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Topic: Linear regression

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	Linear regression
		Linear regression analyzes the relationship between two variables, X and Y. For each subject (or experimental unit), you know both X and Y and you want to find the best straight line through the data.
		In general, the goal of linear regression is to find the line that best predicts Y from X. Linear regression does this by finding the line that minimizes the sum of the squares of the vertical distances of the points from the line.
		The goal of linear regression is to adjust the values of slope and intercept to find the line that best predicts Y from X. More precisely, the goal of regression is to minimize the sum of the squares of the vertical distances of the points from the line.
	www.graphpad.com /curvefit/linear_regression.htm (2787 words)

	PlanetMath: regression model
		Some well known non-normal regression models are the logistic regression for binary data and the Poisson regression for count data.
		Linear regression models belong to a more general class of statistical models called the general linear model, where explanatory variables are no longer restricted to be continuous ones only.
		This is version 7 of regression model, born on 2004-07-29, modified 2006-09-24.
	planetmath.org /encyclopedia/RegressionModel.html (473 words)

	Introduction to Simple Linear Regression
		However, regression is usually used to let analysts generalize from the sample in hand to the population from which the sample was drawn.
		The sample regression equation is an estimate of the population regression equation.
		The regression of X on Y is different from the regression of Y on X. If one wanted to predict lean body mass from muscle strength, a new model would have to be fitted (dashed line).
	www.tufts.edu /~gdallal/slr.htm (1333 words)

	WINKS Statistics Software - Simple Linear Regression
		A regression line is the line described by the equation and the regression equation is the formula for the line.
		Examination of the graphs is useful to visually verify that the relationship is linear and that there is no pattern to the residuals.
		Warning: Using the regression equation to predict values of the dependent variable outside the range of the independent variable is not recommended since you have no evidence that the same linear relationship exists outside the observed range.
	www.texasoft.com /winkslr.html (568 words)

	Linear regression
		Linear regression analyzes the relationship between two variables, X and Y. For each subject (or experimental unit), you know both X and Y and you want to find the best straight line through the data.
		In general, the goal of linear regression is to find the line that best predicts Y from X. Linear regression does this by finding the line that minimizes the sum of the squares of the vertical distances of the points from the line.
		The goal of linear regression is to adjust the values of slope and intercept to find the line that best predicts Y from X. More precisely, the goal of regression is to minimize the sum of the squares of the vertical distances of the points from the line.
	www.curvefit.com /linear_regression.htm (2787 words)

	Linear Regression
		Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data.
		Once a regression model has been fit to a group of data, examination of the residuals (the deviations from the fitted line to the observed values) allows the modeler to investigate the validity of his or her assumption that a linear relationship exists.
		Whenever a linear regression model is fit to a group of data, the range of the data should be carefully observed.
	www.stat.yale.edu /Courses/1997-98/101/linreg.htm (1057 words)

	Linear Regression
		Regression is a simple statistical tool used to model the the dependence of a variable on one (or more) explanatory variables.
		Regression is a method by which a functional relationship in the real world may be described by a mathematical model which may then, like all models, be used to explore, describe or predict the relationship.
		For linear regression with one explanatory variable like this analysis, R-squared is the same as the square of r, the correlation coefficient.
	www.le.ac.uk /biology/gat/virtualfc/Stats/regression/regr1.html (699 words)

	General Linear Models (GLM)
		The development of the linear regression model in the late 19th century, and the development of correlational methods shortly thereafter, are clearly direct outgrowths of the theory of algebraic invariants.
		Linear combinations of responses reflecting a repeated measure effect (for example, the difference of responses on a measure under differing conditions) can be constructed and tested for significance using either the univariate or multivariate approach to analyzing repeated measures in the general linear model.
		The general implication of the theory of estimability of linear functions is that hypotheses which cannot be expressed as linear combinations of the rows of X (i.e., the combinations of observed levels of the categorical predictor variables) are not estimable, and therefore cannot be tested.
	www.statsoft.com /textbook/stglm.html (13045 words)

