STATISTICAL DATA ANALYSIS
... begins by giving a statistical view to students and then introduces them to the basics of descriptive statistics. The probability theory and concept, probability distributions and statistical inference are also covered. Students are then introduced to hypothesis testing, comparison of two mean value ...
... begins by giving a statistical view to students and then introduces them to the basics of descriptive statistics. The probability theory and concept, probability distributions and statistical inference are also covered. Students are then introduced to hypothesis testing, comparison of two mean value ...
Simple Linear Regression
... The assumptions of the linear regression model are depicted graphically in Figure 9.2. From this graphic it can be seen that the regression model, the straight line, is the line connecting the average of the y values for each level of the independent variable, x. The actual y values for each level o ...
... The assumptions of the linear regression model are depicted graphically in Figure 9.2. From this graphic it can be seen that the regression model, the straight line, is the line connecting the average of the y values for each level of the independent variable, x. The actual y values for each level o ...
Antonia Rom: Modeling of Binary Data
... In this chapter the logit model is used. In this case h is the logistic distribution function ...
... In this chapter the logit model is used. In this case h is the logistic distribution function ...
Statistical Models in R
... A good model should have predictive value in other data sets and contain only as many explanatory variables as needed for a reasonable fit. To minimize RSS we can set ŷi = yi , for 1 ≤ i ≤ n. However, this “model” may not generalize at all to another data set. It is heavily biased to this sample. W ...
... A good model should have predictive value in other data sets and contain only as many explanatory variables as needed for a reasonable fit. To minimize RSS we can set ŷi = yi , for 1 ≤ i ≤ n. However, this “model” may not generalize at all to another data set. It is heavily biased to this sample. W ...
What is Survival Analysis? - Cornell Statistical Consulting Unit
... Parametric methods assume that the underlying distribution of the survival times follows certain known probability distributions. Popular ones include the exponential, Weibull, and lognormal distributions. The description of the distribution of the survival times and the change in their distribution ...
... Parametric methods assume that the underlying distribution of the survival times follows certain known probability distributions. Popular ones include the exponential, Weibull, and lognormal distributions. The description of the distribution of the survival times and the change in their distribution ...
Proceedings of the 2013 Winter Simulation Conference
... the data are heavy-tailed (Crovella and Lipsky 1997). The empirical estimates become more unstable for larger values of p (Angeletti, Bertin, and Abry 2012). These observations directly apply to the estimation of the L p -norm of the residuals in regression. When these estimates are inaccurate, the ...
... the data are heavy-tailed (Crovella and Lipsky 1997). The empirical estimates become more unstable for larger values of p (Angeletti, Bertin, and Abry 2012). These observations directly apply to the estimation of the L p -norm of the residuals in regression. When these estimates are inaccurate, the ...
Technical Notes on Linear Regression and Information Theory
... Here we briefly overview the basics and logics of these methods. The first part reviews linear regression methods with a certain regularization to find the best linear models. In particular, we will go through how ridge regression is related to the singular value decomposition (for details: [4]). Th ...
... Here we briefly overview the basics and logics of these methods. The first part reviews linear regression methods with a certain regularization to find the best linear models. In particular, we will go through how ridge regression is related to the singular value decomposition (for details: [4]). Th ...
Notes on Two Stage Least Squares
... lated with u. This proxy is going to be called X The rst stage of 2SLS is to generate the proxy, the second stage is to simply substitute the proxy for X , and estimate the resulting equation using OLS. The trick to generating a proxy is to nd a variable that belongs in the second equation (the on ...
... lated with u. This proxy is going to be called X The rst stage of 2SLS is to generate the proxy, the second stage is to simply substitute the proxy for X , and estimate the resulting equation using OLS. The trick to generating a proxy is to nd a variable that belongs in the second equation (the on ...
One-way analysis of variance
... The samples drawn from different populations are random and independent. When carrying out a one way ANOVA, it is important to identify: The dependent variable: This is the random variable under study. The treatment variable: It is the random variable which is assumed to influence the outcome o ...
... The samples drawn from different populations are random and independent. When carrying out a one way ANOVA, it is important to identify: The dependent variable: This is the random variable under study. The treatment variable: It is the random variable which is assumed to influence the outcome o ...
PSI TRAINING COURSE
... The main objective of the course is to introduce attendees to the most important statistical methods for analysing discrete data. Special emphasis will be placed on categorical data, which are very common in practice, and when there are more than two categories, different methods apply for ordered t ...
... The main objective of the course is to introduce attendees to the most important statistical methods for analysing discrete data. Special emphasis will be placed on categorical data, which are very common in practice, and when there are more than two categories, different methods apply for ordered t ...
Linear regression
In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.)In linear regression, data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, linear regression refers to a model in which the conditional mean of y given the value of X is an affine function of X. Less commonly, linear regression could refer to a model in which the median, or some other quantile of the conditional distribution of y given X is expressed as a linear function of X. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of y given X, rather than on the joint probability distribution of y and X, which is the domain of multivariate analysis.Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.Linear regression has many practical uses. Most applications fall into one of the following two broad categories: If the goal is prediction, or forecasting, or error reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y. Given a variable y and a number of variables X1, ..., Xp that may be related to y, linear regression analysis can be applied to quantify the strength of the relationship between y and the Xj, to assess which Xj may have no relationship with y at all, and to identify which subsets of the Xj contain redundant information about y.Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the ""lack of fit"" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares loss function as in ridge regression (L2-norm penalty) and lasso (L1-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms ""least squares"" and ""linear model"" are closely linked, they are not synonymous.