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The variance of a random variable is the expected value of the squared deviation from the mean of , : This definition encompasses random variables that are generated by processes that are discrete, continuous, neither, or mixed. The variance can also be thought of as the covariance of a random variable with itself:
The larger the variance, the greater risk the security carries. Finding the square root of this variance will give the standard deviation of the investment tool in question. Financial time series are known to be non-stationary series, whereas the statistical calculations above, such as standard deviation, apply only to stationary series.
Explained variation. In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation ( dispersion) of a given data set. Often, variation is quantified as variance; then, the more specific term explained variance can be used. The complementary part of the total variation is called unexplained ...
e. In statistics, the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean. The variance function is a measure of heteroscedasticity and plays a large role in many settings of statistical modelling. It is a main ingredient in the generalized linear model framework and a tool used in non ...
Analysis of variance. Analysis of variance ( ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher.
Variance inflation factor. In statistics, the variance inflation factor ( VIF) is the ratio ( quotient) of the variance of a parameter estimate when fitting a full model that includes other parameters to the variance of the parameter estimate if the model is fit with only the parameter on its own. [ 1] The VIF provides an index that measures ...
Sum ← Sum + x. SumSq ← SumSq + x × x. Var = (SumSq − (Sum × Sum) / n) / (n − 1) This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to ...
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [ 1] Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered.
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