 |
Business | Industries | Finance | Tax |
| Index: > A B C D E F G H I J K L M N O P Q R S T U V W X Y Z |
|
|||||
| First Prev [ 1 2 ] Next Last |
The result obtained is equivalent to dividing the covariance between the two variables by the product of their standard deviations. In general the quantity of a correlation coefficient is the square root of the coefficient of determination (r2), which is the ratio of explained variation to total variation:
where:
The correlation coefficient adds a sign to show the direction of the relationship. The formula for the Pearson coefficient conforms to this definition, and applies when the relationship is linear.
The coefficient ranges from -1 to 1. A value of 1 shows that a linear equation describes the relationship perfectly and positively, with all data points lying on the same line and with Y increasing with X. A score of -1 shows that all data points lie on a single line but that Y increases as X decreases. A value of 0 shows that a linear model is inappropriate – that there is no linear relationship between the variables.
The Pearson coefficient is a statistic which estimates the correlation of the two given random variables.
The linear equation that best describes the relationship between X and Y can be found by linear regression. If X and Y are both normally distributedProbability density function of Gaussian distribution (bell curve). The normal distribution is an extremely important probability distribution in many fields. It is also called the Gaussian distribution especially in physics and engineering. It is actuall, this can be used to "predict" the value of one measurement from knowledge of the other. That is, for each value of X the equation calculates a value which is the best estimate of the values of Y corresponding the specific value of X. We denote this predicted variable by Y.
Any value of Y can therefore be defined as the sum of Y′ and the difference between Y and Y′:
The varianceThis article is about mathematics. Alternate meaning: variance (land use). In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically of Y is equal to the sum of the variance of the two components of Y:
Since the coefficient of determination implies that sy.x2 = sy2(1 − r2) we can derive the identity
The square of r is conventionally used as a measure of the strength of the association between X and Y. For example, if the coefficient is .90, then 81% of the variance of Y is said to be explained by the changes in X and the linear relation between X and Y.
r is a parametric statisticParametric inferential statistical methods are mathematical procedures for statistical hypothesis testing which assume that the distributions of the variables being assessed have certain characteristics. Analysis of variance assumes that the underlying di. It assumes that the variables being assessed are normally distributed. If this assumption is violated, a non-parametricNon-parametric (or distribution-free inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the frequency distributions of the variables being assessed. alternative such as Spearman's ρIn statistics, Spearman's rank correlation coefficient often denoted by the Greek letter ρ (rho), is a non-parametric measure of correlation that is, it assesses how well an arbitrary monotonic function could describe the relationship between two vari may be more successful in detecting a linear relationship.
| Politics | Business | Finance |
 |
 |
 |
|