Linear Regression for Business Statistics

Regression Analysis is perhaps the single most important Business Statistics tool used in the industry. Regression is the engine behind a multitude of data analytics applications used for many forms of forecasting and prediction.

This is the fourth course in the specialization, "Business Statistics and Analysis". The course introduces you to the very important tool known as Linear Regression. You will learn to apply various procedures such as dummy variable regressions, transforming variables, and interaction effects. All these are introduced and explained using easy to understand examples in Microsoft Excel.

The focus of the course is on understanding and application, rather than detailed mathematical derivations.

Note: This course uses the ‘Data Analysis’ tool box which is standard with the Windows version of Microsoft Excel. It is also standard with the 2016 or later Mac version of Excel. However, it is not standard with earlier versions of Excel for Mac.

WEEK 1

Module 1: Regression Analysis: An Introduction

In this module you will get introduced to the Linear Regression Model. We will build a regression model and estimate it using Excel. We will use the estimated model to infer relationships between various variables and use the model to make predictions. The module also introduces the notion of errors, residuals and R-square in a regression model.

Topics covered include:

• Introducing the Linear Regression

• Building a Regression Model and estimating it using Excel

• Making inferences using the estimated model

• Using the Regression model to make predictions

• Errors, Residuals and R-square

WEEK 2

Module 2: Regression Analysis: Hypothesis Testing and Goodness of Fit

This module presents different hypothesis tests you could do using the Regression output. These tests are an important part of inference and the module introduces them using Excel based examples. The p-values are introduced along with goodness of fit measures R-square and the adjusted R-square. Towards the end of module we introduce the ‘Dummy variable regression’ which is used to incorporate categorical variables in a regression.

Topics covered include:

• Hypothesis testing in a Linear Regression

• ‘Goodness of Fit’ measures (R-square, adjusted R-square)

• Dummy variable Regression (using Categorical variables in a Regression)

WEEK 3

Module 3: Regression Analysis: Dummy Variables, Multicollinearity

This module continues with the application of Dummy variable Regression. You get to understand the interpretation of Regression output in the presence of categorical variables. Examples are worked out to re-inforce various concepts introduced. The module also explains what is Multicollinearity and how to deal with it.

Topics covered include:

• Dummy variable Regression (using Categorical variables in a Regression)

• Interpretation of coefficients and p-values in the presence of Dummy variables

• Multicollinearity in Regression Models

WEEK 4

Module 4: Regression Analysis: Various Extensions

The module extends your understanding of the Linear Regression, introducing techniques such as mean-centering of variables and building confidence bounds for predictions using the Regression model. A powerful regression extension known as ‘Interaction variables’ is introduced and explained using examples. We also study the transformation of variables in a regression and in that context introduce the log-log and the semi-log regression models.

Topics covered include:

• Mean centering of variables in a Regression model

• Building confidence bounds for predictions using a Regression model

• Interaction effects in a Regression

• Transformation of variables

• The log-log and semi-log regression models