discriminant function analysis examples?
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This link provides an intro and "how-to" to DFA using an example.
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You might try DAP. You can find it here along with a lot of other free statistical software.\nhttp://members.aol.com/johnp71/javasta2.html
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Domain ~ x values\nRange ~ y values\n\nYou have to work the function and figure them out.
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umm none that im aware of, what kind of mathamatics leval are you looking at?
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A few that come to mind at Euler, Maxima and Octave. Unfortunately, I don't think any of the free packages come close to Mathematica or Matlab, but maybe one of them will still meet your needs.
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1) plug y=4-x in for y in the equation of your circle.  foil it out and bring everything to the left hand side.  now you have a quadratic equation that you can solve by using your quadratic formula.  once you have values for x, the corresponding value of y is just 4-x.  you should get (3,1) and (5,-1) as your answers.\n\n2) for this one, try to do the same thing you did in (1).  this time plug in x = 3-2y for x, just because y is the easier variable to try and solve for.  when you use your quadratic formula, you'll see your discriminant is negative, and thus you get no real solutions.  therefore the 2 equations don't intersect\n\n3) find the points of intersection of the circle and the line, exactly as you did in problem (1) and tried to do in problem (2).  i.e. plug in x = 2y-4 in for x, in the equation of your circle, and solve for y.  then, go back and solve for x and you should have 2 ordered pairs (the 2 points of intersection).  the length of the chord is just the distance between these 2 points.  remember your distance formula:\n\nd = sqrt( (x1 - x2)^2 + (y1-y2)^2 )
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Singular value decomposition and principal component analysis\n\n\nMichael E. Wall, Andreas Rechtsteiner, Luis M. Rocha\nModeling, Algorithms, and Informatics Group (CCS-3)\nLos Alamos National Laboratory, MS B256\nLos Alamos, New Mexico 87545, USA\n\n\n\nCitation: Wall, Michael E., Andreas Rechtsteiner, Luis M. Rocha."Singular value decomposition and principal component analysis". in A Practical Approach to Microarray Data Analysis. D.P. Berrar, W. Dubitzky, M. Granzow, eds. pp. 91-109, Kluwer: Norwell, MA (2003). LANL LA-UR-02-4001.\n\nAlso available in the arXiv.org e-Print archive and in Adobe Acrobat (.pdf) format. \n\nAbstract.\n\nThis chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a smaller number of variables, and detection of patterns in noisy gene expression data. In addition, we describe the precise relation between SVD analysis and Principal Component Analysis (PCA) when PCA is calculated using the covariance matrix, enabling our descriptions to apply equally well to either method. Our aim is to provide definitions, interpretations, examples, and references that will serve as resources for understanding and extending the application of SVD and PCA to gene expression analysis.\n\nKeywords: bioinformatics, computational biology, linear algebra, data mining, singular value decomposition, principal component analysis, gene expression analysis, SVD, PCA, microarray analysis techniques.\n\n1. Introduction\nOne of the challenges of bioinformatics is to develop effective ways to analyze global gene expression data. A rigorous approach to gene expression analysis must involve an up-front characterization of the structure of the data. In addition to a broader utility in analysis methods, singular value decomposition (SVD) and principal component analysis (PCA) can be valuable tools in obtaining such a characterization. SVD and PCA are common techniques for analysis of multivariate data, and gene expression data are well suited to analysis using SVD/PCA. A single microarray  For simplicity, we use the term microarray to refer to all varieties of global gene expression technologies.