correlation coefficient is a useful tool when we work with a set of data. Imagine that we have a graph showing the age and height of a group of children.
What we'll try to do is to find the right line that almost crossed most of the points on the graph, I'll give you some options!
Which line seems to adjust the better to the black points?
First, we have to distinguish between positive and negative correlation coefficients.
The following are examples of the negative case:
So, if these are lines that adjust to our data, whatever it is, we will say that the correlation coefficient is negative. (Notice that the slope of each one of the lines is negative)
On the other hand, if the line that adjusts the best to our data has any of the next shapes:
We'll say that it has a positive correlation coefficient (Notice that their slopes are positive)
Then, A and D have a negative correlation coefficient! None of those is the answer we are looking for!
Finally, the better our line adjusts to our data, the closer its value will be to 1.
So, as you can see on the C graph, the data is quite scattered, and no line will adjust quite well to our data. However, 0.94 is quite close to 1, right? So, we expect that there will be a line that adjusts almost perfectly to our data. This is not the case on C but it is on B! B is the answer!
B is the actual answer for two important characteristics:
- A line that adjusts to the data shown on B will have a positive slope.
- There is a line that adjusts almost perfectly to the data on B, as the points are not so scattered but close to each other