How can we  guess the value of correlation coefficient from a sample space?
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The correlation coefficient is a number between -1 and 1 that measures the degree in which values in a sample space are linearly related. Graph the points and see how they are related spatially, if the points form something that looks like a blob  then the correlation coefficient is zero, or there is no linear relationship. If the points form a perfect line with a positive slope, then the correlation coefficient  is  1. If the points form a perfect line with a negative slope, then the correlation coefficient is  -1. So when you graph your sample space make a guess at where the data falls within the range of -1 to 1. Hope this helps.\n\nP.S. Use excel and you can graph those points quickly.
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I'm wondering why you created the data 1-3500?  I would think you would use the set of data available and figure the standard deviation and average.  With that information, you would be able to predict tomorrows value at a certain confidence level.  I forget is that the p test or the t test.  its been a while since I took statistics.
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I haven't tried it, but check out MatPy (linked below).  Another possibility is Numerical Python (also linked below).
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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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You can either look it up or determine it experimentally.\nI cant get much more specific without additional details.
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Study of data with respect to different spectral responses
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Probably a t-test. \n\nTell us what hypothesis you are testing.
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You can calculate Pearson's r for any two variables, including number of inadequate questions vs stupid answers, my weight vs my points in Y!Answers, and anything that you feel like. \nJust remember that correlation does not imply causation.
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Beta is a measure of the market's risk measured by randomness of data. Correlation is whether stocks lose or gain value with each other. Similarity is that a risky stock is more likely to be uncorrelated with the market.
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In statistics, the generalized canonical correlation analysis (gCCA), is a way of making sense of cross-correlation matrices between the sets of random variables when there are more than two sets. It is a generalization of the Principal component analysis (PCA) to more than two sets of random variables like a conventional CCA also does the same thing for only two sets. The canonical variables represent those common factors that can be found by a large PCA of all of the transformed random variables after each set underwent its own PCA.
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The CORREL() function in many major spreadsheet packages, such as Microsoft Excel and Gnumeric calculates Pearson's correlation coefficient.
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The no of degrees of freedom for a chi-square distribution ia n-1
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You might be looking for Regression analysis.\nThis is the statistical technique used to look for correlations between variables.
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(1) The correlation answers the STRENGTH of linear association between paired variables, say X and Y. On the other hand, the regression tells us the FORM of linear association that best predicts Y from the values of X.\n\n(2a) Correlation is calculated whenever:\n* both X and Y is measured in each subject and quantify how much they are linearly associated.\n* in particular the Pearson's product moment correlation coefficient is used when the assumption of both X and Y are sampled from normally-distributed populations are satisfied \n* or the Spearman's moment order correlation coefficient is used if the assumption of normality is not satisfied.\n* correlation is not used when the variables are manipulated, for example, in experiments.\n \n(2b) Linear regression is used whenever:\n* at least one of the independent variables (Xi's) is to predict the dependent variable Y. Note: Some of the Xi's are dummy variables, i.e. Xi = 0 or 1, which are used to code some nominal variables.\n* if one manipulates the X variable, e.g. in an experiment. \n\n\n(3) Linear regression are not symmetric in terms of X and Y. That is interchanging X and Y will give a different regression model (i.e. X in terms of Y) against the original Y in terms of X.\nOn the other hand, if you interchange variables X and Y in the calculation of correlation coefficient you will get the same value of this correlation coefficient.\n\n(4) The "best" linear regression model is obtained by selecting the variables (X's) with at least strong correlation to Y, i.e. >= 0.80 or <= -0.80 \n\n(5) The same underlying distribution is assumed for all variables in linear regression. Thus, linear regression will underestimate the correlation of the independent and dependent when they (X's and Y) come from different underlying distributions.
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The variables invovled can be correlated.  Below is a link for the multiviate normal.  Notice that the variance-covariance matrix Σ is not restricted to be diagonal; it can be a general matrix, it just has to be positive semi-definite.  Note that if |Σ| = 0, then the pdf does not exist.  Anyway, the link includes the pdf (in the positive definite case of course), bivariate case, and the conditional distribution, which is also normal.  I have been using this distribution a lot in my research.
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The most common correlation (there are several) is described at:\n\nhttp://mathworld.wolfram.com/CorrelationCoefficient.html\n\nThis is sometimes known as the "product moment correlation".  Some others are: Spearman's rank order correlation and Kendall's tau.
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correlation coefficient i really couldnt tell you a formula, but there is a button on your graphing calculator that tells you it, correlation coefficient is a number from 0 to 1, stating how close a best fit line is to a series of points, 1 being perfectly on the line, so unless your dealing with a best fit line i have no idea...