Forum: Univariate Linear Regression

Introduction:
Welcome to the Univariate Linear Regression Forum! This space is dedicated to discussions and knowledge sharing on key statistical concepts and performance metrics in regression analysis. Whether you're a researcher, data analyst, or student, feel free to ask questions, share insights, and collaborate on various statistical and machine learning topics.

1.Confidence Interval

A confidence interval provides a range of values within which the true parameter of the population is expected to fall, with a certain level of confidence (e.g., 95%). Discuss methods to compute confidence intervals in regression and their significance in hypothesis testing.

# Fit model

model = sm.OLS(y, X).fit()

print(model.conf_int(alpha=0.05))  # 95% Confidence Interval

2. P-Values

P-values help determine statistical significance in regression analysis. A small p-value (typically <0.05) suggests strong evidence against the null hypothesis. Engage in discussions on interpreting p-values and their role in model validation.

print(model.pvalues)  # Display p-values for model coefficients

3. Confusion Matrix

While primarily used in classification problems, confusion matrices can also help in threshold-based regression applications. Discuss how to construct and interpret confusion matrices to evaluate model performance.

y_true = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0]

y_pred = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0]

print(confusion_matrix(y_true, y_pred))

4. Sensitivity & Specificity

• Sensitivity (True Positive Rate): Measures the model's ability to correctly identify positive cases.
• Specificity (True Negative Rate): Measures the model’s ability to correctly identify negative cases.     

5.Positive and Negative Predictive Values (PPV & NPV)

• Positive Predictive Value (PPV): Probability that a positive prediction is correct.
  print(f"PPV: {ppv}, NPV: {npv}")

 

6. Precision and Recall

• Precision: The proportion of correctly predicted positive cases among all predicted positives.
• Recall: The proportion of actual positive cases that were correctly predicted.
  print (f"Precision: {precision}, Recall: {recall}")

7. Accuracy

Accuracy measures the proportion of correctly predicted cases among total cases. However, it may not be a reliable metric for imbalanced datasets. Join discussions on when and how to use accuracy in model evaluation.
accuracy = accuracy_score(y_true, y_pred

print(f"Accuracy: {accuracy}"

8. Incidence & Prevalence

• Incidence: The rate of occurrence of new cases in a population over time.
• Prevalence: The total number of cases (new and existing) in a population at a given time.

incidence = new_cases / population

prevalence = (new_cases + existing_cases) / population

print(f"Incidence: {incidence}, Prevalence: {prevalence}"

9. Quantifying Risk

• Regression models are often used to estimate risk. Discuss different risk measures such as:
• Risk Ratios (RR)
• Odds Ratios (OR)
• Hazard Ratios (HR)

print(f"Odds Ratio: {odds_ratio}")