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Basic Univariate Statistics
Published in Jhareswar Maiti, Multivariate Statistical Modeling in Engineering and Management, 2023
If we denote the first, second and third quartiles as Q1, Q2, and Q3, then the inter-quartile range (IQR) is Q3–Q1. But the measure that is widely used to define variability is standard deviation. Standard deviation is the square root of variance of a given data set where variance is the average squared deviation of the data points from their mean. Consider a sample of size n with mean x¯. The variance of the sample, denoted by s2, is computed using the following formula:s2=1n−1∑i=1n(xi−x¯)2
Cognitive Internet of Things
Published in J P Patra, Gurudatta Verma, Cognitive IoT, 2022
In statistics, the mean squared error or mean squared deviation of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors – that is, the average squared difference between the estimated values and what is actually estimated. Multiple linear regression can model more complex relationship, which comes from various features together. They should be used in cases where one variable is not evident enough to map the relationship between the independent and the dependent variable.
Analysis of Variance
Published in Nicholas P. Cheremisinoff, Practical Statistics for Engineers and Scientists, 2020
The mean squared deviations are the variances (i.e., column and residual). The ratio between the column mean squared deviations and that of the residual constitutes an F-ratio. That is, the F-value is the ratio between the explained and unexplained variances. For a large F, the factor is significant (the level of significance is the probability value, P).
Design of advanced intrusion detection systems based on hybrid machine learning techniques in hierarchically wireless sensor networks
Published in Connection Science, 2023
Gebrekiros Gebreyesus Gebremariam, J. Panda, S. Indu
Mean squared error (MSE). Mean squared error (MSE) measures the amount of error in statistical machine learning models for computing the position and distance of the wormhole attack between two points as in Equation (11). It assesses the average squared difference between the observed and predicted values of each sensor node's position and location, having its unique identity to detect routing attacks. When a model has no error, the MSE equals zero. As model error increases, its value increases. The mean squared error is also known as the mean squared deviation (MSD). Where. , and is the ith observed values., and are the corresponding predicted values.n is the number of observations.
On volatile growth: Simple fitting of exponential functions taking into account values of every observation with any signs, applied to readily calculate a novel covariance-invariant CAGR
Published in The Engineering Economist, 2023
(b) Nonlinear regression: Nonlinear least-squares regression (e.g., Seber & Wild, 2003) applied to the growth model might be viewed the best approach to deal with volatility since it gives the best fit to the growth model in the minimum least-squares sense. The sum of squared deviations between observations and model are a measure of performance and volatility. However, the method is experienced not easy to apply in general, unless a software package is used. Although the approach rarely fails, it may fail under certain conditions, and it requires needs the highest computational effort to capture wrong results. One major source for failures is the need of a reasonably good initial guess of the parameters to force an iteration algorithm to converge. The algorithm requires to find a single root of a polynomial of order which may become ambiguous for a high number of observations when the polynomial tends to have several local minima and maxima. Further, a high number of observations generally implicates steep gradients that the iteration has to cope with, resulting in an undesired sensitivity.—The problems can be overcome using linearizing transformations such as the log-linear model discussed in Section 2.5 (a), featuring no limitation on the number of observed values—maybe the biggest advantage of this method.
A parametric study on the dynamic ultimate strength of a stiffened panel subjected to wave- and whipping-induced stresses
Published in Ships and Offshore Structures, 2021
George Jagite, Fabien Bigot, Quentin Derbanne, Šime Malenica, Hervé Le Sourne, Patrice Cartraud
Figures 12 and 13 are presenting the dynamic load factors obtained for the wave load and wave+whipping load scenarios, respectively. For each whipping period, six different wave periods have been used. Hence, in order to simplify the representation of the results, the dynamic load factors obtained for wave+whipping scenarios are presented as the mean value, shown as a solid line, and the standard deviation of the results, shown as the shaded area. The mean value is simply the sum of the results divided by the number of elements (i.e. ). While the standard deviation is the square root of the average of the squared deviations from the mean (i.e. ).