Unable to understand correlation coefficient / auto correlation Suppose I have a vector say: [5 5 5 5 4 5] then common sense says that there is a very high auto-correlation for the vector because it is more or less the same values. But when I try to calculate the auto-correlation coefficient, I'm getting a very low value(<0.3) for all lags. What does this mean? shouldn't it be higher because the series is very similar? Am I missing something? does correlatiom mean not similarity but similarity in rate(Rate of change)?

Jazmyn Pugh 2022-09-25 Answered
Unable to understand correlation coefficient / auto correlation
Suppose I have a vector say:
[5 5 5 5 4 5]
then common sense says that there is a very high auto-correlation for the vector because it is more or less the same values. But when I try to calculate the auto-correlation coefficient, I'm getting a very low value(<0.3) for all lags. What does this mean? shouldn't it be higher because the series is very similar?Am I missing something?does correlatiom mean not similarity but similarity in rate(Rate of change)?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Katelyn Chapman
Answered 2022-09-26 Author has 13 answers
A similar situation arises when you fit a regression line to perfectly horizontal data — you get a “linear” relationship that is nearly perfect but also completely uninformative.
Correlation measures how changes in X about its mean are related to changes in Y about its mean. In the case where one of the variables is (or is almost) constant, then there isn’t much variation left to attribute to the other variable:
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-07-20
Correlation of Rolling Two Dice
If A is a random variable responsible for calculating the sum of two independent rolls of a die, and B is the result of calculating the value of first roll minus the value second roll, is is true that A and B have a c o v ( A , B ) 0? In other words, is it true that they are correlated?
I've come to the conclusion that they must be correlated because they are not independent, that is, the event of A can have an impact on event B, but I remain stuck due to the fact that causation does not necessarily imply correlation.
I know that independence −> uncorrelation, but that the opposite isn't true.
asked 2022-09-26
Meaning of 'obligatory disclaimer'
Can you explain to me what 'obligatory disclaimer' means in probability. Is it like a lack of information or what?
The context is the following:
Second, we found that the marginal distribution of Y is Bern(0.08), whereas the conditional distribution of Y given X = 1 is Bern(0.2) and the conditional distribution of Y given X = 0 is Bern(0.04). Since conditioning on the value of X alters the distribution of Y , X and Y are not independent: learning whether or not the sampled individual is a current smoker gives us information about the probability that he will develop lung cancer. This example comes with an obligatory disclaimer. Although we have found that X and Y are dependent, we cannot make conclusions about whether smoking causes lung cancer based on this association alone. (Joseph K. Blitzstein, Jessica Hwang--Introduction to Probability)
asked 2022-09-17
Conditional Probability and Independence nonsense in a problem
The statement:
Suppose that a patient tests positive for a disease affecting 1% of the population. For a patient who has the disease, there is a 95% chance of testing positive, and for a patient who doesn't has the disease, there is a 95% chance of testing negative. The patient gets a second, independent, test done, and again tests positive. Find the probability that the patient has the disease.
The problem:
I can solve this problem, but I'm unable to understand what is wrong with the following:
Let T i be the event that the patient tests positive in the i-th test, and let D be the event that the patient has the disease.
The problem says that P ( T 1 , T 2 ) = 0.95 2 0.01 + 0.05 2 0.99 = 0.0115, because the tests are independent.
By law of total probability we know that:
P ( T 1 , T 2 ) = 0.95 2 0.01 + 0.05 2 0.99 = 0.0115
Replacing, and assuming conditional independence given D, we have:
P ( T 1 , T 2 ) = 0.95 2 0.01 + 0.05 2 0.99 = 0.0115
This is the correct result, but now let's consider that:
P ( T 1 , T 2 ) = P ( T 1 ) 2
We know that P ( T 1 , T 2 ) = P ( T 1 ) 2 for all i because of symmetry, so we have P ( T 1 , T 2 ) = P ( T 1 ) 2 . Again, by law of total probability:
P ( T 1 ) = 0.95 0.01 + 0.05 0.99 0.059
P ( T 1 ) = 0.95 0.01 + 0.05 0.99 0.059
So we have:
P ( T 1 , T 2 ) = P ( T 1 ) 2 0.059 2 0.003481
The second approach is wrong, but it seems legitimate to me, and I'm unable to find what's wrong.
Thank's for your help, you make self studying easier.
asked 2022-08-23
Determining correlation given 2 other correlation
Hi I'm given a rather ambigious question on correlations. My question is how do we determine the correlation between 2 varibles given their correlation with other variables?
Correlation between chocolate consumption per capita and number of Nobel laureates per 10 million persons for a broader list of 90 countries = 0.45
Perfect positive association bewteen chocolate consumption and chili consumption per capita (correlation = 1)
Correlation between chili consumption per capita and nobel laureates per 10 million persons: ?
1) > 0.45
2) = 0.45
3) < 0.45
4) cannot determine
asked 2022-08-13
What’s Wrong?
Motorcycles and Sour Cream In recent years, there has been a strong correlation between per capita consumption of sour cream and the numbers of motorcycle riders killed in noncollision accidents. Therefore, consumption of sour cream causes motorcycle fatalities.
asked 2022-11-15
True or false?
The amount of hours you work babysitting and the amount of money you earn- has correlation, but no causation
asked 2022-10-28
Correlation and heteroscedasticityI'm studying a dataset and observed a positive correlation between two variables, but when I plot them, it seems that they are heteroscedastics, what conclusions can I get from it ? (Can I really assume that the positive correlation is real ?)

New questions