Scott Hartshorn [Hartshorn - Linear Regression And Correlation: A Beginner’s Guide

This book covers linear regression. In doing so, this book covers several other necessary topics in order to understand linear regression. Those topics include correlation, as well as the most common regression metric, R .

Linear regression is a way of predicting an unknown variable using results that you do know. If you have a set of x and y values, you can use a regression equation to make a straight line relating the x and y. The reason you might want to do this is if you know some information, and want to estimate other information. For instance, you might have measured the fuel economy in your car when you were driving 30 miles per hour, when you were driving 40 miles per hour, and when you were driving 75 miles per hour. Now you are planning a cross country road trip and plan to average 60 miles per hour, and want to estimate what fuel economy you will have so that you can budget how much money you will need for gas.

The chart below shows an example of linear regression using real world data. It shows the relationship between the population of states within the United States, and the number of Starbucks (a coffee chain restaurant) within that state.

Likely this is information that is useful to no one. However, the result of the regression equation is that I can predict the number of Starbucks within a state by taking the population (in millions), multiplying it by 38.014, and subtracting 71.004. So if I had a state with 10 million people, I would predict it had (10 * 38.014 71.004 = 309.1) just over 309 Starbucks within the state.

This is a book on linear regression, which means the result of the regression will be a line when we have two variables, or a plane with 3 variables, or a hyperplane with more variables. The above chart was generated in Excel, which can do linear regression. This book shows how to do the regression analysis manually, and more importantly dives deeply into understanding exactly what is happening when the regression analysis is done.

The final result of the regression process was the equation for a line. The equation for a line has this form

Multiple linear regression is linear regression when you have more than one independent variable. If you have a single independent variable, the regression equation forms a line. With two independent variables, it forms a plane. With more than two independent variables, the regression equation forms a hyperplane. The resulting equation for multiple regression is

One metric for measuring how good of a prediction was made is R . This metric measures how much error remains in your prediction after you did the regression vs. how much error you had if you did no regression.

Correlation is nearly the same as linear regression. Correlation is a measure of how much two variables change together. A high value of correlation (high magnitude) will result in a regression line that is a good prediction of the data. A low correlation value (near zero) will result in a poor linear regression line.

This book covers all of the above topics in detail. The order that they are covered in is

• R
• Correlation
• Linear Regression
• Multiple Linear Regression

The reason they are covered in that order, instead of skipping straight to linear regression, is that R builds up some information that is useful to know for correlation. And then correlation is 80% of what you need to know to understand simple linear regression.

Initially, it appears that multiple linear regression is a more challenging topic. However, as it turns out, you can solve multiple regression problems just by doing simple linear regression multiple times. This method for multiple regression isnt the best in terms of number of steps you need to take for very large problems, but the process of repeated simple linear regression is great for understanding how multiple regression works, and that is what is covered in this book.