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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 ...
Root mean square. In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of numbers is the square root of the set's mean square. [1] Given a set , its RMS is denoted as either or . The RMS is also known as the quadratic mean (denoted ), [2][3] a special case of the generalized mean. The RMS of a continuous function is denoted ...
The Pearson's chi-squared test statistic is defined as . The p-value of the test statistic is computed either numerically or by looking it up in a table. If the p-value is small enough (usually p < 0.05 by convention), then the null hypothesis is rejected, and we conclude that the observed data does not follow the multinomial distribution.
The concept of rounding is very old, perhaps older than the concept of division itself. Some ancient clay tablets found in Mesopotamia contain tables with rounded values of reciprocals and square roots in base 60. [40] Rounded approximations to π, the length of the year, and the length of the month are also ancient – see base 60 examples.
Square root of 2, Pythagoras constant. [4] 1.41421 35623 73095 04880 [Mw 2] [OEIS 3] Positive root of = 1800 to 1600 BCE [5] Square root of 3, ...
Chi-squared distribution, showing χ2 on the x -axis and p -value (right tail probability) on the y -axis. A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical ...
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
An n×n matrix with n distinct nonzero eigenvalues has 2 n square roots. Such a matrix, A, has an eigendecomposition VDV−1 where V is the matrix whose columns are eigenvectors of A and D is the diagonal matrix whose diagonal elements are the corresponding n eigenvalues λi. Thus the square roots of A are given by VD1/2 V−1, where D1/2 is ...