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A strong positive correlation does not prove causation.
People only get sunburned during daylight hours. Sundials only work during daylight hours. Therefore sundials cause sunburns.
The above sentences show how absurd such predicate thinking could be.
Simply because two events usually occur at the same time does not mean they are related.
One man found a perfect correlation between the price of whiskey and Chicago school teachers' salaries. No possible relationship could possibly exist except the rate of prosperity and inflation.
Causation is difficult to prove.
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Does Correlation alone complicates causation?
does not prove
Why can one not say that correlation proves causation?
You cannot say it because it is not true.First of all, correlation simple states that two variables change so in such a way that a change in one leads to a change in the other. Changes of the same magnitude in the first variable brings about the consistent changes in the second variable. There is no way to determine whetherthe first causes the second,the second causes the first,they cause one another, orthey are both caused by an unknown third variable.A simplistic example from economics will illustrate the first three. Capital investment (spending on machinery, for example) by a company and the company's profits are positively correlated. But the direction of the causal relationship is not simple to establish. A company needs to be profitable before it can raise the money to invest. On the other hand, by investing well, it becomes more competitive and so is more profitable.As an example of the fourth type, in the UK there is a significant correlation between the sales of ice cream and swimming accidents. This is not because ice cream causes swimming accidents nor that ice cream is caused (?) by swimming accidents. The hidden variable is hot weather. People are more likely to eat ice cream. They are also more likely to go to beaches.The converse of the statement in the question is also untrue: the absence of correlation does not prove that there is no causation. Suppose you have one variable X which is defined on a the interval (-p, p) for some positive number a. And then let Y = X^2. There is clearly a perfect relationship between the two variables. However, if the X-values are symmetric, then the symmetry of the relationship ensures that the correlation coefficient is 0! No correlation but a perfect relationship.
What should be the value of R squared for a good correlation?
1 is the best, 0 is the worst. So the closer you are to 1, the better. Beyond that, I can't tell you a specific cutoff. It depends on what you're trying to prove. Sometimes, you won't settle for anything less than 0.99. Other times, you'll be tickled pink to get a 0.3. But the whole point of an R-squared is to give a numerical representation of how close the correlation is without resorting to vague terms like "good correlation". Publish the value of R-squared and let the readers make their own decisions about whether it's "good" or "bad".
What are two possible outcomes to prove an experiments hypothesis?
To prove the hypothesis. To disprove the hypothesis.
How do you prove something is prime in discrete structures?
you dont silly :)
