Negative Correlation - Variables that Move in Opposite Direction
Is that possible or does it have to be positive? to the relationship between two positive quantities or two negative quantities--never between a. Explore the relationship between positive and negative correlations. variables have a negative correlation, they have an inverse relationship. The graph of an inversely proportional function is called a hyperbola (see the figure to the right). If you rewrite the formula for k positive, y is negative.
To go from negative 3 to negative 6, you're also multiplying by 2. So we grew by the same scaling factor. To go from negative 3 to negative 1, we also divide by 3.
We also scale down by a factor of 3. So whatever direction you scale x in, you're going to have the same scaling direction as y. That's what it means to vary directly. Now, it's not always so clear. Sometimes it will be obfuscated. So let's take this example right over here. And I'm saving this real estate for inverse variation in a second.
You could write it like this, or you could algebraically manipulate it. Or maybe you divide both sides by x, and then you divide both sides by y. These three statements, these three equations, are all saying the same thing. So sometimes the direct variation isn't quite in your face. But if you do this, what I did right here with any of these, you will get the exact same result. Or you could just try to manipulate it back to this form over here.
And there's other ways we could do it. We could divide both sides of this equation by negative 3.
And now, this is kind of an interesting case here because here, this is x varies directly with y. Or we could say x is equal to some k times y. And in general, that's true.
If y varies directly with x, then we can also say that x varies directly with y. It's not going to be the same constant. It's going to be essentially the inverse of that constant, but they're still directly varying. Now with that said, so much said, about direct variation, let's explore inverse variation a little bit. Inverse variation-- the general form, if we use the same variables.
And it always doesn't have to be y and x. It could be an a and a b. It could be a m and an n. If I said m varies directly with n, we would say m is equal to some constant times n. Now let's do inverse variation.
Inversely proportional function
So let me draw you a bunch of examples. And let's explore this, the inverse variation, the same way that we explored the direct variation. And let me do that same table over here. So I have my table.Correlation, Positive, Negative, None, and Correlation Coefficient
I have my x values and my y values. If x is 2, then 2 divided by 2 is 1. So if you multiply x by 2, if you scale it up by a factor of 2, what happens to y? You're dividing by 2 now. Here, however we scaled x, we scaled up y by the same amount.
Now, if we scale up x by a factor, when we have inverse variation, we're scaling down y by that same. So that's where the inverse is coming from.
And we could go the other way. So if we were to scale down x, we're going to see that it's going to scale up y. So here we are scaling up y. So they're going to do the opposite things. And you could try it with the negative version of it, as well. So here we're multiplying by 2. And once again, it's not always neatly written for you like this. It can be rearranged in a bunch of different ways. But it will still be inverse variation as long as they're algebraically equivalent.
So you can multiply both sides of this equation right here by x. And you would get xy is equal to 2. This is also inverse variation. A correlation is a single numerical value that describes a relationship between two things, or variables.
The Pearson product moment correlation is the most common measure of correlation and is usually represented by the letter r. A correlation has two qualities: The two directions of a correlation are positive and negative. In a positive correlation, both variables move in the same direction.
In other words, as one variable increases, so does the other. For example, there is a positive correlation between smoking and alcohol use. As alcohol use increases, so does smoking.
When two variables have a negative correlation, they have an inverse relationship. This means that as one variable increases, the other decreases, and vice versa. Negative correlations are indicated by a minus - sign in front of the correlation value. In the example above, we noted that students who spent the higher amount of time playing video games each week had the lowest GPAs. As the hours spent playing video games decreased, the GPAs increased.
Some other examples of variables that are negatively correlated are: The weight of a car and miles per gallon: School achievement and days absent from school: The more that people are vaccinated for a specific illness, the less that illness occurs.
Determining Correlation Strength So, how do we determine the strength of a relationship? We look at the numbers.