Types of Correlation
Date: 06/25/2002 at 15:18:25 From: Katie Subject: Correlation Hello! I am really stuck on a question that deals with weak, strong, positve, and negative correlation in scatter plots. You have a post about this topic but I really don't know what correlation is so it didn't help. In the problem it shows you a scatter plot and it asks you to tell what kinda of correlation is shown. If you could just tell me what all this correlation stuff is about I think I can get it from there. Thanks!
Date: 06/25/2002 at 22:54:42 From: Doctor Achilles Subject: Re: Correlation Hi Katie, Thanks for writing to Dr. Math. A correlation is when two variables are related. That definition is probably not terribly helpful, so let me give you a few examples. First, there is a positive correlation between the amount of education a person has and the amount of money that person makes (at least I hope there is, since I'm a college student). That is really just a fancy way of saying: "On average, if someone has more education, then that person will make more money." You might graph that using a scatter plot by taking a random sample of people, finding out how much money they make and asking how much education they have. Then for each person you put a point down. The farther to the right the point is, the more education that person has; the higher up the point is the more money that person makes. I've made up some data that look like this: | . | . .. m | ... o | . . n | . . e | . y | ... | . . | . ----------------- education Notice that the highest paid person actually only has about an average education. But still, on average more education means more money. So there is a POSITIVE correlation between education and money. For another example, let's look at the relationship between the number of cars on the freeway and the average speed. Here's my (made-up) scatter plot: | . . |. s | . . p | . e | . e | . d | . . | .. | .. ----------------- number of cars Again, there are a few exceptions, but for the most part, the more cars there are, the slower the average speed. (Think of rush hour, when there are a lot of cars but everyone goes really slowly.) This means that there is a NEGATIVE correlation between the number of cars and the average speed. Finally, let's imagine that we go to a mall and take a survey. What we do is we ask random people to tell us their height. Then we look to see if there is any correlation between the answer they give and the time of day it is. Here's my made up scatter plot: | . | . h | . .. e | . . i | . . g | . h | . . t | . . | . .. ----------------- time of day This time the points are all over. There doesn't seem to be any relationship at all. So we answer that there is NO correlation here. As far as strong vs. weak correlations, that just has to do with how many exceptions there are to the general rule. The examples of car speed and money are moderate or weak correlations. Here's a very strong (positive) correlation: | . | . | . | . A | . | . | . | . |. ------------------- B Hope this helps. If you have other questions about this or you're still stuck, please write back. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/
Date: 06/26/2002 at 16:15:36 From: Katie Subject: Thank you (Correlation) I just wanted to say thanks again for your time. Your examples really helped! -Katie
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