Correlation coefficient



I was reading a blog on correlation coefficient. It is as stated below

" For example, suppose a study is conducted to assess the relationship between outside temperature and heating bills. The study concludes that there is a negative correlation between the prices of heating bills and the outdoor temperature. The correlation coefficient is calculated to be -0.96. This strong negative correlation signifies that as the temperature decreases outside, the prices of heating bills increase and vice versa"

Here as temp decreases price of heating bill increases but in vice versa if prices of heat bills decreases temp wont shoot up right. Then how can we capture this?


Hi @raviteja1993,

The possible hypothesis could be that when the temperature decreases, people tend to use more heating appliances like room heater, etc. to keep themselves warm and hence the price of heating bill increases.

Whereas, when the temperature increases, the usage of heating appliances decreases as the temperature is not that cool. So, in this case due to less usage of heating appliances, the heating bill will also decrease.

Hence as stated here:

“The correlation coefficient is calculated to be -0.96. This strong negative correlation signifies that as the temperature decreases outside, the prices of heating bills increase and vice versa”

seems logical to me.


Yeah that is true.
But there may be some external factors which resulted in drop of heating bill price which does not effect the temp.


Hi @raviteja1993,

Sure. There can be N number of hypothesis. This is just one of them which can affect the heating bill.


Got it Thank you.


@raviteja1993 Can’t there be a possibility of increase in heating bill with no change in temperature but due to some external factors?!

Either of our hypothesis are ruled out because of the very strong correlation value. Here from the correlation value we can conclude that there are no external factors involved.


@abdul38 Correlation is not always causation. Thre seems to be high correlation between two variables( say a and b) but it can’t be said always that the change in variable b is because of variable a. For example, there is a correlation between ice cream sales and the temperature , as when temperature increases ice cream sales increases. But decrease in ice cream sales does not make temparature to decrease. So, causation may be because of some external factor. So, you cannot conclude as such.


Thank you… your ans is convincing


@raviranjankarn Thanks for the details but I believe we can’t statistically decide which is a & b here!

To answer the actual question of this post, it may be logically wrong to assume reverse causation depending on the scenario but we can’t statistically prove it, as correlation of a&b is no different from correlation of b&a. There are some cases despite getting a strong correlation value it is difficult to decide which is causing what. For instance, Athletes who practice more perform better. This can be vice versa, as high performing athletes tends to practice more than the rest.


You need to start with a good definition of your model, this is attempting to reverse the logic of an existing simple two variable model. If you need a model with additional variables to account for seasonality, changes to the heating technology, cost of energy you need to build that complex model at the start or you need to change the model you are attempting to use adding the dimensions for the other variables. You can also smooth the data, use the mean and not the average values, use a longer window of time. Good luck.


What’s happening in the comments people.
raviteja1993, everything is OK but the last part “Vice Versa” , vice versa means it’s strong positive correlation and that’s not true in this problem between the prices of heating bills and the outdoor temperature .
To be more clear,
strong negative correlation means low price, high temp
but in
strong positive correlation means high price, high temp.


Thank you


Thank you all


@mdbleachit is very correct, that vice versa is not necessarily correct. Regarding the price of heating, I think it would be more logical to relate the Outdoor Temperature with amount of heating required. But this wasn’t my blog so it’s speculation.


Very nice.


@smuzoka you’re right.
The problem in some topics and questions that they’re not clear to understand and answer.
When we want to answer a question we must look at it from a logical perspective and then we build our own solution.