	Linear regression
		One assumption of Model I linear regression is that the X variable is set by the experimenter and there is no error, either measurement error or biological variation.
		Linear regression assumes that the data points are independent of each other, meaning that the value of one data point does not depend on what the value of any other data point is. The most common violation of this assumption is in time series data, where some Y variable has been measured at different times.
		Linear regression assumes that the Y variables for any value of X would be normally distributed and homoscedastic; if these assumptions are violated, Spearman's rank correlation, the non-parametric analog of linear regression, may be used.
	udel.edu /~mcdonald/statregression.html (2158 words)

	MULTIVARIATE LINEAR REGRESSION
		The multivariate linear regression analysis was tested as a method for use in complex terrain since the use of the three spatial dimensions is consistent and simple.
		The linear fit of the regression analysis can be improved upon in data rich areas by the additional use of a Barnes' objective analysis of the differences between the regression fit and the actual data.
		Multivariate linear regression analysis of meteorological data has been shown to be a useful tool for objective analysis of surface data in complex terrain.
	www.met.utah.edu /jhorel/homepages/msplitt/regress.html (1520 words)

	PA 765: Multiple Regression
		Multiple regression shares all the assumptions of correlation: linearity of relationships, the same level of relationship throughout the range of the independent variable ("homoscedasticity"), interval or near-interval data, absence of outliers, and data whose range is not truncated.
		Cubic regression splines operate similar to local polynomial regression, but a constraint is imposed that the regression line in a given bin must join to the start of the regression line in the next bin, thereby avoiding discontinuities in the curve, albeit by increasing error a bit.
		Local regression fits a regression surface not for all the data points as in traditional regression, but for the data points in a "neighborhood." Researchers determine the "smoothing parameter," which is a specified percentage of the sample size, and neighborhoods are the points within the corresponding radius.
	www2.chass.ncsu.edu /garson/pa765/regress.htm (19411 words)

	Linear Regression (REGRESSN)
		The variables for the regression equation are specified in the regression parameters DEPVAR and VARS.
		Standard regression with six independent variables and with two variables each with 3 categories transformed to 6 dummy variables; raw data are used as input; residuals are to be computed and written into a dataset (cases are identified by variable V2).
		Two-stage regression; the first stage uses variables V2-V6 to estimate values of the dependent variable V122; in the 2nd stage, two additional variables V12, V23 are used to estimate the predicted values of V122, i.e.
	www.unesco.org /webworld/portal/idams/html/english/E1regres.htm (2762 words)

	Linear Regression
		For example, one might want to estimate the increase in global temperature per decade by performing a linear regression of the global mean temperature on time.
		The basic idea of any least squares fit whether it is a linear least squares fit or a polynomial fit is to find the curve which minimizes the sum of the vertical distances squared between all data point and the least squares line.
		Linear regression Applet describes estimates, residuals, and confidence bands.
	serc.carleton.edu /introgeo/teachingwdata/StatRegression.html (632 words)

	Multiple Linear Regression
		This task includes performing a linear regression analysis to predict the variable oxygen from the explanatory variables age, runtime, and runpulse.
		In the analysis of variance table displayed in Figure 11.10, the F value of 38.64 (with an associated p-value that is less than 0.0001) indicates a significant relationship between the dependent variable, oxygen, and at least one of the explanatory variables.
		The diagnostics displayed in Figure 11.11, though indicating unfavorable dependencies among the estimates, are not so excessive as to dismiss the model.
	www.asu.edu /it/fyi/dst/helpdocs/statistics/sas/sasdoc/sashtml/analyst/chap11/sect3.htm (873 words)

	Microsoft OLAP by Mosha Pasumansky : Using Linear Regression MDX functions for forecasting
		MDX provides several functions for computing linear regression, however those functions are anything but intuitive or easy to use.
		Calculates the linear regression of a set and returns the value of y in the regression line y = ax + b.
		Linear regression that uses the least-squares method calculates the equation of the best-fit line for a series of points.
	www.sqljunkies.com /WebLog/mosha/archive/2004/12/21/5689.aspx (1275 words)

	Excel Tutorial on Linear Regression
		Instead, we can apply a statistical treatment known as linear regression to the data and determine these constants.
		Finally, use the above components and the linear regression equations given in the previous section to calculate the slope (m), y-intercept (b) and correlation coefficient (r) of the data.
		It is plain to see that the slope and y-intercept values that were calculated using linear regression techniques are identical to the values of the more familiar trendline from the graph in the first section; namely m = 0.5842 and b = 1.6842.
	phoenix.phys.clemson.edu /tutorials/excel/regression.html (664 words)

