Examples of coefficient of variation in the following topics:
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- Another statistical measure that can be used to assess stand-alone 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.
- The coefficient of variation, an example of which is plotted in this graph, can be used to measure the ratio of volatility to expected return.
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- In simple cases, for example, where the coefficients $A_1(t)$ and $A_2(t)$ are constants, the equation can be analytically solved.
- (Either the method of undetermined coefficients or the method of variation of parameters can be adopted.)
- In general, the solution of the differential equation can only be obtained numerically.
- However, there is a very important property of the linear differential equation, which can be useful in finding solutions.
- then any arbitrary linear combination of $y_1(t)$ and $y_2(t)$ —that is, $y(x) = c_1y_1(t) + c_2 y_2(t)$ for constants $c_1$ and $c_2$—is also a solution of that differential equation.
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- The coefficient of determination provides a measure of how well observed outcomes are replicated by a model.
- The coefficient of determination (denoted $r^2$) is a statistic used in the context of statistical models.
- The coefficient of determination is actually the square of the correlation coefficient.
- Therefore, the coefficient of determination is $r^2 = 0.6631^2 = 0.4397$.
- Interpret the properties of the coefficient of determination in regard to correlation.
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- 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:
- r2 , when expressed as a percent, represents the percent of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression (best fit) line.
- 1-r2 , when expressed as a percent, represents the percent of variation in y that is NOT explained by variation in x using the regression line.
- Approximately 44% of the variation (0.4397 is approximately 0.44) in the final exam grades can be ex- plained by the variation in the grades on the third exam, using the best fit regression line.
- Therefore approximately 56% of the variation (1 - 0.44 = 0.56) in the final exam grades can NOT be explained by the variation in the grades on the third exam, using the best fit regression line.
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- Limits involving infinity can be formally defined using a slight variation of the $(\varepsilon, \delta)$-definition.
- Limits involving infinity can be formally defined using a slight variation of the $(\varepsilon, \delta)$-definition.
- If the degree of $p$ is greater than the degree of $q$, then the limit is positive or negative infinity depending on the signs of the leading coefficients;
- If the degree of $p$ and $q$ are equal, the limit is the leading coefficient of $p$ divided by the leading coefficient of $q$;
- If the degree of $p$ is less than the degree of $q$, the limit is $0$.
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- 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
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- A rank correlation coefficient measures the degree of similarity between two rankings and can be used to assess the significance of the relation between them.
- A rank correlation coefficient can measure that relationship, and the measure of significance of the rank correlation coefficient can show whether the measured relationship is small enough to be likely to be a coincidence.
- They are best seen as measures of a different type of association rather than as alternative measure of the population correlation coefficient.
- However, in the extreme case of perfect rank correlation, when the two coefficients are both equal (being both $+1$ or both $-1$), this is not in general so, and values of the two coefficients cannot meaningfully be compared.
- This graph shows a Spearman rank correlation of 1 and a Pearson correlation coefficient of 0.88.
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- Genetic variation is a measure of the variation that exists in the genetic makeup of individuals within population.
- Genetic variation is a measure of the genetic differences that exist within a population.
- The genetic variation of an entire species is often called genetic diversity.
- Populations of wild cheetahs have very low genetic variation.
- An enormous amount of phenotypic variation exists in the shells of Donax varabilis, otherwise known as the coquina mollusc.
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- 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).