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In the top figure the fraction 1/9000 in Excel is displayed. Although this number has a decimal representation that is an infinite string of ones, Excel displays only the leading 15 figures. In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum ...
The sum of the a 2-column and the b 2-column must be bigger than the sum within entries of the a 2-column, since all the entries within the b 2-column are positive (except when the population mean is the same as the sample mean, in which case all of the numbers in the last column will be 0). Therefore: The sum of squares of the distance from ...
These observations can be arranged into N column vectors, each with K entries, with the K×1 column vector giving the i-th observations of all variables being denoted (i=1,...,N). The sample mean vector x ¯ {\displaystyle \mathbf {\bar {x}} } is a column vector whose j -th element x ¯ j {\displaystyle {\bar {x}}_{j}} is the average value of ...
That is, = +, where, is the design matrix whose rows correspond to the observations and whose columns correspond to the independent or explanatory variables. The leverage score for the i t h {\displaystyle {i}^{th}} independent observation x i {\displaystyle {\boldsymbol {x}}_{i}} is given as:
Had the parameter space been finite and with a number of elements less than or equal to n, it might be possible to solve the linear equations in g(t) obtained by substituting the values of r and get solutions different from 0. For example, if n = 1 and the parameter space is {0.5}, a single observation and a single parameter value, T is not ...
Numbers '09 contains 262 built-in functions that can be used in formulas. [14] This contrasts with Excel 2007's 338 functions. [15] Many of the functions in Numbers are identical to those in Excel; missing ones tend to be related to statistics, although this area was greatly improved in Numbers '09. [16] Numbers '09 includes a system for ...
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The following example shows 20 observations of a process with a mean of 0 and a standard deviation of 0.5. From the Z {\displaystyle Z} column, it can be seen that X {\displaystyle X} never deviates by 3 standard deviations ( 3 σ {\displaystyle 3\sigma } ), so simply alerting on a high deviation will not detect a failure, whereas CUSUM shows ...