# When Y is a linear function of X then the correlation coefficient between X and Y is?

## When Y is a linear function of X then the correlation coefficient between X and Y is?

The size of |r| indicates the strength of the linear relationship between x and y: If |r| is near 1 (that is, if r is near either 1 or −1) then the linear relationship between x and y is strong. If |r| is near 0 (that is, if r is near 0 and of either sign) then the linear relationship between x and y is weak.

**What are the 5 types of correlation?**

Types of Correlation:

- Positive, Negative or Zero Correlation:
- Linear or Curvilinear Correlation:
- Scatter Diagram Method:
- Pearson’s Product Moment Co-efficient of Correlation:
- Spearman’s Rank Correlation Coefficient:

**When there is no correlation between X and Y then?**

A negative correlation implies a negative relationship between X and Y: as X increases, Y decreases. A correlation of zero implies that there is no linear relationship between X and Y (see below for details).

### What is the correlation between X and Y in regression?

By design, we have perfect correlation of x and y: However, when we do a regression, we are looking for a function that relates x and y so the results of the regression coefficients depend on which one we use as the dependent variable, and which we use as the independent variable.

**What is the formula for linear correlation coefficient?**

Linear Correlation Coefficient Formula. The linear correlation coefficient formula is given by the following formula. Sample Correlation Coefficient Formula [latex]large r_{xy}=frac{S_{xy}}{S_{x}S_{y}}latex] Here, S x and S y are the sample standard deviations, and S xy is the sample covariance. Population Correlation Coefficient Formula

**Is the Pearson correlation coefficient of X and Y the same?**

The Pearson correlation coefficient of x and y is the same, whether you compute pearson(x, y) or pearson(y, x). This suggests that doing a linear regression of y given x or x given y should be the Stack Exchange Network

#### What does the covariance of X and y necessarily reflect?

The covariance of X and Y necessarily reflects the units of both random variables. It is helpful instead to have a dimensionless measure of dependency, such as the correlation coefficient does. Let X and Y be any two random variables (discrete or continuous!) with standard deviations σ X and σ Y, respectively.