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In August 1908, a white mob attacked Springfield, Illinois’s Black community, destroying homes and businesses and lynching two Black men. National outrage over the violence helped spur the movement that created the NAACP the following year.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
In statistics, more specifically in biostatistics, line-intercept sampling (LIS) is a method of sampling elements in a region whereby an element is sampled if a chosen line segment, called a “transect”, intersects the element.[1]
Line intercept sampling has proven to be a reliable, versatile, and easy to implement method to analyze an area containing various objects of interest.[2] It has recently also been applied to estimating variances during particulate material sampling.[3]
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In statistics, more specifically in biostatistics, line-intercept sampling (LIS) is a method of sampling elements in a region whereby an element is sampled if a chosen line segment, called a “transect”, intersects the element. Line intercept sampling has proven to be a reliable, versatile, and easy to implement method to analyze an area containing various objects of interest. It has recently also been applied to estimating variances during particulate material sampling.
A nomogram (from Greek νόμος (nomos) 'law' and γράμμα (gramma) 'that which is drawn'), also called a nomograph, alignment chart, or abac, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function. The field of nomography was invented in 1884 by the French engineer Philbert Maurice d'Ocagne (1862–1938) and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision. Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates. A nomogram consists of a set of n scales, one for each variable in an equation. Knowing the values of n − 1 variables, the value of the unknown variable can be found, or by fixing the values of some variables, the relationship between the unfixed ones can be studied. The result is obtained by laying a straightedge across the known values on the scales and reading the unknown value from where it crosses the scale for that variable. The virtual or drawn line, created by the straightedge, is called an index line or isopleth. Nomograms flourished in many different contexts for roughly 75 years because they allowed quick and accurate computations before the age of pocket calculators. Results from a nomogram are obtained very quickly and reliably by simply drawing one or more lines. The user does not have to know how to solve algebraic equations, look up data in tables, use a slide rule, or substitute numbers into equations to obtain results. The user does not even need to know the underlying equation the nomogram represents. In addition, nomograms naturally incorporate implicit or explicit domain knowledge into their design. For example, to create larger nomograms for greater accuracy, the nomographer usually includes only scale ranges that are reasonable and of interest to the problem. Many nomograms include other useful markings such as reference labels and colored regions. All of these provide useful guideposts to the user. Like a slide rule, a nomogram is a graphical analog computation device. Also like a slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. Unlike the slide rule, which is a general-purpose computation device, a nomogram is designed to perform a specific calculation with tables of values built into the device's scales. Nomograms are typically used in applications for which the level of accuracy they provide is sufficient and useful. Alternatively, a nomogram can be used to check an answer obtained by a more exact but error-prone calculation. Other types of graphical calculators—such as intercept charts, trilinear diagrams, and hexagonal charts—are sometimes called nomograms. These devices do not meet the definition of a nomogram as a graphical calculator whose solution is found by the use of one or more linear isopleths.
In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s). It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model. There are several definitions of R2 that are only sometimes equivalent. In simple linear regression (which includes an intercept), r2 is simply the square of the sample correlation coefficient (r), between the observed outcomes and the observed predictor values. If additional regressors are included, R2 is the square of the coefficient of multiple correlation. In both such cases, the coefficient of determination is always smaller than 1 and usually greater than 0. Cases where R2 is negative can arise when the predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data. Even if a model-fitting procedure has been used, R2 may still be negative, for example when linear regression is conducted without including an intercept, or when a non-linear function is used to fit the data. In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular criterion. The coefficient of determination can be more intuitively informative than MAE, MAPE, MSE, and RMSE in regression analysis evaluation, as the former can be expressed as a percentage, whereas the latter measures have arbitrary ranges. It also proved more robust for poor fits compared to SMAPE on certain test datasets. When evaluating the goodness-of-fit of simulated (Ypred) versus measured (Yobs) values, it is not appropriate to base this on the R2 of the linear regression (i.e., Yobs=m·Ypred + b). The R2 quantifies the degree of any linear correlation between Yobs and Ypred, while for the goodness-of-fit evaluation only one specific linear correlation should be taken into consideration: Yobs=1·Ypred + 0 (i.e., the 1:1 line).
In statistics, simple linear regression (SLR) is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor. It is common to make the additional stipulation that the ordinary least squares (OLS) method should be used: the accuracy of each predicted value is measured by its squared residual (vertical distance between the point of the data set and the fitted line), and the goal is to make the sum of these squared deviations as small as possible. In this case, 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. The intercept of the fitted line is such that the line passes through the center of mass (x, y) of the data points.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Joe Louis.