Statistics and Mathematics for Data Science and Data Analytics

1. Welcome!

This is a welcome introduction by the author where he explains in detail what the course is all about, what you will learn from the course, and a brief outline of the entire course's content.

2. What Will You Learn in This Course?

In this video, the author briefly introduces what it would take to become a data scientist and then goes over in detail what one can learn from this course.

3. How Can You Get the Most Out of It?

In this lesson, the author explains how to use the course best and the techniques and tools best applicable.

1. Introduction

This brief introduction to the section outlines what you will be learning from this section, including the basics of statistics.

2. Mean

In this video, we will discuss the measures of central tendency. Here, you will learn more about the first measure, the mean.

3. Median

In this lesson, we will discuss the second important measure of central tendency, the median.

4. Mode

In this lecture, we will elaborate more about the third and final measure of central tendency, the mode.

5. Mean or Median?

In this lesson, the author explains more about the mean and median and when to use them for the best results.

6. Skewness

In this video, you will learn about skewness, the symmetry you learned about in the previous lesson.

7. Practice: Skewness

This is a practice lesson/exercise to better understand the concept of skewness.

8. Solution: Skewness

This video is an explanation of the practice lesson/exercise of skewness.

9. Range and IQR

In this lesson, we will understand the measures of spread or dispersion, which is the range, and we will look at the interquartile range in detail.

10. Sample Versus Population

This lecture will explain the fundamental difference between a sample and a population in statistical data.

11. Variance and Standard Deviation

After learning about the measures of spread, the range, and IQR, we will now learn more about the two most common measures of spread, the variance, and standard deviation.

12. Impact of Scaling and Shifting

In this video, we will look at the impact of the data changes we make with underlying data in the measures of central tendency or dispersion.

13. Statistical Moments

Here, we will understand the concepts of statistical moments, which generalizes what we already know about the central tendency measures and spread/dispersion.

1. What Is a Distribution?

This brief introduction to distribution elaborates on what constitutes data distribution and the kinds of distribution you will learn about.

2. Normal Distribution

After understanding the data distribution concept, we will look at the first type, the normal distribution.

3. Z-Scores

In this lesson, you will learn more about a precise distribution score, the Z score, and the Z score table.

4. Practice: Normal Distribution

This is a practical exercise in understanding normal distribution with examples to learn the concept better.

5. Solution: Normal Distribution

This video provides the solution and explanations to the practice exercise on the normal distribution in the previous video.

1. Introduction

This brief introductory video to this section lets us know what you will learn in terms of probability and its elements.

2. Probability Basics

This lesson will shift our focus from descriptive statistics to a more mathematical probability theory.

3. Calculating Simple Probabilities

In this lecture, you will learn to calculate the probability of events using a simple probability distribution.

4. Practice: Simple Probabilities

In this quick practice exercise, we will apply what we already learned about simple probabilities and solve an exercise.

5. Quick Solution: Simple Probabilities

This video provides the solution and explanation to the exercise provided in the previous lecture.

6. Detailed Solution: Simple Probabilities

This video provides a more elaborate explanation of the solution to the exercise provided in the previous practice exercise.

7. Rule of Addition

In this video, you will learn about calculating a combination of the probability of two events.

8. Practice: Rule of Addition

This is a practice exercise to understand better the rule of addition concept with a practical exercise.

9. Quick Solution: Rule of Addition

This video provides a quick solution to the practice exercise of the rule of addition concept.

10. Detailed Solution: Rule of Addition

This video provides a more elaborate and detailed solution to the practice exercise of the rule of addition concept.

11. Rule of Multiplication

In this lesson, we will look at the multiplication rule, which also enables us to calculate the combination of events and the combination of both events.

12. Practice: Rule of Multiplication

This is a practice exercise to understand better the rule of multiplication concepts with a practical exercise.

13. Solution: Rule of Multiplication

This video provides an elaborate and detailed solution to the practice exercise of the rule of multiplication concept.

14. Bayes Theorem

This video is a detailed explanation of the Bayes theorem, which is an important theorem of probability, with a simple example.

15. Bayes Theorem - Practical Example

This is a practice exercise to understand better the Bayes theorem concept with a more advanced practical exercise.

16. Expected Value

In this lesson, you will learn about an important concept in probability, the expected value or outcome.

17. Practice: Expected Value

This is a practice exercise to better understand the expected value concept with a practical exercise.

18. Solution: Expected Value

This video provides an elaborate solution to the expected value concept practice exercise.

19. Law of Large Numbers

This lesson will explore the famous mathematical law, the law of large numbers, and its misconceptions.

20. Central Limit Theorem - Theory

In this video, you will learn about a fundamental concept of probability, the central limit theorem. The author explains this comprehensively as the base for the following lectures.

21. Central Limit Theorem - Intuition

In this video, we will understand the central limit theorem intuitively. We will explore this concept online using the onlinestatbook.com webpage.

22. Central Limit Theorem - Challenge

This is a hands-on challenge to understand better the central limit theorem concept with a practical example.

23. Central Limit Theorem - Exercise

This is a hands-on practice exercise to understand the central limit theorem concept better with a practical example.

