Correlation « PreviousHomeNext » The correlation is one of the most common and most useful statistics. A correlation is a single number that describes the degree of relationship between two variables. Let's work through an example to show you how this statistic is computed. Correlation Example Let's assume that we want to look at the relationship between two variables, height (in inches) and self esteem. Now, let's take a quick look at the histogram for each variable: And, here are the descriptive statistics: Finally, we'll look at the simple bivariate (i.e., two-variable) plot: You should immediately see in the bivariate plot that the relationship between the variables is a positive one (if you can't see that, review the section on types of relationships) because if you were to fit a single straight line through the dots it would have a positive slope or move up from left to right. What does a "positive relationship" mean in this context? Calculating the Correlation report this ad The Correlation Matrix
List of probability distributions Many probability distributions are so important in theory or applications that they have been given specific names. Discrete distributions[edit] With finite support[edit] With infinite support[edit] Continuous distributions[edit] Supported on a bounded interval[edit] Supported on semi-infinite intervals, usually [0,∞)[edit] Supported on the whole real line[edit] With variable support[edit] The generalized extreme value distribution has a finite upper bound or a finite lower bound depending on what range the value of one of the parameters of the distribution is in (or is supported on the whole real line for one special value of the parameterThe generalized Pareto distribution has a support which is either bounded below only, or bounded both above and belowThe Tukey lambda distribution is either supported on the whole real line, or on a bounded interval, depending on what range the value of one of the parameters of the distribution is in.The Wakeby distribution Joint distributions[edit]
Living in the Present Is a Disorder | Wired Opinion The opening titles sequence of Game of Thrones conveys a presentist style. Image: HBO We’re living in the now, we no longer have a sense of future direction, and we have a completely new relationship to time. That’s the premise of Douglas Rushkoff’s latest book Present Shock: When Everything Happens Now, a sort-of update to Alvin Toffler’s influential Future Shock from decades ago. I met Rushkoff back when I was editor of the cyberpunk magazine Mondo 2000, when he was working on his first book about digital culture. But the original publishers canceled that book, thinking the internet was a fad and would be over by the time it hit stands. The internet is still with us (to put it mildly) … so Rushkoff’s latest book is for everybody. R.U. Douglas Rushkoff: Narrative Collapse is what happens when we no longer have time in which to tell a story. Think Game of Thrones. Remote controls and DVRs give us the ability to break down narratives — particularly the more abusive ones. R.U. R.U. R.U.
Correlation and dependence In statistics, dependence is any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. Several sets of (x, y) points, with the Pearson correlation coefficient of x and y for each set. Pearson's product-moment coefficient[edit] The most familiar measure of dependence between two quantities is the Pearson product-moment correlation coefficient, or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". where E is the expected value operator, cov means covariance, and, corr a widely used alternative notation for the correlation coefficient.
Stable distribution The importance of stable probability distributions is that they are "attractors" for properly normed sums of independent and identically-distributed (iid) random variables. The normal distribution is one family of stable distributions. By the classical central limit theorem the properly normed sum of a set of random variables, each with finite variance, will tend towards a normal distribution as the number of variables increases. Without the finite variance assumption the limit may be a stable distribution. q-analogs of all symmetric stable distributions have been defined, and these recover the usual symmetric stable distributions in the limit of q → 1.[1] Definition[edit] A non-degenerate distribution is a stable distribution if it satisfies the following property: Let X1 and X2 be independent copies of a random variable X. A random variable X is called stable if its characteristic function can be written as[2][3] where sgn(t) is just the sign of t and Φ is given by Parameterizations[edit]
Recognition primed decision Decision-making model Recognition-primed decision (RPD) is a model of how people make quick, effective decisions when faced with complex situations. In this model, the decision maker is assumed to generate a possible course of action, compare it to the constraints imposed by the situation, and select the first course of action that is not rejected. Overview[edit] The RPD model identifies a reasonable reaction as the first one that is immediately considered. RPD reveals a critical difference between experts and novices when presented with recurring situations. Variations[edit] There are three variations in RPD strategy. Variation 2 occurs when the decision maker diagnoses an unknown situation to choose from a known selection of courses of action. In Variation 3, the decision maker is knowledgeable of the situation but unaware of the proper course of action. Application[edit] See also[edit] References[edit] Gary A.
