# Linear relationship statistics example

### What is linear relationship? definition and meaning - raznomir.info

Linear relationship is a statistical term used to describe the directly Examples. Example 1: Linear relationships are pretty common in daily life. Since r measures direction and strength of a linear relationship, the value of r For example, consider the relationship between the average fuel usage of. In linear relationships, any given change in an independent variable will always produce a corresponding change in the dependent variable. For example, a.

So let's just first think about whether there's a linear or non-linear relationship. And I'll get my little ruler tool out here. So, this data right over here, it looks like I could get a, I could put a line through it that gets pretty close through the data. You're not gonna, it's very unlikely you're gonna be able to go through all of the data points, but you can try to get a line, and I'm just doing this.

There's more numerical, more precise ways of doing this, but I'm just eyeballing it right over here. And it looks like I could plot a line that looks something like that, that goes roughly through the data. So this looks pretty linear. And so I would call this a linear relationship. And since, as we increase one variable, it looks like the other variable decreases. This is a downward-sloping line. I would say this is a negative. This is a negative linear relationship. But this one looks pretty strong.

So, because the dots aren't that far from my line.

This one gets a little bit further, but it's not, there's not some dots way out there. And so, most of 'em are pretty close to the line. So I would call this a negative, reasonably strong linear relationship. Negative, strong, I'll call it reasonably, I'll just say strong, but reasonably strong, linear, linear relationship between these two variables. Now, let's look at this one. And pause this video and think about what this one would be for you.

I'll get my ruler tool out again. And it looks like I can try to put a line, it looks like, generally speaking, as one variable increases, the other variable increases as well, so something like this goes through the data and approximates the direction. And this looks positive. As one variable increases, the other variable increases, roughly.

So this is a positive relationship. But this is weak. A lot of the data is off, well off of the line. But I'd say this is still linear. It seems that, as we increase one, the other one increases at roughly the same rate, although these data points are all over the place. So, I would still call this linear. Now, there's also this notion of outliers.

### Statistics review 7: Correlation and regression

If I said, hey, this line is trying to describe the data, well, we have some data that is fairly off the line. So, for example, even though we're saying it's a positive, weak, linear relationship, this one over here is reasonably high on the vertical variable, but it's low on the horizontal variable.

And so, this one right over here is an outlier. It's quite far away from the line. You could view that as an outlier. And this is a little bit subjective.

Outliers, well, what looks pretty far from the rest of the data? This could also be an outlier. Let me label these. Now, pause the video and see if you can think about this one. Is this positive or negative, is it linear, non-linear, is it strong or weak?

I'll get my ruler tool out here. So, this goes here. It seems like I can fit a line pretty well to this.

## Bivariate relationship linearity, strength and direction

So, I could fit, maybe I'll do the line in purple. I could fit a line that looks like that. And so, this one looks like it's positive. As one variable increases, the other one does, for these data points. So it's a positive. I'd say this was pretty strong. The dots are pretty close to the line there.

It really does look like a little bit of a fat line, if you just look at the dots. So, positive, strong, linear, linear relationship. And none of these data points are really strong outliers. Nonlinear relationship The data points in Plot 3 appear to be randomly distributed.

They do not fall close to the line indicating a very weak relationship if one exists.

### Linear, nonlinear, and monotonic relationships - Minitab Express

If a relationship between two variables is not linear, the rate of increase or decrease can change as one variable changes, causing a "curved pattern" in the data. This curved trend might be better modeled by a nonlinear function, such as a quadratic or cubic function, or be transformed to make it linear. Plot 4 shows a strong relationship between two variables.

This relationship illustrates why it is important to plot the data in order to explore any relationships that might exist. Monotonic relationship In a monotonic relationship, the variables tend to move in the same relative direction, but not necessarily at a constant rate. In a linear relationship, the variables move in the same direction at a constant rate.

Plot 5 shows both variables increasing concurrently, but not at the same rate.

This relationship is monotonic, but not linear. The Pearson correlation coefficient for these data is 0. Linear relationships are also monotonic. For example, the relationship shown in Plot 1 is both monotonic and linear.