Examples of Positive Correlation and Negative Correlation?

[timmydoeslsat]

This question I have stems from the PT 50 S4 Q19 about recent studies and smokers.

What would be an example of a positive correlation?

Negative correlation?

[chike_eze]

What would be an example of a positive correlation?
Negative correlation?

Positive correlation (direct relationship): Basically means X and Y are going in the same direction. E.g., As one gets older, one gets wiser. Or As the ocean level falls, the fish population size decreases.
- As X increases, Y increases.
- As X decreases, Y decreases

If you are math inclined, think about a positive slope y = mx + b
> where m is positive.

Negative correlation (inverse relationship): Basically means X and Y are going in opposite directions. E.g., As one gets older, one exercises less (not necessarily true, but you get the gist). Or As the Ocean level falls, more fish die.
- As X increases, Y decreases
- As X decreases, Y increases

Negative slope: y = -mx + b
> (not sure why I still remember this stuff...)

[timmydoeslsat]

Thanks for that!

In a positive correlation, you stated as an example: As one gets older, one gets wiser.

As X increase, Y increases. This is a positive correlation.

Does a positive correlation include as Y increases, X increases...aka the reverse?

If it does not include that, what would you call that relationship? Something like a perfect correlation?

[chike_eze]

As X increase, Y increases. This is a positive correlation.

Does a positive correlation include as Y increases, X increases...aka the reverse?

Probably a better way to think about positive correlation is
As X increases, Y tends to increase. No cause-n-effect is implied. With this in mind, I think the answer to your question is yes-- the reverse could be true; i.e., As Y increases, X tends to increase.

For Example:
Between 2000 and 2011, the crime rate in City X increased. During that same period, the number of guns sold in City X increased.

2000-2011:
crime rate correlates (positively) with guns sold
guns sold correlates (positively) with crime rate

(no cause and effect implied)

If it does not include that, what would you call that relationship? Something like a perfect correlation?

Perfect correlation means both X and Y increase or decrease by the same degree; i.e., Slope of 1 or -1. An example would be the perfect negative correlation between a car's fuel efficiency (X miles per gallon) and the money spent per X miles the car is driven. However, No cause and effect is implied.

[ManhattanPrepLSAT1]

Nice explanation Chike!

[khuranatanishq35]

Your example of negative correlation was not quite correct, negative correlation means that one variable decreases while the other variable increases. So a legit example could be, Years of education and years in jail: those who spend more years in education tend to spend less time in jail.

[tommywallach]

All the explanations given in this thread are correct. There is no switch of negative/positive that I see...

-t