Negative relationship In statistics, a relationship between two variables is negative if the slope in a corresponding graph is negative, or—what is in some contexts equivalent—if the correlation between them is negative. Negative correlation is also variously called anti-correlation or inverse correlation. Example: "They observed a negative relationship between illness and vaccination." As incident of vaccination is increasing, incidence of illness is decreasing, and vice versa. Compare to a positive relationship: Observed a positive relationship between illness and missed work. As incidence of illness increased, sick days taken also increased.
Gompertz function A Gompertz curve or Gompertz function, named after Benjamin Gompertz, is a sigmoid function. It is a type of mathematical model for a time series, where growth is slowest at the start and end of a time period. The right-hand or future value asymptote of the function is approached much more gradually by the curve than the left-hand or lower valued asymptote, in contrast to the simple logistic function in which both asymptotes are approached by the curve symmetrically. It is a special case of the generalised logistic function. Formula[edit] where Differentiation[edit] The function curve can be derived from a Gompertz law of mortality, which states the rate of mortality (decay) falls exponentially with current size. is the rate of growth.k is an arbitrary constant. Example uses[edit] Examples of uses for Gompertz curves include: Growth of tumors[edit] In the 1960s A.K. where: independently on X(0)>0. α is a constant related to the proliferative ability of the cells.log() refers to the natural log.
Decision theory Normative and descriptive decision theory[edit] Since people usually do not behave in ways consistent with axiomatic rules, often their own, leading to violations of optimality, there is a related area of study, called a positive or descriptive discipline, attempting to describe what people will actually do. Since the normative, optimal decision often creates hypotheses for testing against actual behaviour, the two fields are closely linked. Furthermore it is possible to relax the assumptions of perfect information, rationality and so forth in various ways, and produce a series of different prescriptions or predictions about behaviour, allowing for further tests of the kind of decision-making that occurs in practice. In recent decades, there has been increasing interest in what is sometimes called 'behavioral decision theory' and this has contributed to a re-evaluation of what rational decision-making requires.[1] What kinds of decisions need a theory? Choice under uncertainty[edit]
Simple linear regression Okun's law in macroeconomics is an example of the simple linear regression. Here the dependent variable (GDP growth) is presumed to be in a linear relationship with the changes in the unemployment rate. In statistics, simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model (that is, vertical distances between the points of the data set and the fitted line) as small as possible. The adjective simple refers to the fact that this regression is one of the simplest in statistics. The slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. Other regression methods besides the simple ordinary least squares (OLS) also exist (see linear regression model). Fitting the regression line[edit] and into yields
Gumbel distribution In probability theory and statistics, the Gumbel distribution is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. Such a distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur. The potential applicability of the Gumbel distribution to represent the distribution of maxima relates to extreme value theory which indicates that it is likely to be useful if the distribution of the underlying sample data is of the normal or exponential type. The Gumbel distribution is a particular case of the generalized extreme value distribution (also known as the Fisher-Tippett distribution). The Gumbel distribution is named after Emil Julius Gumbel (1891–1966), based on his original papers describing the distribution.[1][2]
7 Skills To Become Super Smart People aren’t born smart. They become smart. And to become smart you need a well-defined set of skills. Memory If you can’t remember what you’re trying to learn, you’re not really learning. If you want to amaze your friends with remembering faces, names, and numbers, look to the grand-daddy of memory training, Harry Lorayne. Reading Good scholars need to be good readers. Evelyn Woodski Slow Reading Course Announcer … Dan Aykroyd Man … Garrett Morris Woman … Jane Curtin Surgeon … Bill Murray … Ray Charles Announcer V/O: [The following words rapidly appear on a blue screen as they are read by the fast-talking announcer:] This is the way you were taught to read, averaging hundreds or thousands of words per minute. Psychologists have found that many people who take speed reading courses increase their reading speed for a short time but then fall right back to the plodding pace where they started. But the bottom line in reading is always comprehension. Writing Speaking Numeracy Empathy