Welcome to my repository for the MATH 3070 course! This repository contains 12 different lab solutions where I applied various statistical methods, including regression, data analysis, and visualization, all using the R programming language.

In this repository, you'll find solutions to 12 different lab exercises focused on different aspects of data analysis, including but not limited to:

• Linear and Logistic Regression
• Hypothesis Testing
• Data Visualization
• Exploratory Data Analysis (EDA)
• Statistical Inference

These labs cover both theoretical and practical applications of regression and other statistical techniques to analyze real-world datasets.

• Objective: Predict house prices based on various features like square footage and number of bedrooms.
• Techniques Used: Simple and multiple linear regression.
• Results: The model had an R-squared value of 0.85, indicating a strong relationship between house features and price.

• Objective: Predict survival chances on the Titanic based on passenger details.
• Techniques Used: Logistic regression with binary outcome (survived or not).
• Results: The model's accuracy was 80%, with the most influential features being age, sex, and passenger class.

• Objective: Explore relationships between various variables through scatter plots, box plots, and heatmaps.
• Techniques Used: Exploratory Data Analysis (EDA) and visualization techniques.
• Results: Several strong correlations were observed between features like "Fare" and "Class."

• Objective: Fit a polynomial regression model to predict outcomes in a non-linear dataset.
• Techniques Used: Polynomial regression for curve fitting.
• Results: The model significantly improved the prediction accuracy for non-linear data, achieving a lower mean squared error than the linear model.

• Objective: Test the hypothesis that the means of multiple groups are equal using ANOVA.
• Techniques Used: One-way ANOVA.
• Results: The analysis revealed a significant difference in means across the groups, supporting the hypothesis that group means are not equal.

• Objective: Forecast future values based on historical data.
• Techniques Used: ARIMA model for time series forecasting.
• Results: The ARIMA model performed well with an accuracy of 90%, capturing seasonality and trend in the data.

• Objective: Cluster data into groups based on similarities.
• Techniques Used: K-means clustering.
• Results: The algorithm grouped customers into 4 distinct clusters based on spending behavior.

• Objective: Reduce the dimensionality of a large dataset while preserving as much variance as possible.
• Techniques Used: PCA for dimensionality reduction.
• Results: PCA reduced the dataset from 15 dimensions to 3, while retaining 90% of the variance.

• Objective: Predict whether a patient has a certain disease based on their medical records.
• Techniques Used: Logistic regression and ROC curve analysis.
• Results: The model achieved an AUC score of 0.87, showing good predictive power.

• Objective: Test if two categorical variables are independent.
• Techniques Used: Chi-square test of independence.
• Results: The chi-square test suggested that the variables were dependent, with a p-value of 0.03.

• Objective: Evaluate and validate a regression model.
• Techniques Used: Residual analysis and cross-validation.
• Results: The model's residuals appeared normally distributed, and cross-validation showed minimal overfitting.

• Objective: Predict a continuous outcome based on multiple predictors.
• Techniques Used: Multivariate regression analysis.
• Results: The model identified key predictors, with an adjusted R-squared of 0.78.

• R: All solutions are implemented using the R programming language.
• ggplot2: For data visualization.
• dplyr: For data manipulation.
• caret: For model training and validation.
• titanic: For Titanic dataset used in regression problems.

These lab solutions represent a wide range of data analysis techniques and provide a practical understanding of statistical methods. From basic regression to more complex machine learning algorithms, these solutions offer insights into how data science is applied to real-world problems. The results from these analyses demonstrate the power of statistical methods in making data-driven decisions.

Feel free to explore each lab to understand the methods, data, and results in more detail. Happy analyzing!