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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 whether
- the first causes the second,
- the second causes the first,
- they cause one another, or
- they 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.
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What does correlation of data mean?
Correlation of data means that two different variables are linked in some way. This might be positive correlation, which means one goes up as the other goes up (for instance, people who are heavier tend to be taller) or negative correlation, which means one goes up as the other goes down (for instance, people who are older tend to play video games less often). Correlation just means a link. It means that knowing one variable (a person is really tall) is enough to make a guess at the other one (that person is probably also pretty heavy). Note that there is a very common mistake people make about correlation, and this needs to be addressed. In short, the mistake is "correlation implies causation". It doesn't. If I have data which shows people who volunteer more often tend to be happier, I cannot then say "volunteer. It makes you happy!" because correlation doesn't imply causation - it might be that if you're happy you're more likely to volunteer, and the causation is the other way around. Or it might be that if you're rich, you're both more likely to be happy, and more likely to volunteer, so the data is affected by a different variable entirely.
Why do economists often say that correlation does not necessarily imply causality?
It's not only economists that offer this warning. It's true anywhere that correlation coefficients are to be interpreted. Let me offer an example from psychology. In many populations there's a significant correlation between the shoe sizes of people and their intelligence quotients. But no-one would say that increasing a person's shoe size would increase their intelligence!
What must be present in order to say that a correlation exists?
A relationship between variables
What correlation indicates a strong positive straight line relationship?
If by positive you mean that an increase in the independent variable is accompanied by an increase in the dependent variable then this will be indicated by a correlation close to one. What is considered 'close to one' depends on the field of study. In some fields where it can be quite difficult to establish relationships between variables a correlation of, say, 0.35 might be considered important, provided of course that it has been shown to be statistically significant.
How would you interpret the findings of a correlation study that reported a linear correlation coefficient of -0.13?
There is not enough information to say much. To start with, the correlation may not be significant. Furthermore, a linear relationship may not be an appropriate model. If you assume that a linear model is appropriate and if you assume that there is evidence to indicate that the correlation is significant (by this time you might as well assume anything you want!) then you could say that the dependent variable decreases by 0.13 units for every unit change in the independent variable - within the range of the independent variable.
How correlation differs from causeation?
Correlation means that when one quantity increases, the other tends to increase as well. Causation means that the increase in one quantity CAUSES an increase in another quantity. It is a common error to assume that correlation implies causation; sometimes correlation is caused by causation, but not always. For example: let's say that the price of sugar gradually went up over the last 10 years; so did the price of cooking oil. Neither one is caused by the increase of the other; rather, they are both part of a larger tendency, namely, inflation. As another example, during the same 10-year period, the population of your country gradually increased. This is independent of the inflation; both prices and population simply tend to increase over time.
What does correlation of data mean?
Correlation of data means that two different variables are linked in some way. This might be positive correlation, which means one goes up as the other goes up (for instance, people who are heavier tend to be taller) or negative correlation, which means one goes up as the other goes down (for instance, people who are older tend to play video games less often). Correlation just means a link. It means that knowing one variable (a person is really tall) is enough to make a guess at the other one (that person is probably also pretty heavy). Note that there is a very common mistake people make about correlation, and this needs to be addressed. In short, the mistake is "correlation implies causation". It doesn't. If I have data which shows people who volunteer more often tend to be happier, I cannot then say "volunteer. It makes you happy!" because correlation doesn't imply causation - it might be that if you're happy you're more likely to volunteer, and the causation is the other way around. Or it might be that if you're rich, you're both more likely to be happy, and more likely to volunteer, so the data is affected by a different variable entirely.
What can you say about the correlation coefficient and the correlation description of the correlation when the points lie exactly on either vertical line or horizontal line?
The observed relationship indicates that the a one-to-one correspondence exists between the variables of interest. In effect, the value of the obtained r-value is -1 or 1.
What does it mean if two variables have a negative correlation?
A positive correlation between two variables, say X and Y, means that if one increases, the other will too. No correlation means that they are not related. A negative correlation means that as one increases, the other decreases. Normally you will see this in studies as "Recent studies demonstrated a positive correlation between eating too much and obesity." Or, "recent studies demonstrate a negative correlation between a healthy, balanced diet and obesity".
What can you say about the relationship between a correlation r and the slope b of the least squares line form of data?
You can say that the correlation is positive if and only if the slope is positive. The correlation is zero if and only if the slope is zero. And the correlation is negative if and only if the slope is negative. On the other hand, slope does change when your measurement units change, while correlation does not change. (For example, the correlation between height in inches and weight in pounds will be the same as the correlation between height in centimeters and weight in kilograms, as long as both sets of measurements were taken on the same observations.)
What is a positive negative correlation?
Correlation determines relationship between two variables. For example changes in one variable influence another variable, we can say that there is a correlation between the two variables. For example, we can say that there exists a correlation between the number of hours spent on reading and preparation and the scores obtained in the examination. One can infer that higher the amount of time spent on preparation may result in better performance in examination leading to higher scores. Hence the above is a case of positive correlation. If an increase in independent variable leads to an increase in dependent variable, it is a case of positive correlation. On the other hand if an increase in independent variable leads to a reduction in dependent variable, it is a case of negative correlation. An example for negative correlation could be the relationship between the age advancement and resistance to diseases. As age advances, resistance to disease reduces.
Why do economists often say that correlation does not necessarily imply causality?
It's not only economists that offer this warning. It's true anywhere that correlation coefficients are to be interpreted. Let me offer an example from psychology. In many populations there's a significant correlation between the shoe sizes of people and their intelligence quotients. But no-one would say that increasing a person's shoe size would increase their intelligence!
When the points on a graph tend to scatter randomly you say they indicate?
No Correlation
What is more correct negative correlation or inverse correlation?
Those are both perfectly valid terms, which you would use according to context. You might say, for example, that obesity has a negative correlation to longevity. And in an aqueous solution there is an inverse correlation between hydrogen ions and hydroxide ions.
When a maths question say show that what does it mean?
It means proves and/or demonstrate.
Why correlation does not guarantee causation?
Correlation shows a possible relationship between two random variables. It does not say one variable causes a result in another. It further is wrong to conclude if event B occurs after event A, then A caused B. An example from Darrell Huff's book, "How to Lie with Statistics": A correlation is found between smoking and low grades. Does that mean that smoking causes low grades, or low grades cause people to smoke? It seems a good deal more probable that neither of these things produced the other, but that both are a product of some third factor. The inches of rain in Spain may correlate with the temperatures in Mexico, only because there is similarity of seasons. Small or improperly taken sample may show excellent correlations. The cumulative sum of births in China in one year (each day the total is the sum of all other previous days) will show an excellent correlation with the cumulative sum of rainfall in Germany. This correlation is because the the same values are repeated in the cumulative sums.
What must be present in order to say that a correlation exists?
A relationship between variables
