Data Analysis and Statistical Modeling in R

Understanding your data is crucial before building any data science model. This course provides a comprehensive exploration of statistical modeling fundamentals and practical applications, using the R programming language for hands-on analysis.

We'll begin with the essential mathematical and statistical concepts, including data distributions and interpretation through insightful plots and charts. Learn to use statistical modeling to validate your claims and confidently draw inferences using hypothesis testing.

The course is structured into three parts:

Part 1: Foundations of Statistical Distributions

• Normal Distribution: Understand the bell curve and its significance.
• Binomial Distribution: Analyze probabilities in discrete events.
• Chi-Square Distribution: Explore distributions for categorical data.
• Densities & Cumulative Distribution Function (CDF): Visualize and calculate probability densities.
• Quantiles: Identify key data points for percentiles.
• Random Numbers: Generate and utilize random data for simulations.
• Central Limit Theorem (CLT): Learn about the distribution of sample means.
• R Statistical Distributions: Master built-in distributions in R.
• Distribution Functions: Apply functions to analyze data distributions.
• Descriptive Statistics:
  • Mean: Calculate the average.
  • Median: Find the middle value.
  • Range: Determine the spread of data.
  • Standard Deviation: Measure data dispersion.
  • Variance: Calculate the average squared deviation.
  • Sum of Squares: Understand the total variation in data.
  • Skewness: Assess data asymmetry.
  • Kurtosis: Evaluate the peakedness of data.

Part 2: Data Visualization with R

• Bar Plots: Compare categorical data.
• Histograms: Visualize data distribution.
• Pie Charts: Represent proportions of a whole.
• Box Plots: Summarize data distribution and identify outliers.
• Scatter Plots: Explore relationships between two variables.
• Dot Charts: Visualize data points and density.
• Mat Plots: Create multiple plots in a single figure.
• Plots for Groups: Compare data across different categories.
• Plotting Datasets: Effectively visualize your data.

Part 3: Inferential Statistics & Hypothesis Testing

• Parametric Tests vs. Non-Parametric Tests: Choose the right test for your data.
• Statistical Significance: Determine if results are meaningful.
• P-Value: Understand the probability of observing results.
• Hypothesis Testing: Formulate and test hypotheses.
• Two-Tailed Test: Test for differences in either direction.
• One-Tailed Test: Test for differences in a specific direction.
• True Population Mean: Estimate population means.
• Proportional Test: Analyze proportions.
• T-tests:
  • Default t-test / One Sample t-test: Compare a sample to a known value.
  • Two-Sample t-test / Independent Samples t-test: Compare means of two independent groups.
  • Paired Sample t-test: Compare means of related groups.
• F-Tests: Analyze variances between groups.
• Mean Square Error (MSE): Measure the average squared difference between predicted and actual values.
• F-Distribution: Understand the distribution used in F-tests.
• Variance & Sum of Squares: Key components of ANOVA.
• ANOVA Table: Interpret the results of Analysis of Variance.
• Post-hoc Tests: Identify significant differences between groups after ANOVA.
  • Tukey HSD: A common post-hoc test.
• Chi-Square Tests:
  • One Sample Chi-Square Goodness of Fit Test: Assess if a distribution fits a hypothesized distribution.
  • Chi-Square Test for Independence: Determine if two categorical variables are related.
• Correlation:
  • Pearson Correlation: Measure linear relationships between two continuous variables.
  • Spearman Correlation: Measure monotonic relationships between two variables.

Throughout the course, you'll apply these techniques to real-world datasets, including CSV files and R's built-in datasets and packages, gaining practical experience in data analysis and statistical inference.