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Matlab: Linear Methods, Quantiles
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Matlab: Linear Methods, Quantiles

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Matlab: Linear Methods, Quantiles

Matlab: Linear Methods, Quantiles

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Matlab: Linear Methods, Quantiles Presentation Transcript

  • 1. Matlab:Linear Methods
  • 2. Quantile
    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.
  • 3. Quantile
    Some quantiles have special names:
    The 2-quantile is called the median
    The 3-quantiles are called tertiles or terciles -> T
    The 4-quantiles are called quartiles -> Q
    The 5-quantiles are called quintiles -> QU
    The 9-quantiles are called noniles (common in educational testing)-> NO
    The 10-quantiles are called deciles -> D
    The 12-quantiles are called duo-deciles -> Dd
    The 20-quantiles are called vigintiles -> V
    The 100-quantiles are called percentiles -> P
    The 1000-quantiles are called permillages -> Pr
  • 4. Quantile
    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.
  • 5. Quantile
    Examples:
    y = quantile(x,.50); % the median of x
    y = quantile(x,[.025 .25 .50 .75 .975]); % Summary of x
  • 6. Least Squares Fitting
    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 ("the residuals") of the points from the curve.
  • 7. Least Squares Fitting
  • 8. Least Squares Fitting
    In practice, the vertical offsets from a line (polynomial, surface, hyper-plane, etc.) are almost always minimized instead of the perpendicular offsets.
  • 9. mldivide, mrdivide
    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.
  • 10. mldivide, mrdivide
    mrdivide(B,A) and the equivalent B/A perform matrix right division (forward slash). B and A must have the same number of columns.
  • 11. Generalized Linear Models
    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.
  • 12. Visit more self help tutorials
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    The tutorials section is free, self-guiding and will not involve any additional support.
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