The R implementation of Generalized Additive Models for
... Generalized Additive Models for Location, Scale and Shape (GAMLSS) were introduced by Rigby and Stasinopoulos (2001, 2002) as way of overcoming some of the limitations associated with Generalized Linear Models (GLM) and Generalized Additive Models (GAM) (Nelder and Wedderburn, 1972 and Hastie and Ti ...
... Generalized Additive Models for Location, Scale and Shape (GAMLSS) were introduced by Rigby and Stasinopoulos (2001, 2002) as way of overcoming some of the limitations associated with Generalized Linear Models (GLM) and Generalized Additive Models (GAM) (Nelder and Wedderburn, 1972 and Hastie and Ti ...
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
... 1. A cyclist pedals from his house to his college at a speed of 10 m.p.h. and back from college to his house at 15 m.p.h. Find the average speed. 2. Define coefficient of variation. 3. State Pearson’s β coefficients. 4. State any two properties of regression coefficients. 5. If A and B are independe ...
... 1. A cyclist pedals from his house to his college at a speed of 10 m.p.h. and back from college to his house at 15 m.p.h. Find the average speed. 2. Define coefficient of variation. 3. State Pearson’s β coefficients. 4. State any two properties of regression coefficients. 5. If A and B are independe ...
Basic principles of probability theory
... Q-Q plot can be used to check normality assumption. Q-Q plot is plot of quantiles of two distributions (in this case frequency distribution of residuals vs normal distribution). If assumption on distribution is correct then this plot should be nearly linear. Cook’s distance: Observations in turn are ...
... Q-Q plot can be used to check normality assumption. Q-Q plot is plot of quantiles of two distributions (in this case frequency distribution of residuals vs normal distribution). If assumption on distribution is correct then this plot should be nearly linear. Cook’s distance: Observations in turn are ...
View/Open
... largest residuals more carefully to check if there is some discernible reason why the parameter estimates fit these observations so poorly. The commonsense understanding of observations with large residuals is that they are the observations for which the values of the dependent variable are most “sur ...
... largest residuals more carefully to check if there is some discernible reason why the parameter estimates fit these observations so poorly. The commonsense understanding of observations with large residuals is that they are the observations for which the values of the dependent variable are most “sur ...
Detecting Structural Change Using SAS ETS Procedures
... has on the dependent variable, ceteris paribus. In addition, a correctly specified regression model allows for the use of numerous statistical tests and summary statistics, such as R-square, which indicate how well the model fits the data. For most of these tests to be statistically correct, there a ...
... has on the dependent variable, ceteris paribus. In addition, a correctly specified regression model allows for the use of numerous statistical tests and summary statistics, such as R-square, which indicate how well the model fits the data. For most of these tests to be statistically correct, there a ...
Coefficient of determination
In statistics, the coefficient of determination, denoted R2 or r2 and pronounced R squared, is a number that indicates how well data fit a statistical model – sometimes simply a line or a curve. An R2 of 1 indicates that the regression line perfectly fits the data, while an R2 of 0 indicates that the line does not fit the data at all. This latter can be because the data is utterly non-linear, or because it is random.It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, as the proportion of total variation of outcomes explained by the model (pp. 187, 287).There are several definitions of R2 that are only sometimes equivalent. One class of such cases includes that of simple linear regression where r2 is used instead of R2. In this case, if an intercept is included, then r2 is simply the square of the sample correlation coefficient (i.e., r) between the outcomes and their predicted values. If additional explanators are included, R2 is the square of the coefficient of multiple correlation. In both such cases, the coefficient of determination ranges from 0 to 1.Important cases where the computational definition of R2 can yield negative values, depending on the definition used, arise where the predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data, and where linear regression is conducted without including an intercept. Additionally, negative values of R2 may occur when fitting non-linear functions to data. In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular criterion.