Recent questions in Correlation And Causation

Correlation And Causation
Answered

Freddy Friedman
2022-07-23

Hi everyone I have a question about the following problem:

Events for a family: ${A}_{1}$ = ski, ${A}_{2}=$= does not ski, ${B}_{1}$ = has children but none in 8-16, ${B}_{2}$ = has some children in 8-16, and ${B}_{3}$ = has no children. Also, $P({A}_{1})=0.4$, $P({B}_{2})=0.35$, $P({B}_{1})=0.25$ and $P({A}_{1}\cap {B}_{1})=0.075$, $P({A}_{1}\cap {B}_{2})=0.245$. Find $P({A}_{1}\cap {B}_{1})=0.075$.

Here is my solution:

Since P(A1 and B1) = 0.075, P(A2 and B1) = 0.25-0.075= 0.175. Also since P(A1 and B2) = 0.245, P(A2 and B2) = 0.35 - 0.245 = 0.105. From this we can find P(A2 and B3) which is 0.6-0.175-0.105 = 0.32. But when I use the formula for independent events formula $P({A}_{2}\cap B3)=P({A}_{2})\ast P(B3)$ I get 0.24. Does this mean that the events are not independent? If so, how are these events not independent?

Correlation And Causation
Answered

Israel Hale
2022-07-22

What are some real life examples (data) in which high correlation:

1) implies causation

2) doesn't imply causation.

I know that there is a lot of data out there of weird correlations, like divorce rate and consuption of margarine, but the problem with this data is, that we don't really know if one is caused by the other, because nobody tested it, so we cannot strictly say that they're unrelated.

Correlation And Causation
Answered

Lillie Pittman
2022-07-21

causation

Let P := |corr(X,Y) > .5| let Q := exits a relation F: $X\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}Y$

Then the often stated line of correlation does not imply causation is simply! $Q\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}P$.

It is also true that causation does not imply correlation. So! $Q\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}P$

But $(P\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}Q)\vee (Q\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}P)$ is a tautology.

Correlation And Causation
Answered

scherezade29pc
2022-07-20

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 $cov(A,B)\ne 0$? 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.

Correlation And Causation
Answered

Tamara Bryan
2022-07-20

2. What is the difference between the independent and dependent variable? How do you determine which goes on which axis on your graph?

3. What are the four types of correlation?

4. How do they differ from one another?

5. In your own words, explain the difference between correlation and causation.

Correlation And Causation
Answered

wstecznyg5
2022-07-18

Provide examples.

Correlation And Causation
Answered

Libby Owens
2022-07-18

I understand the concept of correlation (similarity) between two signals. But I fail to understand how it translates to the formula that it does.

All the texts I have seen so far start with this formula and explain cross correlation, auto correlation, etc. None of them attempt to explain how the formula was derived in the first place.

Correlation And Causation
Answered

Shannon Andrews
2022-07-16

What is the relationship between (first) principal component(s) and the correlation matrix or the average correlation of the data. For example, in an empirical application I observe that the average correlation is almost the same as the ratio of the variance of the first principal component (first eigenvalue) to the total variance (sum of all eigenvalues).

Is there a mathematical relationship?