How to Calculate Slope of a Line in Statistics

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A slope of a line in statistics is a very valuable way to take a look at how different pieces of information are related. Calculate the slope of a line in statistics with help from a mathematics educator in this free video clip.

Part of the Video Series: Statistics 101
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to calculate the slope of a line in statistics. Now, to find the slope of a line in algebra is one thing, but a slope of a line in statistics is frankly another and that you actually want to use the data points to help you find the slope. Now, let's talk about the notation for a slope and let's just use M just as a generic variable for a slope. But, let's write the formula down and that you'll see how all of these gets developed. So, you have n times sum of xy minus sum of x sum of y over n sum of x squared minus in parenthesis sum of x quantity squared. Now, what's all these stuff mean? Let's start from the very beginning. Notice this n shows up twice, the top and the bottom. N refers to the number of data points or number of pairs if you will. Now, given the, you have xy coordinates. Now, this sum xy means that you're going to take every x coordinate and multiply by the corresponding y coordinate and then, once you do all that, you're going to add all the xy products together. Now, minus the sum of x means you want to add all the x coordinates together. Yes, you want to add all the x data points and then you want to do the same thing with the y coordinates; add all the y coordinates together. And then, you're going to take the sums of each and you're going to multiply these. So, if you think, want to think about it is it's you want to take sum of the x coordinates and you want to multiply by the sum of the y coordinates. So, that's your numerator, somewhat complicated as is. And the denominator, this n is the number of pairs; what you want to do is you want to take each coordinate, you're going to square it and then you're going to add all those numbers together. So, take all the x coordinates, square each of them and then add what you have going on. And then this one here, that means if you look at the way this is written, you're going to add all your x coordinates, that's going to be some kind of a large number and then you're going to square that result. So, at the end of the day, what you're really doing here is you're going to create a bunch of columns, add all your x's, add all your y's, multiply them when necessary and you want to create separate column for the x squared. At the end of the day, it's just really a lot of number crunching and you'll have your slope at the very end. So, I'm Jimmy Chang and that's how to calculate the slope of a line in statistics.


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