# Strong nonlinear relationship between two variables in statistics

### What Is a Non Linear Relationship? | Sciencing

Assume that we are talking about a non-linear relationship between a continuous is to first plot out the two variables in a scatter plot and view the relationship . In your statistical analysis try to use nonparametric statistical methods as much. Math·AP® Statistics·Exploring bivariate numerical data·Making and Form: Is the association linear or nonlinear? Direction: Is the association positive or negative? Strength: Does the association appear to be strong, moderately strong, It's also important to include the context of the two variables in the description of. Often, a scatter plot of two variables can help to illustrate the type of relationship between them. There are also statistical tools for testing various relationships. For example, the relationship between height and weight in humans is nonlinear, A relationship between two variables may be strong or weak.

You could view that as an outlier. And this is a little bit subjective.

### Describing scatterplots (form, direction, strength, outliers) (article) | Khan Academy

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. So, I could fit, maybe I'll do the line in purple. I could fit a line that looks like that.

## Linear, nonlinear, and monotonic relationships

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. This one's a little bit further out. But they're all pretty close to the line, and seem to describe that trend roughly.

- Bivariate relationship linearity, strength and direction
- Describing scatterplots (form, direction, strength, outliers)

All right, now, let's look at this data right over here. So, let me get my line tool out again. So, it looks like I can fit a line. So it looks, and it looks like it's a positive relationship. The line would be upward sloping. It would look something like this. And, once again, I'm eyeballing it. You can use computers and other methods to actually find a more precise line that minimizes the collective distance to all of the points, but it looks like there is a positive, but I would say, this one is a weak linear relationship, 'cause we have a lot of points that are far off the line.

So, not so strong. So, I would call this a positive, weak, linear relationship. And there's a lot of outliers here.

This one over here is pretty far, pretty far out. Pause this video and think about, is it positive or negative, is strong or weak? Is this linear or non-linear?

Well, the first thing we wanna do is let's think about it with linear or non-linear. I could try to put a line on it. But if I try to put a line on it, it's actually quite difficult.

If I try to do a line like this, you'll notice everything is kind of bending away from the line. It looks like, generally, as one variable increases, the other variable decreases, but they're not doing it in a linear fashion.

It looks like there's some other type of curve at play.

So, I could try to do a fancier curve that looks something like this, and this seems to fit the data a lot better. So this one, I would describe as non-linear. And it is a negative relationship. As one variable increases, the other variable decreases. So, this is a negative, I would say, reasonably strong non-linear relationship. And once again, this is subjective. So, I'll say negative, reasonably strong, non-linear relationship.

And maybe you could call this one an outlier, but it's not that far, and I might even be able to fit a curve that gets a little bit closer to that. And once again, I'm eyeballing this. Now let's do this last one. And so, this one looks like a negative linear relationship to me, a fairly strong negative linear relationship, although there are some outliers. So, let me draw this line. So that seems to fit the data pretty good. A linear relationship is a trend in the data that can be modeled by a straight line.

For example, suppose an airline wants to estimate the impact of fuel prices on flight costs. This describes a linear relationship between jet fuel cost and flight cost. Strong positive linear relationship Plot 2: Strong negative linear relationship When both variables increase or decrease concurrently and at a constant rate, a positive linear relationship exists. The points in Plot 1 follow the line closely, suggesting that the relationship between the variables is strong.

When one variable increases while the other variable decreases, a negative linear relationship exists. The points in Plot 2 follow the line closely, suggesting that the relationship between the variables is strong. Weak linear relationship Plot 4: 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. 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.