Matlab: Linear Methods, Quantiles


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Matlab: Linear Methods, Quantiles

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Matlab: Linear Methods, Quantiles

  1. 1. Matlab:Linear Methods<br />
  2. 2. Quantile<br />Quantiles are points taken at regular intervals from the cumulative distribution function (CDF) of a random variable. Dividing ordered data into n essentially equal-sized data subsets is the motivation for n-quantiles; the quantiles are the data values marking the boundaries between consecutive subsets.<br />
  3. 3. Quantile<br />Some quantiles have special names:<br />The 2-quantile is called the median<br />The 3-quantiles are called tertiles or terciles -> T<br />The 4-quantiles are called quartiles -> Q<br />The 5-quantiles are called quintiles -> QU<br />The 9-quantiles are called noniles (common in educational testing)-> NO<br />The 10-quantiles are called deciles -> D<br />The 12-quantiles are called duo-deciles -> Dd<br />The 20-quantiles are called vigintiles -> V<br />The 100-quantiles are called percentiles -> P<br />The 1000-quantiles are called permillages -> Pr<br />
  4. 4. Quantile<br />Y = quantile(X,p) returns quantiles of the values in X. p is a scalar or a vector of cumulative probability values. When X is a vector, Y is the same size as p, and Y(i) contains the p(i)thquantile. When X is a matrix, the ith row of Y contains the p(i)thquantiles of each column of X. For N-dimensional arrays, quantile operates along the first nonsingleton dimension of X.<br />
  5. 5. Quantile<br />Examples:<br />y = quantile(x,.50); % the median of x<br />y = quantile(x,[.025 .25 .50 .75 .975]); % Summary of x<br />
  6. 6. Least Squares Fitting<br />Least squares fitting is a mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets (&quot;the residuals&quot;) of the points from the curve.<br />
  7. 7. Least Squares Fitting<br />
  8. 8. Least Squares Fitting<br />In practice, the vertical offsets from a line (polynomial, surface, hyper-plane, etc.) are almost always minimized instead of the perpendicular offsets.<br />
  9. 9. mldivide, mrdivide<br />mldivide(A,B) and the equivalent AB perform matrix left division (back slash). A and B must be matrices that have the same number of rows, unless A is a scalar, in which case AB performs element-wise division — that is, AB = A.B.<br />
  10. 10. mldivide, mrdivide<br />mrdivide(B,A) and the equivalent B/A perform matrix right division (forward slash). B and A must have the same number of columns.<br />
  11. 11. Generalized Linear Models<br />Linear regression models describe a linear relationship between a response and one or more predictive terms. Many times, however, a nonlinear relationship exists. Nonlinear Regression describes general nonlinear models. A special class of nonlinear models, known as generalized linear models, makes use of linear methods.<br />
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