24. Central Limit Theorem - Solution

This video provides an elaborate solution to the practice exercise of the central limit theorem concept.

25. Binomial Distribution

This video will look at the most important probability distribution applicable in real life, the binomial distribution and the binomial coefficient.

26. Poisson Distribution

We will look at another important distribution named after the French mathematician, Simeon Denis Poisson.

27. Real-Life Problems

This lecture will look at real-life examples to understand the probability distributions, mostly the binomial and Poisson distributions.

1. Introduction

This is a brief synopsis of hypothesis testing and what you will learn about in this section.

2. What Is a Hypothesis?

In this video, you will learn more about influential statistics and what we do in hypothesis testing.

3. Significance Level and P-Value

After learning about hypothesis testing, we will now understand the significance level of a hypothesis.

4. Type I and Type II Errors

This video will look at the errors we make while addressing the significance level or determining the probability value, which we classify as type I and II errors.

5. Confidence Intervals and Margin of Error

This lesson will explore a confidence interval while estimating the significance level and determining an acceptable margin of error.

6. Excursion: Calculating Sample Size and Power

After exploring confidence intervals and margin of error, we will now understand how to determine a sample size to reduce the error size caused by the sample size.

7. Performing the Hypothesis Test

This video elaborates on performing actual hypothesis testing through a demonstration.

8. Practice: Hypothesis Test

This is a practice exercise to implement a hypothesis testing that we have explored comprehensively so far.

9. Solution: Hypothesis Test

This video provides the solution and explanation to the hypothesis testing practice exercise we worked on above.

10. t-test and t-distribution

In this video, you will learn more about the student's t-test and t-distribution in detail.

11. Proportion Testing

In this lesson, we will work through all the steps of hypothesis testing with an example of proportion testing.

12. Important p-z Pairs

While performing the hypothesis testing and general statistics, you will learn more about the p-z combination and the normal distribution.

1. Introduction

In this video, we will briefly understand the concept of regression and how regression analysis predicts data value.

2. Linear Regression

Here, we will understand dependent and independent variables and learn how to predict values using linear regression.

3. Correlation Coefficient

After learning about linear regression and how to calculate the formula for our regression lines, we will now look at the correlation coefficient or Pearson's coefficient.

4. Practice: Correlation

This is a practice exercise on Pearson's coefficient regression analysis.

5. Solution: Correlation

This is the solution to the practice exercise on Pearson's coefficient regression analysis.

6. Practice: Linear Regression

This is a practice exercise on linear regression analysis.

7. Solution: Linear Regression

This is a solution to the practice exercise on linear regression analysis.

8. Residual, MSE, and MAE

This lesson will teach us an intuitively understandable matrix for how our regression works.

9. Practice: MSE and MAE

This is a practice exercise on the mean square error and mean absolute error to check the accuracy of our regression.

10. Solution: MSE and MAE

This is the solution to the practice exercise on the mean square error and mean absolute error to check the accuracy of our regression.

11. Coefficient of Determination

Let's learn more about one significant measure to determine how well our regressions work using the coefficient of determination.

12. Root Mean Square Error

In this lecture, you will learn another important metric to determine the quality of our regression using the root mean square error method.

13. Practice: RMSE

This is a practice exercise to estimate how well a regression works using the root mean square error method.

14. Solution: RMSE

This is the solution to the practice exercise to estimate how well a regression works using the root mean square error method.

1. Multiple Linear Regression

After learning about simple linear regression with two variables, we will now look at multiple linear regression using multiple variables.

2. Overfitting

In this video, we will explore overfitting, which is very commonly used in machine learning.

3. Polynomial Regression

In this lesson, you will learn to use polynomial regression when linear regression is not working well to report accuracy, using the Bayes information criterion.

4. Logistic Regression

This video will look at logistic regression in detail, mainly used for classification problems with one or multiple independent variables.

5. Decision Trees

In this lecture, we will look at a decision tree, how it works, its logic, and how to construct a decision tree.

6. Regression Trees

After learning how decision trees work, we will now look at the application of the decision tree practically that combines a decision tree with regression.

7. Random Forests

Let's now learn more about the Random Forest, which is based on a decision tree (not very robust and more complex) that is now broken down into smaller decision trees, which are not as complex.

8. Dealing with Missing Data

In this lecture, you will learn how to approach this problem of dealing with missing data and look at some practical examples.

1. ANOVA - Basics and Assumptions

This video illustrates the analysis of variance, where we will look at the use of this variance in our dependent variables.

2. One-Way ANOVA

In this video, you will learn to use the one-way ANOVA, where there is only one dependent factor.

3. F-Distribution

After learning how to use the one-way ANOVA, we will try to understand how to use the F-distribution to conclude the analysis results.

4. Two-Way ANOVA - Sum of Squares

Let's explore more about using two factors to perform the two-way ANOVA, which will let us find the influence of two factors.

5. Two-Way ANOVA - F-Ratio and Conclusions

In this video, let's learn to calculate the F ratio for the two-way ANOVA, interpret the results, and draw conclusions.

1. Wrap Up

This final course video concludes with a thank-you note from the author.