\n\n\nClose experiment can generate measurements for thousands, or even tens of thousands of genes. Present experiments typically consist of less than ten assays, but can consist of hundreds (Hughes et al., 2000). Gene expression data are currently rather noisy, and SVD can detect and extract small signals from noisy data. \nThe goal of this chapter is to provide precise explanations of the use of SVD and PCA for gene expression analysis, illustrating methods using simple examples. We describe SVD methods for visualization of gene expression data, representation of the data using a smaller number of variables, and detection of patterns in noisy gene expression data. In addition, we describe the mathematical relation between SVD analysis and Principal Component Analysis (PCA) when PCA is calculated using the covariance matrix, enabling our descriptions to apply equally well to either method. Our aims are 1) to provide descriptions and examples of the application of SVD methods and interpretation of their results; 2) to establish a foundation for understanding previous applications of SVD to gene expression analysis; and 3) to provide interpretations and references to related work that may inspire new advances.\n\nIn section 1, the SVD is defined, with associations to other methods described. A summary of previous applications is presented in order to suggest directions for SVD analysis of gene expression data. In section 2 we discuss applications of SVD to gene expression analysis, including specific methods for SVD-based visualization of gene expression data, and use of SVD in detection of weak expression patterns. Some examples are given of previous applica
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There are two that I've seen used:\n\n-margin for error\n-probability curves (discrete or continuous)
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(-6)^2 - 4(9)(1) = 0\n\nThe discriminant is b^2 - 4ac, where a, b, and c are such that\n\nax^2 + bx + c = 0\n\nFor your formula, 9x^2 - 6x + 1 = 0, so a = 9, b = -6, and c = 1\n\nSince the discriminant is zero, there is only one real root to this equation.  If the discriminant is positive, then the quadratic has two real roots.  If the discriminant is negativ, then there are no real roots (both roots are complex).  This only has one root because\n\n9x^2-6x+1 = (3x - 1)^2 = 0.\n\nSo 3x-1 = 0.\nSo 3x = 1.\nSo x = 1/3.
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Back in the stone ages, we used "Real and Complex Analysis" by Walter Rudin 1966 McGraw Hill.\n\nI think Rundin may have written another book with the title "Functional Analysis", but I'm not sure.
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discriminant formula square root of b^2-4ac\n\nD=square root of 6^2-4(1)(-16)\nD=square root of 36+64\nD=square root of 100 \nD=10\n\nD=square root of 5^2-4(2)(-7)\nD=square root of 25+56\nD=square root of 81\nD=9\n\nif the discriminant is less than zero it has no solution which means the line doesn't touch the x-axis\nif the discriminant is equal to zero,it has one solution meaning the line touches the x-axis once\nif the discriminant is more than zero, it has two solutions which means the line touches the x-axis twice
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A form of linear regression where the outcome of interest is binary instead of continuous.  For example, your dependent variable is over weight vs. not over weight (case for logistic regression)  your dependent variable is continuous weight in lbs. (case for linear regression).  Logistic regression was developed to handle the case of both continuous and discrete independent variables.  Discriminant function analysis was used prior to logistic regression but could only handle continuous independent variables. I am not sure who is credited with developing the procedure.
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Using power points and examples!
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The Law of Statistical Regularity:\n\nhttp://www.tardis.ed.ac.uk/~kate/qmcweb/s9.htm\n\nAn example of the frequency polygon:\n\nhttp://davidmlane.com/hyperstat/A49236.html\n\nAn example of the reducing balance method:\n\nhttp://www.tutor2u.net/business/accounts/assets_fixedassets_depreciation_rbexample.asp\n\nBut these answers are not going to help you understand statistics and statistical interpretation.  Statistics is not like learning History, where the right answer is going to be "1746" or "The Diet of Worms", you need to understand what a frequency polygon is showing you about a set of data.\n\nMaybe you need an on-line tutor.  You can find them on google, too.
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Yes, but depending on the complexity of your problem. If your data is linearly separable, then a simple regression analysis will do. Use neural networks (such as backpropagation) only when the problem is hard.
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Put it into standard form and factor or use the quadratic formula.\n\nYou want the discriminate to be positive\nin standard form b=coeff of x: 2k-8\na = k\nc = k\n\nnow plug and chug and find values of k that make the discriminant positive\nb^2 - 4ac =
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The page below gives many examples