How to figure out if data or a graph shows a linear relationship. The “b” in the slope formula is the y-intercept and the “m” is the slope. Y = mx. This figure shows a scatter plot for two variables that have a strongly positive linear relationship between them. The correlation between X and Y equals Scatterplots plot points (x,y). They give us a Is the relationship positive (x goes up and y goes up, x goes down and y goes down), negative (x goes up, --When dealing with a relation, the x and y variables have particular roles to play. The x.
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.
Example of direction in scatterplots
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. If I said, hey, this line is trying to describe the data, well, we have some data that is fairly off the line.
Bivariate relationship linearity, strength and direction (video) | Khan Academy
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.How to Determine if a Relationship Represented in a Table Is Linear & Write an Equation : Algebra
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.
Bivariate relationship linearity, strength and direction
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.
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.
Now for a certain amount of time studying, some people might do better than others, but it does seem like there's this relationship. Here it doesn't seem like there's really much of a relationship.
You see the shoe sizes, for a given shoe size, some people do not so well and some people do very well. Someone else, looks like they got A minus or a B plus on the exam. And it really would be hard to somehow fit a line here. No matter how you draw a line, these dots don't seem to form a trend.
Example of direction in scatterplots (video) | Khan Academy
So let's see which of these choices apply. There's a negative linear relationship between study time and score. No, that's not true. It looks like there's a positive linear relationship. The more you study, the better your score would be. A negative linear relationship would trend downwards like that. There is a non-linear relationship between study time and score and a negative linear relationship between shoe size and score. Well that doesn't seem right either. A non-linear relationship, it would not be easy to fit a line to it.
And this one seems like a line would be very reasonable.
And it doesn't seem like there's any type of relationship between shoe size and score.