coefficient
Chemistry
A constant by which an algebraic term is multiplied.
Algebra
A quantity (usually a number) that remains the same in value within a problem.
Examples of coefficient in the following topics:

Calculating the Emission and Absorption Coefficients
 We can write the emission and absorption coefficients in terms of the Einstein coefficients that we have just examined.
 The emission coefficient $j_\nu$ has units of energy per unit time per unit volume per unit frequency per unit solid angle!
 The Einstein coefficient $A_{21}$ gives spontaneous emission rate per atom, so dimensional analysis quickly gives
 We can now write the absorption coefficient and the source function using the relationships between the Einstein coefficients as

95% Critical Values of the Sample Correlation Coefficient Table

Rank Correlation
 It is common to regard these rank correlation coefficients as alternatives to Pearson's coefficient, used either to reduce the amount of calculation or to make the coefficient less sensitive to nonnormality in distributions.
 However, this view has little mathematical basis, as rank correlation coefficients measure a different type of relationship than the Pearson productmoment correlation coefficient.
 The coefficient is inside the interval $[1, 1]$ and assumes the value:
 This means that we have a perfect rank correlation and both Spearman's correlation coefficient and Kendall's correlation coefficient are 1.
 For example, for the three pairs $(1, 1)$, $(2, 3)$, $(3, 2)$, Spearman's coefficient is $\frac{1}{2}$, while Kendall's coefficient is $\frac{1}{3}$.

A Physical Aside: Einstein coefficients
 The Einstein coefficients seem to say something magical about the properties of atoms, electrons and photons.
 It turns out that the relationships between Einstein coefficients (1917) are an example of Fermi's Golden Rule (late 1920s).

Coefficient of Correlation
 The most common coefficient of correlation is known as the Pearson productmoment correlation coefficient, or Pearson's $r$.
 Pearson's correlation coefficient when applied to a population is commonly represented by the Greek letter $\rho$ (rho) and may be referred to as the population correlation coefficient or the population Pearson correlation coefficient.
 Pearson's correlation coefficient when applied to a sample is commonly represented by the letter $r$ and may be referred to as the sample correlation coefficient or the sample Pearson correlation coefficient.
 This fact holds for both the population and sample Pearson correlation coefficients.
 Put the summary statistics into the correlation coefficient formula and solve for $r$, the correlation coefficient.

Overview of How to Assess StandAlone Risk
 It is able to accomplish this because the correlation coefficient, R, has been removed from Beta.
 Another statistical measure that can be used to assess standalone risk is the coefficient of variation.
 In probability theory and statistics, the coefficient of variation is a normalized measure of dispersion of a probability distribution.
 It is also known as unitized risk or the variation coefficient.
 A lower coefficient of variation indicates a higher expected return with less risk.

Hypothesis Tests with the Pearson Correlation
 We need to look at both the value of the correlation coefficient $r$ and the sample size $n$, together.
 We decide this based on the sample correlation coefficient $r$ and the sample size $n$.
 If the test concludes that the correlation coefficient is significantly different from 0, we say that the correlation coefficient is "significant."
 If the test concludes that the correlation coefficient is not significantly different from 0 (it is close to 0), we say that correlation coefficient is "not significant. "
 Our null hypothesis will be that the correlation coefficient IS NOT significantly different from 0.

Economic measures
 The Gini coefficient measures the inequality among values of a frequency distribution.
 A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income).
 A Gini coefficient of one (or 100%) expresses maximal inequality among values (for example where only one person has all the income).
 The Gini coefficient was originally proposed as a measure of inequality of income or wealth.
 The global income inequality Gini coefficient in 2005, for all human beings taken together, has been estimated to be between 0.61 and 0.68.

The Coefficient of Determination
 r2 is called the coefficient of determination. r2 is the square of the correlation coefficient , but is usually stated as a percent, rather than in decimal form. r2 has an interpretation in the context of the data:

Testing the Significance of the Correlation Coefficient
 The sample correlation coefficient, r, is our estimate of the unknown population correlation coefficient.
 If the test concludes that the correlation coefficient is significantly different from 0, we say that the correlation coefficient is "significant".
 If the test concludes that the correlation coefficient is not significantly different from 0 (it is close to 0), we say that correlation coefficient is "not significant".
 The test statistic t has the same sign as the correlation coefficient r.
 Suppose you computed the following correlation coefficients.