# Tutorials in Econometrics and Mathematical Economics

## Application of Differential Calculus in Economic Analysis

This tutorial is about the use of differential calculus, especially in the case of the Marginal Rate of Substitution. Differential Calculus is the most used mathematical method in economic analysis. This tutorial uses the Marginal Rate of Substitution as an example to illustrate how Differential Calculus is used extensively. ## How to Become an Economist Without a Degree In Economics?

You can indeed become an Economist if you want even if you do not have a degree in Economics. And the reason why is that Economics is not a regulated profession like medicine or law or the actuarial sciences. Economics is a general field of study like Mathematics or Philosopher, so there not explicit educational requirements for one to become an Economist. In fact, becoming an Economist is a matter of habit. Nonetheless, there are few principles that must be respected in order to become an Economist, and these principles are: 1. Find a subfield of Economics that you like 2. Find a niche within that subfield 3. Learn how to analyze economic data 4. Learn Mathematics and Econometrics 5. Publish books and Working Papers 6. Publish with Academic Journals 7. Be a member of a professional organization 8. Take a certification exam if you can Fulfilling the first five principles will make you eligible to be considered as an independent economist at the very least. ## Introduction to Econometrics

The purpose of this video is to introduce econometrics to the layman. Econometrics, which is the measurement of economic theory through the use of statistical techniques to obtain empirical content, is a complicate and technical sub-field of economics. Consequently, the goal is to make econometrics accessible and easier to understand for any person who doesn’t have a scientific background. ## Data Analysis in Simple Linear Regression

This video explains the methodology to follow when analyzing data in econometrics. A hypothetical data was used to illustrate to the learner the steps to take when analyzing the data before formulating a hypothesis then choosing the statistical model. ## Analysis of the Simple Linear Regression

In the previous video, we analyzed the sample of typical data in a linear regression model. The purpose of this video though is to examine all the steps needed in the statistical model of the linear regression. We analyzed each equation that each element of the simple linear regression model contains. ## Outliers, P-Value, R-square

This video explains the importance of outliers, p-value, and r-square. Outliers are important because they impact the fate of the regression. One outlier can change the whole trajectory of the regression analysis. The p-value determines the statistical significance between two variables. The R-square determines the strength of the correlation. ## Multiple Linear Regression (The Basic calculations)

This video explains the fundamentals of the multiple linear regression. It first explains the difference between the multiple linear regression and the multivariate linear regression. Then it explains the basic calculations needed in order to determine the slope of each explanatory variable. ## Multiple Linear Regression (Slopes and Intercept)

This lecture explains the method to calculate the values of the slopes and that of the intercept in a multiple linear regression analysis. ## Econometrics vs Statistics: Which one is Harder?

This video explains the difference between econometrics and statistics, the kind of data used in both fields, the kind of statistical models used in both fields, and in which academic discipline they are used as well. This video also addresses the career prospect between focusing on econometrics versus focusing on statistics. ## Polynomial Regression Analysis (OVERVIEW)

Time to level up. We now move to Econometrics II. In Econometrics II, we start learning about the Polynomial Regression. The Polynomial Regression is a linear and nonlinear regression that falls into the category of the Ordinary Least Squares since its assumptions are within those of the classical linear regression. ## Polynomial Regression - Model Building, Order of the Model, & Extrapolation

In this section, we mainly talk about model building, the order of the model, and extrapolation. We addressed the methods by which we proceed to build a polynomial regression in order to determine the order of the parameters of the model. We also addressed the concept of extrapolation in the visualization of the scatterplot. ## Multivariate Regression

This video is to clarify the confusion between the multiple linear regression and the multivariate linear regression. Too many videos on YouTube have confused the multivariate regression for the multiple regression. The multiple linear regression is based on one outcome variable that depends on many predictors whereas the multivariate linear regression is based on, at least TWO OUTCOME VARIABLES, that depend on either one predictor or many predictors. ## Introduction to the Autoregression Model (AR)

This video is an introduction to time-series data and the Autoregression Model (AR). It teaches the basic concepts of the Autoregression model such as its definition, and under what conditions it is used. ## Vector Autoregressive Model (VAR)

This tutorial is about the Vector Autoregressive Model (VAR). It starts with a review of multivariate regression analysis before moving into the VAR part. The reason why this tutorial starts with the multivariate regression analysis rather than the VAR is that the VAR is a multivariate type of regression analysis that is strictly designed for time-series data. Hence the VAR model is designed and structured after the multivariate regression. Moreover, this tutorial introduces the VAR model with VAR (1), then more advanced methods are performed throughout. After watching this tutorial, the learner should be able to understand how the VAR works and how to use it. ## Logistic Regression

This tutorial explains the basic concept of the logistic regression. The logistic regression is a statistical model derived from the logistic function. Its particularity is that it is based on a binary dependent variable to gives two possible outcomes. The logistic regression is used everywhere; in politics to predict voting outcome, in healthcare to predict the occurrence of a disease, in finance and banking to predict the outcome for the approval for a loan. ## Application of Integral Calculus in Economic Analysis

This video is a basic introduction to the application of Integral Calculus in economic analysis. Integral Calculus is not extensively used in economics the way Differential Calculus is used. In fact, Integral Calculus in economic analysis essentially focuses on analyzing the cost of various factors of production as a whole rather than a portion of these factors. The use of Integral Calculus in economic analysis is not solely limited to cost theory in microeconomics. It is also used in macroeconomics to analyze monetary policy. ## Application of Differential Equations in Economic Analysis

Differential equations are extremely important and extensively used in economic analysis. As a matter of fact, differential equations are used to analyze how systems evolve with respect to time. Most economic models that involve changes and dynamics are based on the use of differential equations. For example, the Malthusian Growth Model is the first model that analyzes exponential growth, and exponential growth is based on a differential equation. The goal of this video is to explain the significance and usefulness of differential equations in the application of economic analysis. ## Application of Linear Algebra in Economic Analysis: The Input-Output Model

Linear algebra is used in economic analysis through the input-output method. The input-output method is a quantitative model used primarily in macroeconomics to analyze the interdependencies of economic sectors and industries. This method is commonly used for estimating the impacts of positive or negative economic shocks and analyzing the ripple effects throughout the economy. This model was developed by Wassily Leontief, winner of the 1973 Nobel Prize in Economics. ## Application of Multivariable Calculus in Economic Analysis

Multivariable Calculus is perhaps the most used mathematical method in the field of calculus to the application of economics. It is used extensively in microeconomics and macroeconomics because economic phenomena and systems deal with many inputs simultaneously. When facing issues where multiple dependent variables intertwine, the best method to use to determine each dependent variable's quantity is to use multivariable calculus since it is the method that handles many dependent variables at the same time. 