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eBA Encyclopedia Statistics Terminology: Statistical Regression
Given a pair of related measures ( X and Y ) on each of a set of items, the term "regression" is used to characterize the manner in which one of the measures (for example the Y measures) change as the other measure ( in this case, the X measure) changes.
For any set of related measures, it is possible to specify a line that approximates the mean of the Y measures for those items with a given X measure.
By revealing how the mean of the Y measures change as the various X measures change, this line is understood to describe the regression of Y on X.
It is noteworthy that for the same set of related measures there is always a second regression line that describes the regression of X on Y.
The regression line is the predicted value of Y for each value of X.
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eBA Encyclopedia Statistics Terminology: Analogy
Analogy is either the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), or a linguistic expression corresponding to such a process.
In a narrower sense, analogy is an inference or an argument from a particular to another particular, as opposed to deduction, induction, and abduction, where at least one of the premises or the conclusion is general.
The word analogy can also refer to the relation between the source and the target themselves, which is often, though not necessarily, a similarity, as in the biological notion of analogy.
In mathematics and statistics, some types of analogies can have a precise mathematical formulation through the concept of isomorphism.
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eBA Encyclopedia Statistics Terminology: Standard Error
In statistics, the standard error of a measurement, value or quantity is the standard deviation of the process by which it was generated, after adjusting for sample size.
In other words the standard error is the standard deviation of the sampling distribution of the sample statistic (such as sample mean, sample proportion or sample correlation).
Standard errors provide simple measures of uncertainty in a value and are often used because:
• If the standard error of several individual quantities is known then the standard error of some function of the quantities can be easily calculated in many cases;
• Where the probability distribution of the value is known, they can be used to calculate an exact confidence interval; and
• Where the probability distribution is unknown, relationships like Chebyshev’s or the VysochanskiïPetunin inequality can be used to calculate a conservative confidence interval;
• As the sample size tends to infinity the central limit theorem guarantees that the sampling distribution of the mean is asymptotically normal.
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eBA Encyclopedia Statistics Terminology: NBA Basketball Team Heat Map
A heat map is a graphical representation of data where the values taken by a variable in a twodimensional map are represented as colors. A very similar presentation form is a tree map. The term is also used to mean its thematic application as a choropleth map.
There are several different kinds of heat map:
• Web heat maps have been used for displaying areas of a Web page most frequently scanned by visitors.
• Biology heat maps are typically used in molecular biology to represent the level of expression of many genes across a number of comparable samples (e.g. cells in different states, samples from different patients) as they are obtained from DNA microarrays.
• The tree map is a 2D hierarchical partitioning of data that visually resembles a heat map.
• A mosaic plot is a tiled heat map for representing a twoway or higherway table of data. As with treemaps, the rectangular regions in a mosaic plot are hierarchically organized. The means that the regions are rectangles instead of squares. Friendly (1994) surveys the history and usage of this graph.
Each NBA Basketball Team Heat Map shows who was coaching the basketball team that year, who were the top offensive players on the team, and by how many possessions each team won or lost over a 5 year period.
The overall goal of the charts is to be able to observe how time, coaches and players create point spread trends. Win percentage paints a narrow picture of how key personnel react to being put into different game situations. Yearoveryear trends may help people see why their team is gaining or losing ground to the competition.
Each color is a point range that the team won or lost by in that year. Green to red bars are wins, while blues are losses. The lower area provides team information for each year. The right bar shows the average share of games won ad lost by each 3point range over the last 5 year in the NBA.
One of the discovered insights is how certain teams and coaches are more likely to win by 3 or fewer points than they lose by the same margin.
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eBA Encyclopedia Statistics Terminology: Parameter
In mathematics, statistics, and the mathematical sciences, parameters are quantities that define certain characteristics of systems or functions.
When evaluating the function over a domain or determining the response of the system over a period of time, the independent variables are modulated, while the parameters are held constant.
The function or system may then be reevaluated or reprocessed with different parameters, to give a function or system with different behavior.
Loosely speaking, then, parameters are constants in a narrow context but are variables in a larger context.
Moreover, whether a quantity is a parameter or a variable is generally determined by its role in a particular system or function, rather than by anything intrinsic to the quantity.
In nontechnical contexts or in jargon, parameter may also simply be a synonym for criterion.
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Basketball Encyclopedia Terminology:
The Basketball Low Post
"...Defending a player in the low post often means denying him the ball.
A good defender will play a post player closely and reach an arm out in front of the defender to try to deflect any passes to him.
