Introduction to Statistics in Data Science

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Introduction to Statistics in Data Science

This course is designed to provide an introduction to the fundamental concepts and techniques of statistics, specifically tailored for data science applications. Students will learn how to apply statistical methods to analyze and interpret data, derive insights, and make data-driven decisions. By the end of the course, students will be able to apply statistical techniques in various domains such as machine learning, data visualization, and hypothesis testing, and will gain the skills necessary to work with real-world data sets.

Course Objectives:

By the end of this course, students will be able to:

  1. Understand the basic principles and terminology of statistics.
  2. Perform descriptive and inferential statistical analysis on data.
  3. Use statistical methods such as probability, distributions, and sampling techniques.
  4. Apply hypothesis testing to determine statistical significance.
  5. Interpret and visualize statistical results in a clear and effective manner.
  6. Understand how to use statistical techniques in data science projects, including working with real-world data sets.
  7. Gain foundational skills necessary for applying statistical methods to machine learning models and predictive analytics.

Course Prerequisites:

  • Basic knowledge of mathematics (high school level algebra and calculus).
  • Basic proficiency in programming (preferably Python or R).
  • Familiarity with data science concepts is a plus but not required.

Sure! Here's a complete course outline for "Introduction to Statistics in Data Science" that covers the essential topics and objectives:

Course Title: Introduction to Statistics in Data Science

Course Description: This course is designed to provide an introduction to the fundamental concepts and techniques of statistics, specifically tailored for data science applications. Students will learn how to apply statistical methods to analyze and interpret data, derive insights, and make data-driven decisions. By the end of the course, students will be able to apply statistical techniques in various domains such as machine learning, data visualization, and hypothesis testing, and will gain the skills necessary to work with real-world data sets.

Course Objectives:

By the end of this course, students will be able to:

  1. Understand the basic principles and terminology of statistics.
  2. Perform descriptive and inferential statistical analysis on data.
  3. Use statistical methods such as probability, distributions, and sampling techniques.
  4. Apply hypothesis testing to determine statistical significance.
  5. Interpret and visualize statistical results in a clear and effective manner.
  6. Understand how to use statistical techniques in data science projects, including working with real-world data sets.
  7. Gain foundational skills necessary for applying statistical methods to machine learning models and predictive analytics.

Course Prerequisites:

  • Basic knowledge of mathematics (high school level algebra and calculus).
  • Basic proficiency in programming (preferably Python or R).
  • Familiarity with data science concepts is a plus but not required.

Course Outline:

Week 1: Introduction to Statistics & Data Science

  • Overview of Statistics

    • What is statistics?
    • Descriptive vs. inferential statistics.
    • Importance of statistics in data science.

  • Types of Data

    • Qualitative vs. quantitative data.
    • Levels of measurement: nominal, ordinal, interval, and ratio.

  • Introduction to Data Science

    • Role of statistics in the data science lifecycle.
    • Overview of data collection, data cleaning, and data exploration.

Week 2: Descriptive Statistics

  • Measures of Central Tendency

    • Mean, median, and mode.
    • When to use each measure.

  • Measures of Dispersion

    • Range, variance, and standard deviation.
    • Interquartile range (IQR) and boxplots.

  • Data Visualization

    • Histograms, bar charts, and box plots.
    • Visualizing the distribution of data.

  • Applications in Data Science

    • Exploring datasets with descriptive statistics.

Week 3: Probability Theory

  • Basic Probability Concepts

    • Sample space, events, and outcomes.
    • Probability rules (addition and multiplication).

  • Conditional Probability

    • Bayes’ Theorem and its applications.

  • Random Variables and Probability Distributions

    • Discrete vs. continuous random variables.
    • Common distributions: binomial, normal, and Poisson.

Week 4: Probability Distributions & Sampling

  • Normal Distribution

    • Properties of the normal distribution.
    • The empirical rule (68-95-99.7).

  • Sampling and the Central Limit Theorem

    • Random sampling, sample size, and sampling distribution.
    • Understanding the Central Limit Theorem.

  • Introduction to Statistical Inference

    • Estimation and confidence intervals.

Week 5: Inferential Statistics & Hypothesis Testing

  • Hypothesis Testing

    • Null hypothesis (H0) vs. alternative hypothesis (H1).
    • Type I and Type II errors.

  • Test Statistics and P-values

    • Z-test and t-test for one sample.
    • Understanding p-values and significance levels.

  • Confidence Intervals and Effect Sizes

    • Constructing and interpreting confidence intervals.

  • Chi-Square Tests

    • Chi-square test for independence and goodness of fit.

Week 6: Regression & Correlation

  • Correlation Analysis

    • Pearson correlation coefficient.
    • Interpreting correlations in data.

  • Linear Regression

    • Simple linear regression model.
    • Fitting a regression line and understanding residuals.

  • Multivariate Regression

    • Multiple linear regression.
    • Assessing model performance and assumptions.

Week 7: Advanced Topics in Statistical Analysis

  • Analysis of Variance (ANOVA)

    • One-way ANOVA and its applications.
    • Post-hoc tests and pairwise comparisons.

  • Non-Parametric Tests

    • When and why to use non-parametric tests.
    • Mann-Whitney U test and Kruskal-Wallis test.

  • Time Series Analysis (Introduction)

    • Basic time series concepts.
    • Seasonal decomposition and trend analysis.

Week 8: Statistical Tools & Applications in Data Science

  • Statistical Software and Libraries

    • Introduction to Python libraries for statistics (Pandas, NumPy, SciPy).
    • R as a statistical tool.

  • Case Study: Data Analysis Using Python/R

    • Practical example of applying statistical methods to a real-world dataset.
    • Data cleaning, analysis, and visualization.

  • Introduction to Machine Learning and Statistics

    • How statistical methods intersect with machine learning.
    • Use of statistical tests in model evaluation.

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