# Does 0 correlation mean independence?

## Does 0 correlation mean independence?

A correlation of 0 does not imply independence. When people use the term correlation, they are actually referring to a specific type of correlation called “Pearson” correlation. It measures the degree to which there is a linear relationship between the two variables.

### Is correlation and independence the same?

Correlation and independence If the variables are independent, Pearson’s correlation coefficient is 0, but the converse is not true because the correlation coefficient detects only linear dependencies between two variables. are jointly normal, uncorrelatedness is equivalent to independence.

How much is the correlation between factor scores of factors based on orthogonal rotation?

This can indicate whether or not to use an orthogonal rotation. Please see my guide to EFA. Correlations between factors should not exceed 0.7. A correlation greater than 0.7 indicates a majority of shared variance (0.7 * 0.7 = 49% shared variance).

Why does correlation not imply independence?

Correlation measures linear association between two given variables and it has no obligation to detect any other form of association else. So those two variables might be associated in several other non-linear ways and correlation could not distinguish from independent case.

## Does no association mean independence?

H0: There is no association between rows and columns; they are independent.

### Does independence imply zero covariance?

Zero covariance – if the two random variables are independent, the covariance will be zero.

What is a zero correlation?

A value of zero indicates that there is no relationship between the two variables. When interpreting correlation, it’s important to remember that just because two variables are correlated, it does not mean that one causes the other.

What is orthogonal rotation in factor analysis?

Orthogonal rotations constrain the factors to be uncorrelated. Although often favored, in many cases it is unrealistic to expect the factors to be uncorrelated, and forcing them to be uncorrelated makes it less likely that the rotation produces a solution with a simple structure.

## What does a zero correlation implies?

A correlation coefficient greater than zero indicates a positive relationship while a value less than zero signifies a negative relationship. A value of zero indicates no relationship between the two variables being compared.

### Can independents be correlated variables?

So, yes, samples from two independent variables can seem to be correlated, by chance.

Can independent variables be correlated?

Multicollinearity occurs when independent variables in a regression model are correlated. This correlation is a problem because independent variables should be independent. If the degree of correlation between variables is high enough, it can cause problems when you fit the model and interpret the results.

What is the difference between statistical independence and correlation?

Correlation can be used to quantify the linear dependency of two variables. It cannot capture non-linear relationship between variables. Independent variables has NIL correlation, r=0. If r=0, indicates NIL correlation but not a non dependency (Independency), they can be dependent.

## What is an example of a zero correlation?

A zero correlation exists when there is no relationship between two variables. For example there is no relationship between the amount of tea drunk and level of intelligence.

### What are the different types of rotation in factor analysis?

Two main types of rotation are used: orthogonal when the new axes are also orthogonal to each other, and oblique when the new axes are not required to be orthogonal to each other.

What is the purpose of rotation in factor analysis?

Rotations minimize the complexity of the factor loadings to make the structure simpler to interpret. Factor loading matrices are not unique, for any solution involving two or more factors there are an infinite number of orientations of the factors that explain the original data equally well.

What is the difference between orthogonal and oblique rotation in factor analysis?

The major difference between orthogonal and oblique rotation is that the orthogonal rotation preserves the orthogonality of the factors (i.e., the correlations between them remain equal to zero), whereas the oblique rotation allows the new factors to be correlated.

## What is the difference between varimax and Oblimin rotation?

Factor rotation methods preserve the subspace and give you a different basis for it. Varimax returns factors that are orthogonal; Oblimin allows the factors to not be orthogonal.

### When two or more independent variables are highly correlated?

In other words, multicollinearity can exist when two independent variables are highly correlated. It can also happen if an independent variable is computed from other variables in the data set or if two independent variables provide similar and repetitive results.

Are independent variables always uncorrelated?

This means that independent random variables are always uncorrelated, but uncorrelated random variables may not be independent. In other words, independence is a stronger statement than uncorrelation.

What is meant by zero correlation?

## Is rotation necessary in factor analysis?

An important feature of factor analysis is that the axes of the factors can be rotated within the multidimensional variable space.

### When should you use varimax rotation?

In statistics, a varimax rotation is used to simplify the expression of a particular sub-space in terms of just a few major items each. The actual coordinate system is unchanged, it is the orthogonal basis that is being rotated to align with those coordinates.

Should I use varimax or Promax rotation?

Varimax rotation is orthogonal rotation in which assumption is that there is no intercorrelations between components. Promax rotation requires large data set usually < 150. If you hav small data set, you can use oblimin rotation.

Does a zero correlation imply independence?

Zero correlation implies independence if the variables are multivariate normal. This is not the same as each variable being normal – see here for some scatterplots of zero-correlated but dependent normal variables (each variable is individually normal) – Glen_b -Reinstate Monica Oct 31 ’15 at 8:55

Zero correlation will indicate no linear dependency, however won’t capture non-linearity. Typical example is uniform random variable x, and x 2 over [-1,1] with zero mean. Correlation is zero but clearly not independent. Show activity on this post. Let X be any random variable. Let P { I = 1 } = P { I = − 1 } = 1 / 2, with I independent of X.

## What does it mean when there is no correlation?

Does zero correlation mean independence? Solution No, zero correlation does not mean independence. If there is zero correlation (rxy=0), it means the two variables are uncorrelated and there is no linear relation between them. However, other types of relations may be there and they may not be independent.

### Are X and Y uncorrelated but not independent?

(Thus, Y = ± X, each with probability 1 / 2, independent of the value of X .) Then X and Y are uncorrelated but not independent. We could replace I by any zero-mean random variable independent of X. [Could someone please tell me how to insert that first equation correctly?]