Indicative Solutions Institute of Actuaries of India October 2009 Examination CT3: Probability and Mathematical Statistics
... Though the relationship of y on x and z on x are different, as found in the above scatter plots, the correlation coefficient are same and positive. After omitting the values for city 3, we calculate, ...
... Though the relationship of y on x and z on x are different, as found in the above scatter plots, the correlation coefficient are same and positive. After omitting the values for city 3, we calculate, ...
Chapter 11
... Probit regression models the probability that Y=1 using the cumulative standard normal distribution function, evaluated at z = 0 + 1X: Pr(Y = 1|X) = (0 + 1X) is the cumulative normal distribution function. z = 0 + 1X is the “z-value” or “z-index” of the probit model. Example: Suppose ...
... Probit regression models the probability that Y=1 using the cumulative standard normal distribution function, evaluated at z = 0 + 1X: Pr(Y = 1|X) = (0 + 1X) is the cumulative normal distribution function. z = 0 + 1X is the “z-value” or “z-index” of the probit model. Example: Suppose ...
Package `gee`
... summary(gee(breaks ~ tension, id=wool, data=warpbreaks, corstr="AR-M", Mv=1)) if(require(MASS)) { ...
... summary(gee(breaks ~ tension, id=wool, data=warpbreaks, corstr="AR-M", Mv=1)) if(require(MASS)) { ...
Functional Additive Models
... emerged for the implementation of the regularization step. The first approach is projection onto a finite number of elements of a functional basis, which can be either fixed in advance such as the wavelet or Fourier basis, or may be chosen data-adaptively such as the eigenbasis of the auto-covarian ...
... emerged for the implementation of the regularization step. The first approach is projection onto a finite number of elements of a functional basis, which can be either fixed in advance such as the wavelet or Fourier basis, or may be chosen data-adaptively such as the eigenbasis of the auto-covarian ...
Lecture 5 - Categorical and Survival Analyses
... What is Survival Analysis? • Survival analysis is a collection of statistical analysis techniques where the outcome is time to an event. • Survival or time-to-event outcomes are defined by the pair of random variables (ti, δi) that give the observation time and an indicator of whether or not the ev ...
... What is Survival Analysis? • Survival analysis is a collection of statistical analysis techniques where the outcome is time to an event. • Survival or time-to-event outcomes are defined by the pair of random variables (ti, δi) that give the observation time and an indicator of whether or not the ev ...
Panel Data Methods Prof Steve Bond
... effects’, Econometrica, 49, 1377-1398. Hansen, L.P. (1982), ‘Large sample properties of generalized method of moments estimators’, Econometrica, 50, 1029-1054. Holtz-Eakin, D., Newey, W. and Rosen, H. (1988), ‘Estimating vector autoregressions with panel data’, Econometrica, 56, 1371-1395. Mundlak, ...
... effects’, Econometrica, 49, 1377-1398. Hansen, L.P. (1982), ‘Large sample properties of generalized method of moments estimators’, Econometrica, 50, 1029-1054. Holtz-Eakin, D., Newey, W. and Rosen, H. (1988), ‘Estimating vector autoregressions with panel data’, Econometrica, 56, 1371-1395. Mundlak, ...
Linear Regression - math-b
... We want to find a line that goes through our data that comes closer to all the points than any other line. It may turn out that this line doesn’t even hit a single point! But it does minimize the error between the line and each data point. ...
... We want to find a line that goes through our data that comes closer to all the points than any other line. It may turn out that this line doesn’t even hit a single point! But it does minimize the error between the line and each data point. ...
BA 578- 01E: Statistical Methods (CRN # 80257)
... The objective of this course is to provide an understanding for the graduate business student on statistical concepts to include measurements of location and dispersion, probability, probability distributions, sampling, estimation, hypothesis testing, regression, and correlation analysis, multiple r ...
... The objective of this course is to provide an understanding for the graduate business student on statistical concepts to include measurements of location and dispersion, probability, probability distributions, sampling, estimation, hypothesis testing, regression, and correlation analysis, multiple r ...
Document
... ◦ Explain the impact of changes in an independent variable on the dependent variable ...
... ◦ Explain the impact of changes in an independent variable on the dependent variable ...
Advanced Labor Economics II
... • Linearity • Each person’s earnings (Yi) are a linear function of their education (Si), plus an individual-specific error term, νi • νi may be called the error term, the residual, or the deviation. It is a random variable, meaning that the value that any individual gets is a random draw from a dist ...
... • Linearity • Each person’s earnings (Yi) are a linear function of their education (Si), plus an individual-specific error term, νi • νi may be called the error term, the residual, or the deviation. It is a random variable, meaning that the value that any individual gets is a random draw from a dist ...
Package `RPtests`
... Description Performs goodness of fits tests for both high and low-dimensional linear models. It can test for a variety of model misspecifications including nonlinearity and heteroscedasticity. In addition one can test the significance of potentially large groups of variables, and also produce p-valu ...
... Description Performs goodness of fits tests for both high and low-dimensional linear models. It can test for a variety of model misspecifications including nonlinearity and heteroscedasticity. In addition one can test the significance of potentially large groups of variables, and also produce p-valu ...
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.