How to Find Linear Regression Slope by Hand or Excel

Probability and Statistics > Regression Analysis > How to Find Linear Regression Slope

How to Find Linear Regression Slope: Overview

Remember from algebra, that the slope is the “m” in the formula y = mx + b.
In the linear regression formula, the slope is the a in the equation y’ = b + ax.
They are basically the same thing. So if you’re asked to find linear regression slope, all you need to do is find b in the same way that you would find m.
Calculating linear regression by hand is tricky, to say the least. There’s a lot of summation (that’s the Σ symbol, which means to add up). The basic steps are below, or you can watch a video on how to Find a linear regression equation. The video goes into a lot more detail about how to do summation. Finding the equation will also give you the slope. If you don’t want to find the slope by hand (or if you want to check your work), you can also use Excel. Scroll to the bottom for the video on how to find linear regression slope in Excel.

How to Find Linear Regression Slope: Steps

Step 1: Find the following data from the information given: Σx, Σy, Σxy, Σx2, Σy2. If you don’t remember how to get those variables from data, see this article on how to find a Pearson’s correlation coefficient. Follow the steps there to create a table and find Σx, Σy, Σxy, Σx2, and Σy2.

Step 2: Insert the data into the b formula (there is no need to find a).

If formulas scare you, you can find more comprehensive instructions on how to work the formula here: How to find a linear regression equation.

How to Find Regression Slope in Excel 2013

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How to Find Linear Regression Slope by Hand or Excel was last modified: October 15th, 2017 by

13 thoughts on “How to Find Linear Regression Slope by Hand or Excel”

1. Lisa Barcomb

Oh these problems here are something else this is what I am talking about and come to find out, the problem number 1 and 2 on the homework was missing a step and that through me way off. I really was struggling then and finally it came to me. So basically I feel you really need to know what you are doing in statistics because you can really get lost fast and that will put you behind.

2. Lauren Schultz

I have to agree with Ms. Lisa. I got way into this and got stressed opout and had to walk away. But this explination really helped me out alot!!

3. Donna Allen

Lisa is so right. Each lesson builds upon each other. If you don’t understand something, it only snowballs into a mess of confusion. I was doing ok until chapter 8. Since then, I have really struggled to understand the lessons.

4. Jennifer Thomas

I too have had alot more trouble since Chapter 8 but this site has definitely helped me to have a better understanding for most of the course work. I’d like to suggest more step by step examples be provided for Chapter 8.

5. Donna Allen

The equation looks a bit intimidating. But, once you see how to plug in the numbers, it’s really not bad at all.

6. Vanessa DuBarry

These questions may seem very hard when you take the first glance but if you look well into it they are actually not that hard and this page helps. The only thing is that its a lot of work and you just have to be careful with the numbers.

7. Donna Allen

Much agreed. There’s nothing more frustrating than understanding how to work a complex equation and then finding your answer is off by one number. This is where I seriously lack patience when it comes to math :)

8. MJ

These equations are incorrect. They are backwards, b is the slope and a is the intercept.

9. Andale

Hi, MJ,

Thanks for stopping by, but I think you may be reading this wrong?

“B” is indeed the slope — and it’s stated as such (“Insert the data into the b formula”)

Regards,
Stephanie

10. jhon

if the regression line y on x is positive what will be the regresion line x on y negative or positive ,,,,,,,,,,,,,,,,,

11. Andale

Hello, Jhon,

My work load doesn’t give me the time to answer stats questions here. However, please feel free to post on our forum :)

Thanks for stopping by,

Stephanie