How to Automatically Calculate the Multiple Regression Analysis in Excel using Matrix Algebra Form

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Good day and welcome to this wonderful episode of Statistics Video Tutorial. I still remember when I was in School taking up my Degree in Statistics and I terribly missed the traditional method of teaching wherein my professor was trying to teach how to calculate or compute Statistical Test without the use of a Computer Software.  


I am very much thankful that I was able to experience this way of teaching because I was able to understand the concept, rationale and how the formula was derived.

Because of the utilization of Computer Software, there are other steps and procedures which often neglected and set-aside. In a Machine Learning Model such as Multiple Regression, it is a must to understand the behavior and pattern of the data before performing the modelling part. One should test the assumptions involved in a Machine Learning Model. If any of the assumptions is/are violated, it is predominantly important to address the violation, to fix the violated assumptions and once its done, then it is the time that we can start building the model and choosing the best model.

One effect of using Computer Software is the people forget how to compute statistics manually by following the formula guided procedures such as calculating the Sum of Square Regression, Sum of Square Residuals, Mean Square Regression, Mean Square Residuals, F-Ratio, etc. This is one of the main reasons why some of the analysts nowadays don’t understand the behavior of the data if for example, what happened to the R Square if you remove one Independent Variables. Will it go high or go down? If the R Square Change go down because of removing an independent variable, what does it mean? Is it good? Does is affect the accuracy or reliability of the Model?

These are the things that we should consider if we want to build a highly reliable and valid model.

In this Video, I am going to discuss few of the concepts and steps to calculate a Multiple Regression. I will be going to discuss and show how to do Multiple Regression using SPSS, using Microsoft Excel Data Analysis Add-ins, and using the Matrix Algebra Procedures.

As you noticed, it is easy to compute Statistics using Computer Software – SPSS, very straightforward. It is also easy to use the Microsoft Excel Data Analysis Add-ins.

Now, I am going to show you how to calculate Multiple Regression in Excel using Matrix Algebra. Using this Method, I am going to introduce certain key terminology such as Matrices, Inverse Matrix, Transpose Matrix and Vectors. I am also going to introduce certain functions such as Transpose, mmult and minverse. These are the functions we will be using for us to calculate the Slope of the Xs and the Intercept in a Multiple Regression Model.

But before that, we will discuss further about Multiple Regression, Alright

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