If the ball is below the freethrow line, you should try to be between the ball and your opponent, making a lob pass over your head the only viable option.
If the lob pass is successful, you'll have a difficult time stopping your opponent from making a layup unless you get help from a teammate.
Low post defenders also need to be ready to help out a teammate if there is penetration on the other side or down the middle of the lane. ..."
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eBA Encyclopedia Statistics Terminology: Scatter Plot
A scatter plot is a useful summary of a set of bi variate data (two variables), usually drawn before working out a linear correlation coefficient or fitting a regression line.
It gives a good visual picture of the relationship between the two variables, and aids the interpretation of the correlation coefficient or regression model.
Each unit contributes one point to the scatter plot, on which points are plotted but not joined.
The resulting pattern indicates the type and strength of the relationship between the two variables.
lllustrations
1. The more the points tend to cluster around a straight line, the stronger the linear relationship between the two variables (the higher the correlation).
2. If the line around which the points tends to cluster runs from lower left to upper right, the relationship between the two variables is positive (direct).
3. If the line around which the points tends to cluster runs from upper left to lower right, the relationship between the two variables is negative (inverse).
4. If there exists a random scatter of points, there is no relationship between the two variables (very low or zero correlation).
5. Very low or zero correlation could result from a nonlinear relationship between the variables. If the relationship is in fact nonlinear (points clustering around a curve, not a straight line), the correlation coefficient will not be a good measure of the strength.
A scatter plot will also show up a nonlinear relationship between the two variables and whether or not there exist any outliers in the data.
More information can be added to a twodimensional scatter plot  for example, we might label points with a code to indicate the level of a third variable.
If we are dealing with many variables in a data set, a way of presenting all possible scatter plots of two variables at a time is in a scatter plot matrix.
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eBA Encyclopedia Statistics Terminology: Bias
Bias is a term which refers to how far the average statistic lies from the parameter it is estimating, that is, the error which arises when estimating a quantity.
Errors from chance will cancel each other out in the long run, those from bias will not.
A statistic is biased if it is calculated in such a way that is systematically different from the population parameter of interest.
The following illustrates bias and precision, where the target value is the bulls eye:
Example
The police decide to estimate the average speed of drivers using the fast lane of the motorway and consider how it can be done. One method suggested is to tail cars using police patrol cars and record their speeds as being the same as that of the police car.
Precise  Imprecise  
Biased  
Unbiased 
This is likely to produce a biased result as any driver exceeding the speed limit will slow down on seeing a police car behind them. The police then decide to use an unmarked car for their investigation using a speed gun operated by a constable.
This is an unbiased method of measuring speed, but is imprecise compared to using a calibrated speedometer to take the measurement.
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eBA Encyclopedia Statistics Terminology:
Updated today to the eBA Encyclopedia: The Ratio Scale
This is a type of MEASUREMENT SCALE for which it is meaningful to reason in terms of differences in scores ( see INTERVAL SCALE in the eBA Statistics Encyclopedia ) and also in terms of ratios of scores.
When a scale consists not only of equidistant points but also has a meaningful zero point, then we refer to it as a ratio scale.
If we ask respondents their ages, the difference between any two years would always be the same, and ‘zero’ signifies the absence of age or birth.
Hence, a 100year old person is indeed twice as old as a 50year old one. Sales figures, quantities purchased and market share are all expressed on a ratio scale.
Such a scale will have a zero point which is meaningful in the sense that it indicates complete absence of the property which the scale measures. The RATIO SCALE may be either unipolar (negative values not meaningful) or bipolar (both positive and negative values meaningful), and either continuous or discrete.
Ratio scales are the most sophisticated of scales, since it incorporates all the characteristics of nominal (definition of nominal scale), ordinal (definition of ordinal scale) and interval scales (definition of interval scale). As a result, a large number of descriptive calculations are applicable.
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eBA Encyclopedia Statistics Terminology:
Updated today to the eBA Encyclopedia: Contingency Table
"... A contingency table is a way of summarising the relationship between variables, each of which can take only a small number of values .
It is a table of frequencies classified according to the values of the variables in question .
When a population is classified according to two variables it is said to have been 'crossclassified' or subjected to a twoway classification .
Higher classifications are also possible . ..."
A crucial problem of multivariate statistics is finding (direct)dependence structure underlying the variables contained in high dimensional contingency tables. If some of the conditional independences are revealed, then even the storage of the data can be done in a smarter way).
In order to do this one can use information theory concepts, which gain the information only from the distribution of probability, which can be expressed easily from the contingency table by the relative frequencies.
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