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Q: What does a positive correlation between variables x and y imply?

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Correlation is a measure of the degree to which two variables change together. Positive correlation means that the variables increase together and decrease together. Negative correlation means that one variable increases when the other decreases.Correlation does not imply causality.Correlation is a measure of the degree to which two variables change together. Positive correlation means that the variables increase together and decrease together. Negative correlation means that one variable increases when the other decreases.Correlation does not imply causality.Correlation is a measure of the degree to which two variables change together. Positive correlation means that the variables increase together and decrease together. Negative correlation means that one variable increases when the other decreases.Correlation does not imply causality.Correlation is a measure of the degree to which two variables change together. Positive correlation means that the variables increase together and decrease together. Negative correlation means that one variable increases when the other decreases.Correlation does not imply causality.

It suggests that there is very little evidence of a linear relationship between the variables.

correlation implies the cause and effect relationship,, but casuality doesn't imply correlation.

In linear correlation analysis, we identify the strength and direction of a linear relation between two random variables. Correlation does not imply causation. Regression analysis takes the analysis one step further, to fit an equation to the data. One or more variables are considered independent variables (x1, x2, ... xn). responsible for the dependent or "response" variable or y variable.

The correlation coefficient is a statistical measure of the extent to which two variables change. A correlation coefficient of -0.80 indicated that, on average, an increase of 1 unit in variable X is accompanied by a decrease of 0.8 units in variable Y. Note that correlation does not imply causation.

It is a measure of the strength of a linear relationship between one dependent variable and one or more explanatory variables.It is very important to recognise that a high level of correlation does not imply causation. Also, it does not provide information on non-linear relationships.

Pearson's correlation coefficient, also known as the product moment correlation coefficient (PMCC), and denoted by r, is a measure of linear agreement between two random variable. It can take any value from -1 to +1. +1 indicates a perfect positive linear relationship between the two variables, a value of 0 implies no linear relationship whereas a value of -1 shows a perfect negative linear relationship. A low (or 0) correlation does not imply that the variables are unrelated: it simply means a there is no linear relationship: a symmetric relationship will give a very low or zero value for r.The browser which we are compelled to use is not suited for any serious mathematical answer and I suggest that you look up Wikipedia for the formula to calculate r.

Correlation does not imply causality; the fact that there's a statistical association between two facts doesn't mean that one caused the other, in either direction. That said, it is true that there is a slightly positive correlation between breast cancer likelihood and the fact that a woman has not had any children by age 35.

No, it would not. It is possible that the statistical model is under-specified and that the variables being studied are all "caused" by another variable.

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!

As grade point average increases, the number of scholarship offers increases (apex)

Correlation analysis seeks to establish whether or not two variables are correlated. That is to say, whether an increase in one is accompanied by either an increase (or decrease) in the other most of the time. It is a measure of the degree to which they change together. Regression analysis goes further and seeks to measure the extent of the change. Using statistical techniques, a regression line is fitted to the observations and this line is the best measure of how changes in one variable affect the other variable. Although the first of these variables is frequently called an independent or even explanatory variable, and the second is called a dependent variable, the existence of regression does not imply a causal relationship.

It is saying that two occurrences happening in sequence does not have to mean that the first event was the cause of the second event.

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.

Usually the expression is employed in the context of the relationship between a dependent variable and another variable. The latter may or may not be independent: often it is time but that is not necessary. In some cases there is some indication that that there is a linear relationship between the two variables and that relationship is referred to as a trend.Note that a trend is not the same as causation. There may appear to be a strong linear trend between two variables but the variables may not be directly related at all: they may both be related to a third variable. Also, the absence of linear trends does not imply that the variables are unrelated: there may be non-linear relationships.

It is equivalent to dividing by ten to the equivalent positive power.

After calculating the mean and standard deviationvalues each value of the independent variable in the data, these are a few common tests that are used to further analyse the data and highlight its significance:1) Pearson Correlation Coefficient- This is to test for a strong/weak positive/negative correlation between the independent variable and the dependent variable. However, correlation does not necessarily imply causation.2) t-test- This post-hoc test is used to determine the level of significance of the difference between two sets of data.3) Chi2 test- This test tests for whether the difference in Expected and Observed values are significant or not.4) Analysis of variance (ANOVA)- This is like a massive t-test to test an entire set of data, without inflating the error of the analysis results. This is usually coupled with Tukey's Honest Significant Difference test.

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From none to completely. The regression or correlation coefficients measure the degree to which the two APPEAR to be related. However, there are some problems. First, if the model is mis-specified, you may find zero correlation even if there is complete determination. For example, suppose y = x^2 and you [wrongly] assume the reltionship is linear. If you carry out a regression of y on x between -a and a for any a, then the regression coefficient will turn out to be zero even though the dependent variable, y, is completely determined by x. Another mis-specification is where cause and effect are assigned the wrong way round because the system is not well understood.. Yet another problem is that a correlation does not necessarily imply a causal relationship. Each of the two variables may be independently affected by a third variable. For example, my age is probably highly correlated to the world population but neither affects the other. Both are affected by time.

the inverse relationship between price and demand

It you imply it to operating systems, there is no difference.

The term variables imply that those things may be changed or assigned with new value (at numerous places). This make the program harder to debug because it will be difficult to know when and where a global variable being changed and what was the consequence of that value changed.

juxtaposition - one may place two variables or expressions next to each other and imply an operator. e.g. a times b can be written ab.

A covalent bonds imply sharing electrons between atoms.

This is a rather confused question.The first issue is the assumption that there is an independent variable and a dependent variable. If your data comprise measurements of the height and mass (weight) of school children, which one is the independent variable? The answer is: neither. It is most likely to be age.A second issue is the very serious danger of confusing correlation with causality. Yes, statistics may show high correlation but that does not imply causality. A simplistic example from economics: correlation between companies with large profits and large investment in machinery. Profitability is required to enable the company to finance investment. Proper investment helps the company become more competitive and so generate more profits.Finally, consider the two variables X and Y. X is uniform on the interval [-p, p]; Y = X^2. The regression coefficient between X and Y is 0 but the relationship is far from non-existent. You need some educated guesses to find the correct statistics to make educated guesses!