed-io': ['read_csv_data'],
'extra-imports': ['python_ta.contracts', 'csv', 'datetime',
'plotly.graph_objects', 'plotly.subplots',
'math', 'sklearn.linear_model', 'pandas'],
'max-line-length': 100,
'max-args': 6,
'max-locals': 25,
'disable': ['R1705'],
})
import python_ta.contracts
python_ta.contracts.DEBUG_CONTRACTS = False
python_ta.contracts.check_all_contracts()