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# Matlab:Linear Methods, Quantiles

## by DataminingTools Inc on Jan 08, 2010

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Matlab:Linear Methods, Quantiles

Matlab:Linear Methods, Quantiles

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## Matlab:Linear Methods, QuantilesPresentation Transcript

• Matlab:Linear Methods
• 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.
• 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
• 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.
• Quantile
Examples:
y = quantile(x,.50); % the median of x
y = quantile(x,[.025 .25 .50 .75 .975]); % Summary of x
• 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 (&quot;the residuals&quot;) of the points from the curve.
• Least Squares Fitting
• 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.
• 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.
• 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.
• 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.
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