Some Modifications to Calculate Regression Coefficients in Multiple Linear Regression

Linear Regression Under Multiple

This dissertation studies the least squares estimator of a trend parameter in a simple linear regression model with multiple changepoints when the changepoint times are known. The error component in the model is allowed to be autocorrelated. The least squares estimator of the trend and the variance of the trend estimator are derived. Consistency and asymptotic normality of the trend estimator a...

Fuzzy linear regression analysis with trapezoidal coefficients

In this paper, we aim to extended the constraints of Tanaka’s model. Applied coefficients of the fuzzy regression by them is the symmetric triangular fuzzy numbers, while we try to replace it by more general asymmetric trapezoidal one. Possibility of two asymmetric trapezoidal fuzzy numbers is explained by possibility distribution. Two different models is presented and a numerical example is gi...

Interval linear regression

‎In this paper‎, ‎we have studied the analysis an interval linear regression model for fuzzy data‎. ‎In section one‎, ‎we have introduced the concepts required in this thesis and then we illustrated linear regression fuzzy sets and some primary definitions‎. ‎In section two‎, ‎we have introduced various methods of interval linear regression analysis‎. ‎In section three‎, ‎we have implemented nu...

Part II Multiple Linear Regression

Multiple Linear Regression Models in Outlier Detection

Identifying anomalous values in the realworld database is important both for improving the quality of original data and for reducing the impact of anomalous values in the process of knowledge discovery in databases. Such anomalous values give useful information to the data analyst in discovering useful patterns. Through isolation, these data may be separated and analyzed. The analysis of outlie...

Multiple testing in high-dimensional linear regression

In many real-world statistical problems, we observe a large number of potentially explanatory variables of which a majority may be irrelevant. For this type of problem, controlling the false discovery rate (FDR) guarantees that most of the discoveries are truly explanatory and thus replicable. In this talk, we propose a new method named SLOPE to control the FDR in sparse high-dimensional linear...