#Matlab weighted standard deviation manual#
In this way the effect of the weights can immediately be read off the results (and the manual calculations are very easy indeed). It's usually simple to make such a check by creating a small artificial dataset, most of whose values are zeros. The weighting options in Stata are wonderful, especially for probability weights, and I have used them: but I never use them without first conducting a detailed check with a calculation like the one here just to make sure I am interpreting the weights correctly. These calculations are straightforward to do in Stata or in any statistical software, so I omit the software-specific details. In weighted least squares, the fitting process includes the weight as an additional scale factor, which improves the fit. As a result, robust linear regression is less sensitive to outliers than standard linear regression. The square root of this result, equal to 17.28, is the standard deviation. This method is less sensitive to large changes in small parts of the data. If X is a matrix, then Z is a matrix of the same size as X, and each column of Z has mean 0 and. If X is a vector, then Z is a vector of z -scores. Their weighted mean square is obtained exactly as above: multiply each squared residual by its volume, add them up, and divide by the total volume. Z zscore (X) returns the z -score for each element of X such that columns of X are centered to have mean 0 and scaled to have standard deviation 1. The standard deviation is similarly computed: the residual prices are (23 - 36.81), (45 - 36.81), and (60 - 36.81). (In a now-deleted answer, showed us that the unweighted mean is 42.67 and the fweighted mean is 37.00.) Notice that this is not computed by either the fweights nor the pweights options. Thus, the average price per unit must equal 6137 / 116.7 = 36.81 Euros. The total volume is 100 K/month * 1 month + 11 K/month * 1 month + 55.7 K/month * 1 month = 166.7 K units. Jan product B: 11 K/month * 1 month * 45 Euros = 495 000 Eurosįeb product B: 55.7 K/month * 1 month * 60 Euros = 3342 000 Euros Then the totals paid in the three months are Jan product A: 100 K/month * 1 month * 23 Euros = 2300 000 Euros Each cell in Mdl1.DistributionParameters corresponds to a numeric vector containing the mean and standard deviation of each distribution, e.g., the mean and standard. There are four predictors and three class levels.
#Matlab weighted standard deviation software#
Adopting hypothetical units of measurement in order to make the numbers concrete, and pretending that all three records are to be summarized (even though they pertain to two different products), suppose the data give volumes in thousands of units sold per month and the prices are in Euros. By default, the software models the predictor distribution within each class as a Gaussian with some mean and standard deviation. When dealing with such weights, it's easiest to compute totals first. These are descriptive statistics intended to convey information about price ( p) where "volume" ( q) apparently describes how much was sold at each price.
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