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regression_analysis.py
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import pandas as pd
from prettytable import PrettyTable
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt
import numpy as np
import statsmodels.api as sm
class RegressionAnalysis():
train_filepath = "data/filtered/train_data_filtered_useful.csv"
test_filepath = "data/filtered/test_data_filtered_useful.csv"
def __init__(self):
self.get_processed_data()
def get_processed_data(self):
print("getting data")
self.test_df = pd.read_csv(self.test_filepath, sep=',')
self.train_df = pd.read_csv(self.train_filepath, sep=',')
elim_features = self.stepwise_regression()
model = self.regression_analysis(elim_features)
self.t_test_analysis()
self.f_test_analysis(elim_features)
self.confidence_interval_analysis(elim_features)
def regression_analysis(self, eliminated_features):
train_data = self.train_df.copy().sort_values(by=['usefulStandardized'])
x_train = train_data.drop(columns=["usefulStandardized", *eliminated_features])
y_train = train_data["usefulStandardized"]
test_data = self.test_df.copy().sort_values(by=['usefulStandardized'])
x_test = test_data.drop(columns=["usefulStandardized", *eliminated_features])
y_test = test_data["usefulStandardized"]
model = LinearRegression()
model.fit(x_train, y_train)
print(model.coef_)
y_pred = model.predict(x_test)
y_true = y_test
subset_df = y_true[y_true > 1]
print(subset_df)
train_indices = np.arange(len(train_data))
test_indices = np.arange(len(train_data), len(train_data) + len(test_data))
plt.scatter(train_indices, y_train, label="Training Data")
print(len(y_true), len(test_indices))
plt.scatter(test_indices, y_pred, label="Test Predictions")
plt.scatter(test_indices, y_true, label="Test Results")
plt.title("Train, Test, and Predicted Values")
plt.xlabel("Data Points")
plt.ylabel("usefulStandardized")
plt.legend()
plt.grid(True)
plt.show()
return model
def t_test_analysis(self):
sig = 0.05
t_table = PrettyTable()
t_table.title = "T-test Analysis (alpha=0.05)"
t_table.field_names = ["Feature", "t statistic", "p value", "Rejected?"]
x_train = self.train_df.drop(columns=["usefulStandardized"])
y_train = self.train_df["usefulStandardized"]
model = sm.OLS(y_train, x_train).fit()
p_values = model.pvalues
t_stats = model.tvalues
for val in t_stats.index:
t_val = t_stats[val]
p_val = p_values[val]
if p_val < sig:
isRejected="No"
else:
isRejected="Yes"
t_table.add_row([f"{val}", f"{t_val:.3f}", f"{p_val:.3f}", f"{isRejected}"])
print(t_table)
def f_test_analysis(self, eliminated_features):
x_train = self.train_df.drop(columns=["usefulStandardized", *eliminated_features])
y_train = self.train_df["rating"]
model = sm.OLS(y_train, x_train).fit()
print("F-statistic:", model.fvalue)
print("p-value for F-test:", model.f_pvalue)
def confidence_interval_analysis(self, eliminated_features):
x_train = self.train_df.drop(columns=["usefulStandardized", *eliminated_features])
x_test = self.test_df.drop(columns=["usefulStandardized", *eliminated_features])
y_train = self.train_df["usefulStandardized"]
model = sm.OLS(y_train, x_train).fit()
predictions = model.get_prediction(x_test)
pred_mean = predictions.predicted_mean
summary_frame = predictions.summary_frame(alpha=0.01)
lower_bound = summary_frame["mean_ci_lower"]
upper_bound = summary_frame["mean_ci_upper"]
plt.fill_between(range(len(pred_mean)), lower_bound, upper_bound, color="blue", label="CI", alpha=.3)
plt.scatter(range(len(pred_mean)), pred_mean, color="red", label="Predicted usefulStandardized", s=.3)
plt.xlabel('# of Samples')
plt.ylabel('usefulStandardized')
plt.title('usefulStandardized Prediction with Confidence Interval')
plt.legend()
plt.grid(True)
plt.show()
def stepwise_regression(self):
threshold = 0.05
x_train = self.train_df.drop(columns=["usefulStandardized"], inplace=False)
y_train = self.train_df["usefulStandardized"]
x_train = sm.add_constant(x_train)
mse_list = []
aic_list = []
bic_list = []
r_adj_list = []
r_two_list = []
elim_pval_list = []
elim_features = []
total_features = x_train.drop(columns=["const"]).columns.tolist()
features_so_far = []
while True:
model = sm.OLS(y_train, x_train).fit()
p_values = model.pvalues.drop('const')
max_p_value = p_values.max()
aic_list.append(model.aic)
bic_list.append(model.bic)
r_adj_list.append(model.rsquared_adj)
r_two_list.append(model.rsquared)
mse_list.append(model.mse_model)
elim_pval_list.append(p_values.max())
features_so_far.append(p_values.idxmax())
if max_p_value > threshold:
feature_to_remove = p_values.idxmax()
elim_features.append(feature_to_remove)
x_train = x_train.drop(columns=[feature_to_remove])
print(f"Removing {feature_to_remove} from model")
else:
for feature in total_features:
if feature not in features_so_far:
aic_list.append(model.aic)
bic_list.append(model.bic)
r_adj_list.append(model.rsquared_adj)
r_two_list.append(model.rsquared)
mse_list.append(model.mse_model)
elim_pval_list.append(p_values[feature])
features_so_far.append(feature)
break
print(f"Final summary is:\n {model.summary().as_text()}")
reg_table = PrettyTable()
reg_table.title = "Backwards Stepwise Regression Feature Elimination (alpha = 0.05)"
reg_table.field_names = ["Feature", "AIC Value", "BIC Value", "MSE Value", "Adjusted R squared", "R Squared", "P-value", "Eliminated?"]
count = len(mse_list)
for num in range(count):
isEliminated = "No"
if features_so_far[num] in elim_features:
isEliminated = "Yes"
reg_table.add_row(
[f"{features_so_far[num]}", f"{aic_list[num]:.3f}", f"{bic_list[num]:.3f}", f"{mse_list[num]:.3f}", f"{r_adj_list[num]:.3f}",
f"{r_two_list[num]:.3f}", f"{elim_pval_list[num]:.3f}", isEliminated])
print(reg_table)
return elim_features
if __name__ == "__main__":
obj = RegressionAnalysis()