Changes

where the summation is made over the n sample values available and where

where the summation is made over the n sample values available and where

* ''x''_''i'' = ith observation of the first variable

* <math> x_i</math> = ith observation of the first variable

* ''y''_''i'' = corresponding ith observation of the second variable

* <math> y_i</math> = corresponding ith observation of the second variable

* ''x, y'' = corresponding sample (arithmetic) means

* <math> \bar{x}, \bar{y}</math> = corresponding sample (arithmetic) means

Many useful types of correlation other than simple linear correlation exist. Correlation based on the ranks (numerical ordering) of measurements of two variables is an important alternative for simple linear correlation when the number of samples is small and/or the joint distribution of the two variables is not simple. Multiple correlation and partial correlation are useful when studying relationships involving more than two variables. Cross correlation and autocorrelation are important to the analysis of repeated patterns observed in time and space, such as depth-related data recorded from geological stratigraphic sequences. Autocorrelation can also be used to measure the degree of similarity among [[porosity]] values measured at different locations.

Many useful types of correlation other than simple linear correlation exist. Correlation based on the ranks (numerical ordering) of measurements of two variables is an important alternative for simple linear correlation when the number of samples is small and/or the joint distribution of the two variables is not simple. Multiple correlation and partial correlation are useful when studying relationships involving more than two variables. Cross correlation and autocorrelation are important to the analysis of repeated patterns observed in time and space, such as depth-related data recorded from geological stratigraphic sequences. Autocorrelation can also be used to measure the degree of similarity among [[porosity]] values measured at different locations.

The simplest type of regression analysis involves fitting a straight line between two variables (Figure 1). In this case, one of the quantities is called the ''independent or predictor variable'' (usually denoted x), while the other is called the ''dependent or predicted variable'' (usually denoted y). This approach is often referred to as ''simple linear regression,'' or y-on-x regression. It leads to the development of an empirical straight-line relationship between the two variables and has the following form:

The simplest type of regression analysis involves fitting a straight line between two variables (Figure 1). In this case, one of the quantities is called the ''independent or predictor variable'' (usually denoted x), while the other is called the ''dependent or predicted variable'' (usually denoted y). This approach is often referred to as ''simple linear regression,'' or y-on-x regression. It leads to the development of an empirical straight-line relationship between the two variables and has the following form:

:<math>\mathbf{Equation}</math>

:<math>\widehat{y} = ax + b</math>

where

where