Statistics 2 - Correlation Coefficient and Coefficient of Determination
We can see that in both cases, the direction of the relationship is positive and the However, the calculation of the correlation (r) is not the focus of this course. Since the value of r indicates that the linear relationship is moderately strong, but . However, you can take the idea of no linear relationship two ways: 1) If no and 2) If a strong relationship exists but it's not linear, the correlation may be. My suggestion is to establish a strong decision that there is NO Linear Relationship between X and Y. In this case Spearman's correlation would suffice a little!.
So, for example, in this one here, in the horizontal axis, we might have something like age, and then here it could be accident frequency. And I'm just making this up. And I could just show these data points, maybe for some kind of statistical survey, that, when the age is this, whatever number this is, maybe this is 20 years old, this is the accident frequency. And it could be a number of accidents per hundred. And that, when the age is 21 years old, this is the frequency. And so, these data scientists, or statisticians, went and plotted all of these in this scatter plot.Pearson r Correlation in SPSS - How to Calculate and Interpret (Part 1)
This is often known as bivariate data, which is a very fancy way of saying, hey, you're plotting things that take two variables into consideration, and you're trying to see whether there's a pattern with how they relate.
And what we're going to do in this video is think about, well, can we try to fit a line, does it look like there's a linear or non-linear relationship between the variables on the different axes? How strong is that variable? Is it a positive, is it a negative relationship?
And then, we'll think about this idea of outliers. 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.
- Correlation and dependence
- Pearson Product-Moment Correlation
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.
Statistics review 7: Correlation and regression
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. 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.
I think that education influences the number of children that people have. There is no linear relationship between education and the number of children that people have. There is a linear relationship between education and the number of children that people have. There is a weak negative relationship between education and the number of children that people have.
As education increases, the number of children that people have tends to decrease slightly. I think that age influences how many siblings that people have.
Specifically, I think that older people tend to have more siblings than younger people.
There is no linear relationship, or there is a negative relationship, between age and the number of siblings that people have. There is a linear positive relationship between age and the number of siblings that people have. There is a weak positive relationship between age and the number of siblings that people have.
As age increases, the number of siblings that people have tends to increase a little. What if alpha was. There is no linear relationship between age and the number of siblings that people have. I think that the number of hours that people work per week influences how many times they have sex. There is no linear relationship between the number of hours that people work per week and the number of times they have sex.
Bivariate relationship linearity, strength and direction (video) | Khan Academy
There is a linear relationship between the number of hours that people work per week and the number of times they have sex. There is no linear relationship between the number of hours worked last week and the number of times that people have sex.
Take Home Example I think people with higher income measured in dollars watch less television measured in hours than people with lower incomes.