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# The Classical Linear Regression Model

### Overview

##### Class Central Tips
In this course, you will discover the type of questions that econometrics can answer, and the different types of data you might use: time series, cross-sectional, and longitudinal data.

During the course you will:

– Learn to use the Classical Linear Regression Model (CLRM) as well as the Ordinary Least Squares (OLS) estimator, as you discuss the assumptions needed for the OLS to deliver true regression parameters.
– Look at cases with only one independent variable for one dependent variable, before progressing to regression analysis by generalising the bivariate model to multiple regression.
– Explore different model-building philosophies, with particular focus on the general-to-specific approach, and learn how to use goodness-of-fit statistics as the measures of “how well your model explains variations in the dependent variable”.

Throughout this course, you will see examples to help clarify which kind of relationship is of interest, and how we can interpret it. You will also have the opportunity to apply your learning to estimating the Capital Asset Pricing Model using real data with R.

The course is for beginners, so little prior knowledge is required, but you will benefit from an ability to graph two variables in the xy framework, an understanding of basic algebra and taking derivatives. Knowledge of matrix algebra is not a requirement but will also provide you with an advantage.

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

– Describe the problems that econometrics can help addressing and the type of data that should be used
– Explain why some hypotheses are needed for the approach to produce an estimate
– Calculate the coefficients of interest in the classical linear regression model
– Interpret the estimated parameters and goodness of fit statistics
– Estimate single and multiple linear regression models with R.

### Syllabus

• Aims and Uses of Econometrics
• Welcome to Coursera and Queen Mary University of London, we are excited to have you studying with us. We are going to help you prepare for your studies by ensuring you know exactly what is expected of you throughout your course and how to most effectively engage with the platform. We will look at how the platform works as well as how you will interact with your peers. You will be introduced to the university you are studying with and we will share some top tips on how to succeed with Coursera. This week we shall start by getting to know Coursera as you will be introduced to the platform and explore how to use the various functions which will support your learning journey. You will see how you can make the most of your learning experience which will enable you to succeed on this course.

This week we are going to explore the aims and uses of econometrics for economists and finance professionals and consider some of the questions that econometrics can address. We will also look at the types of data we can work with, and discuss the transformation and manipulation of this data. This week will be focussing on the single regression model.
• The Classical Linear Regression Model
• This week we shall be focussing on the Classical Linear Regression Model as well as the classical linear regression model. We will explore the assumptions of the OLS approach and see why we need those assumptions. We shall also discuss the Multiple Linear Regression Model and consider why we use linear algebra.
• Interpretation of the Ordinary Least Squares Parameters
• This week we are going to discuss the interpretation of the Ordinary Least Squares parameters as well as the goodness of fit statistics: R-squared and the adjusted R-squared. We will also consider some CAPM introductory results, model building and determinants of bus driving in the USA.
• Capital Asset Pricing Model
• This week we are going to focus on a real example of estimating and interpreting the Capital Asset Pricing Model with R. We are also going to look at data description, manipulation, estimations of the CAPM and interpretations of the estimated parameters. We shall discuss expanding the model using the three factors Fama and French (1993) model.

Dr Leone Leonida

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