In this module, you will learn about the theory and practice of simple linear regression with one dependent variable and one independent variable. Simple linear regression is a statistical method that allows us to summarize and study relationships between two variables and goes beyond exploring the simple correlation between them. You will first learn the estimation and interpretation of the estimators of a regression model. Then, you will be able to understand those estimators’ numerical and statistical properties. Lastly, you will work with some practical, functional forms to handle nonlinearities in regression models.

In this module, you will move from the simple linear regression model with one regressor to the multiple linear regression model with two or more regressors. We use the adjective “simple” to denote that a model has only one regressor and the adjective “multiple” to indicate that a model has at least two regressors. In learning the practice of multiple linear regression, importance is accorded to building an intuitive understanding without using matrix algebra, mainly by analogy with simple linear regression. Lastly, you can derive and learn the algebraic properties of a regression model with k explanatory variables.

In this module, you will continue with the multiple linear regression model and use that to learn statistical inference, allowing you to infer something about the population model from a random sample. The sixth assumption of the classical linear model is the additional assumption that the population error is normally distributed. In the model, you will understand the sample distributions of the OLS estimators. Further, you will be able to review how to carry out a hypothesis test, assuming the six assumptions are true. You will also be able to do several specifications of hypothesis testing, including restrictions on a single parameter, a combination of two parameters, exclusion restrictions, tests of overall significance, and multiple linear restrictions. To conclude, you will be using the t-statistic and F-statistic.

In this module, you will continue with the multiple linear regression model and explore the asymptotic properties of the OLS estimators, which holds true when you transition from a small sample to a large sample. These properties are also known as the large sample properties. Post OLS asymptotics, you will learn about some extensions of the linear regression model, which are mostly used in applied work. You will further explore regression models, which are three different functional forms of explanatory models. Starting with the case when you have quadratic terms of the explanatory variable, you will discuss regression models with categorical explanatory variables. Finally, you will understand the regression models involving the interaction of explanatory variables as regressors.

In this module, you will keep using the multiple linear regression model and analyze the standard linear regression model considering the three problems that crop up most frequently when analyzing cross-sectional data. You will learn, in particular, about the bias and inconsistency arising from omitting important variables, as well as the effects of multicollinearity and heteroscedasticity in your data. You will also learn how to identify multicollinearity and heteroscedasticity in your model, test for it, and correct it using various techniques.

In this module, you will learn about data and specification errors commonly encountered in multiple linear models. You will also learn about the tests to check for model misspecification, using proxy as a possible solution for model misspecification. Further, you will be introduced to issues that crop due to measurement error in the dependent and independent variables. You will also gain an understanding of two advanced models. First is the binary response model, which is used when the dependent variable is binary in nature. Next, you will learn about the time series model. You will also get some insights into the problem of autocorrelation, which is usually encountered when we have specification errors in time series data.