what is in stadistics a inverse correlation?
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A correlation in statistics represents a relationship between two variables.  A positive correlation indicates that the two variables move together, and the higher the correlation the more related they are.  A negative correlation shows that the two variables move in opposite directions. (For example, if you are looking at the correlation between the number of days it was sunny and the number of umbrellas sold, that would be an inverse correlation because if there are lots of sunny days, very few people will want umbrellas.)  The more negative the correlation, the stronger the relationship between two variables.  Correlation is on a scale from -1 to 1.  The closer to -1 or 1, the stronger the relationship.  A correlation of 0 indicates no relationship.  (So, if your correlation coefficicent is -1, the variables are very inversely related, but if it is just -.02 they are not very related at all)
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Just apply the formulas you gave and the definitions.\nNote that the mean of the measurements (usually mu) is L here.\n\nThe expected value of S(1) is, expanding and using the independence of L(1) and L(2), \n\nES(1) = E[0.5(L(1)+ L(2))]^2\n= (1/4){E[L(1)^2] + 2E[L(1)L(2)] + E[L(2)^2]}\n= (1/4){...............+ 2E[L(1)]E[L(2)] +  ........}\n= (1/4)[(sigma^2+L^2) + 2L^2 + (sigma^2+L^2)]\n= L^2 + sigma^2/2 = A + (1/2)sigma^2\n\nso S(1) is biased upwards (as an estimator of A).\n\nSimilarly \n\nES(2) = E[0.5(L^2(1) + L^2(2))] = (1/2){E[L(1)^2] + E[L(2)^2]}\n= (1/2)[(sigma^2+L^2) + (sigma^2+L^2)] = L^2 + sigma^2\n= A + sigma^2\n\nwhich is more biased tahn S(1).\nHow about S(3) = L(1)L(2)? Using the independence of L(1) and L(2), \n\nE[L(1)L(2)] = E[L(1)] E[L(2)] = L^2\n\nso S(3) is unbiased.
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One cool way that I have seen it derived is based on Jayne's Formalism.\n\nAssume we sample process, and measure the mean and standard devation of the samples. There are many possible distributions that will produce those exact mean and standard deviation. \n\nJayne's Formalism chooses the distribution which maximizes the entropy of the distribuiton. This is viewed mathematically as the distribution that makes the minimum number of assumptions regarding the distribution.\n\nI always thought that was kinda cool.
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umm none that im aware of, what kind of mathamatics leval are you looking at?
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additive inverse of any number 'a' simply means a number 'b' such that a+b=0, that is b = -a\n\nSo, if the complex number is 'p + iq', its additive inverse is: - p - iq\n\nIf you need to know abt multiplicative inverse, google on it, i am attaching a good link i know.
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inverse of f(x) is (x-1)/2\n\nworking:\nlet inverse of f(x) be y\n       2x+1  = y\n       2x    = y-1\n        x    = (y-1)/2\nthus, inverse of f(x)= (x-1)/2
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In mathematics, the inverse trigonometric functions are a set of relationships closely related to the trigonometric functions. The principal inverses are listed in the following table.\nName Usual notation Definition Range of x for real result Range of usual principal value\narcsine y = arcsin(x) x = sin(y) −1 to +1 −π/2 ≤ y ≤ π/2\narccosine y = arccos(x) x = cos(y) −1 to +1 0 ≤ y ≤ π\narctangent y = arctan(x) x = tan(y) all −π/2 < y < π/2\narccosecant y = arccsc(x) x = cosec(y), y = arcsin(1/x) −∞ to −1 and 1 to ∞ −π/2 ≤ y < 0, or\n0 < y ≤ π/2\narcsecant y = arcsec(x) x = sec(y), y = arccos(1/x) −∞ to −1 and 1 to ∞ 0 ≤ y < π/2, or\nπ/2 < y ≤ π\narccotangent y = arccot(x) x = cot(y), y = arctan(1/x) all −π/2 ≤ y < 0, or\n0 < y ≤ π/2\n\nThe notations sin−1, cos−1, etc are often used for arcsin, arccos, etc, but this notation sometimes causes confusion between (e.g.) arcsin(x) and 1/sin(x).\n\nIn computer programming languages the functions arcsin, arccos, arctan, are usually called asin, acos, atan.\n\nThe inverse trigonometric function atan2(y,x) is available in many computer programming languages. It is defined as r = arctan(y/x), taking:\n\n    * if x = y = 0, then r = indefinite,\n    * if x > 0 and y = 0, then r = 0,\n    * if x < 0 and y = 0, then r = π, else\n    * if y < 0, then −π < r < 0,\n    * if y > 0, then 0 < r < π.\n\nThis function is used to find the direction from one point to another in 2-dimension Euclidean space.