	Correlation and regression (Site not responding. Last check: )
		The applet draws the regression line and the correlation coefficient.
		When more than two points are given, the correlation coefficient and the regression line are shown.
		Every time a point is added, the correlation coefficient and the regression line are updated.
	www.stattucino.com /berrie/dsl/regression/regression.html (84 words)

	Simple linear regression with PHP, Part 2
		The data-exploration tool you are building implements the statistical decision procedure for a linear model (the T test) and provides summary data that can be used to construct the theoretical and statistical arguments necessary to establish a linear model.
		From a learning point of view, simple linear regression modeling is worth further study because it is arguably the gateway to understanding more advanced forms of statistical modeling.
		Even though simple linear regression only uses one variable to account for, or predict, the variance in another variable, looking for simple linear relations between all your study variables is often the first step in exploratory data analysis.
	www-106.ibm.com /developerworks/web/library/wa-linphp2 (3844 words)

	Linear Regression (Site not responding. Last check: )
		Linear regression and correlation are similar and easily confused.
		It makes a difference which variable is called X and which is called Y, as linear regression calculations are not symmetrical with respect to X and Y. If you swap the two variables, you will obtain a different regression line.
		Linear regression works by by minimizing the sum of the square of the vertical distances of the points from the regression line, hence is known as the "least squares" method.
	www-micro.msb.le.ac.uk /1010/DH4.html (922 words)

	Multiple Regression
		The general purpose of multiple regression (the term was first used by Pearson, 1908) is to learn more about the relationship between several independent or predictor variables and a dependent or criterion variable.
		Once this so-called regression line has been determined, the analyst can now easily construct a graph of the expected (predicted) salaries and the actual salaries of job incumbents in his or her company.
		First of all, as is evident in the name multiple linear regression, it is assumed that the relationship between variables is linear.
	www.statsoft.com /textbook/stmulreg.html (2189 words)

	Linear Regression
		There is variability in real data that needs to be explained and measured, and it is the task of the student to find the function that best 'fits' the data in some sense.
		The first functions we study in Maths B are linear, so it makes sense to start with problems that are whose data are linear in nature.
		Students are asked to find a linear model for each set of data, and predict the gold medal performance in Sydney in the year 2000.
	exploringdata.cqu.edu.au /lin_reg.htm (390 words)

	Predictions by Regression
		Regression models are often constructed based on certain conditions that must be verified for the model to fit the data well, and to be able to predict accurately.
		A confidence interval for a single future value of Y corresponding to a chosen value of X. A confidence interval for a single pint on the line.
		Linear Interpolation: To estimate the lower (and upper) limits at given value X, one may use the following by taking a linear interpolations at two known neighboring points to X, say XL and XU, as follow:
	home.ubalt.edu /ntsbarsh/Business-stat/otherapplets/Regression.htm (1209 words)

	Linear Regression Curve Technical Analysis
		Think of the Linear Regression Curve as numerous lines, but both extreme ends of the lines are hidden, while the center portion is shown and is connected to other center portions of lines.
		The Linear Regression Curve is used mainly to identify trend direction and is sometimes used to generate buy and sell signals.
		Many traders view the Linear Regression curve as the fair value for the stock, future, or forex currency pair, and any deviations from the curve as buy and sell opportunities.
	www.onlinetradingconcepts.com /TechnicalAnalysis/LinRegCurve.html (270 words)

	Citations: A linear regression model for the analysis of life times - Aalen (ResearchIndex)
		The typical use of the frailty modelling concept is that the hazard rate for an individual i takes the form Z i ff(s) where the latent Z i s are not observed but come from some distribution.
		A general nonparametric regression model for survival data, without assuming additive or multiplicative hazards, is considered in Mc Keague and Utikal (1990) and in Keiding (1990) but dimensionality, i.e.
		An other possible model is to use a proportional hazards model where, rather then stratifying on the treatments, a series of time dependent indicators are used for the....
	citeseer.ist.psu.edu /context/409157/0 (1246 words)

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