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conditional statement and its inverse
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When dealing with inverse variation there are two different equations you can use, y= k/x or first y/new y= new x/ first x. So in this case you can either do I= k/d^2 then do I= k/2d^2 and compare the I's. Another way you can do it is I original/ I new= 2d^2/ d^2 then you compare the first I and the second I. Unfortunetly in this case you dont have numbers so you just look at the fact that in the firt equation your dividing by the d^2 or the 2d^2 and you look that in the first one your just dividing by d^2 or 12 inches, while in the second your dividing by 2d^2 or 4d or 24 inches, which is more. Then when you divide by more than the I is smaller or lest intense.
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Spaced pair (A/B)\nCoincident or near-coincident pair (X-Y configuration)\nMid-Side (M-S) technique.
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I assume you mean invertible, not convertible.\n\nIt depends on how detailed you want to get. If you do not want to dig in extremely deeply, you can just do it by construction. \n\n1. A symmetric matrix M has an orthogonal decomposition\n\nM=O'DO\n\nwhere O is an orthogonal matrix, O'O=I, the identity, and D is a diagonal matrix with eigenvalues of M down the diagonal.\n\n2. If M is positive definite, then the diagonal elements of D are >0\n\n3. Produce the matrix \n\nA=O'(D^(-1))O\n\n\n4. Verify that A is the inverse of M\n\ni.e., \n\nA*M=M*A=I
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Any equation explaning the relationship between two or more observations (or data points) could be called a regression. It's really an extrapolation of the underlying line (or non-linear relationship) that explains the variance.\n\nPerhaps you could do a simple one- pick a stock and use the closing price over a period (say 3 weeks, 15 observations). Then try to come up with a formula to explain the pattern.\n\nActually, that one is kind of hard without stats software. But there are others- such as average temperatures in a given area...
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If your matrix is not square, then you can compute a generalized inverse matrix.  There are some links below.  There are many generalized inverses for matrices (other than those that are square and invertible; those only have one generalized inverse, which is its inverse).  But there is only one Moore-Penrose inverse for any given matrix.\n\nedit: reetz, I have already reported you for copying.  I suggest you back off.
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Sorry Baea, if the risk/return relationship had inverse correlation, your return would go down as you took on more risk. This is obviously not the case. Risk and return generally have a direct, positive correlation.
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it states that intensity of x rays at a point is inversely proportional to the square of distance of the point from the source
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Think about it -- if you are told that the soil at a given spot has a certain property (e.g., hydraulic conductivity, mineralogical composition, abundance of organic material, etc.), and you are asked for your best guess for that property in a soil that's a foot away, what would you say?  Would it be more likely that the unknown soil is similar to a nearby soil, or completely different?  If it's more likely that the nearby soil is similar, then the properties are spatially correlated.  \n\nIn fact, soil property do tend to be highly correlated spatially, with the correlation decreasing with increasing distance.  Correlations tend to persist over longer horizontal distances than vertical distances because the processes responsible to soil formation tend to create horizontal layers.  \n\nBecause it is a practical impossibility to measure soil properties at every point, these spatial correlations are very important when trying to model things like water or nutrient transport in soils.  One typically needs to know the values of specific properties at every grid point in the model, so statistical correlations developed from limited field data are used to infer the likely values of the properties at points where actual measurements are not available.
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(1) The correlation answers the STRENGTH of linear association between paired variables, say X and Y. On the other hand, the regression tells us the FORM of linear association that best predicts Y from the values of X.\n\n(2a) Correlation is calculated whenever:\n* both X and Y is measured in each subject and quantify how much they are linearly associated.\n* in particular the Pearson's product moment correlation coefficient is used when the assumption of both X and Y are sampled from normally-distributed populations are satisfied \n* or the Spearman's moment order correlation coefficient is used if the assumption of normality is not satisfied.\n* correlation is not used when the variables are manipulated, for example, in experiments.\n \n(2b) Linear regression is used whenever:\n* at least one of the independent variables (Xi's) is to predict the dependent variable Y. Note: Some of the Xi's are dummy variables, i.e. Xi = 0 or 1, which are used to code some nominal variables.\n* if one manipulates the X variable, e.g. in an experiment. \n\n\n(3) Linear regression are not symmetric in terms of X and Y. That is interchanging X and Y will give a different regression model (i.e. X in terms of Y) against the original Y in terms of X.\nOn the other hand, if you interchange variables X and Y in the calculation of correlation coefficient you will get the same value of this correlation coefficient.\n\n(4) The "best" linear regression model is obtained by selecting the variables (X's) with at least strong correlation to Y, i.e. >= 0.80 or <= -0.80 \n\n(5) The same underlying distribution is assumed for all variables in linear regression. Thus, linear regression will underestimate the correlation of the independent and dependent when they (X's and Y) come from different underlying distributions.