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"This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response transformations for multiple linear regression or experimental design models."

""This book offers a practical, concise introduction to regression analysis for upper-level undergraduate students of diverse disciplines including, but not limited to statistics, the social and behavioral sciences, MBA, and vocational studies. The book’s overall approach is strongly based on an abundant use of illustrations, examples, case studies, and graphics. It emphasizes major statistical software packages, including SPSS(r), Minitab(r), SAS(r), R, and R/S-PLUS(r). Detailed instructions for use of these packages, as well as for Microsoft Office Excel(r), are provided on a specially prepared and maintained author web site. Select software output appears throughout the text. To help readers understand, analyze, and interpret data and make informed decisions in uncertain settings, many of the examples and problems use real-life situations and settings. The book introduces modeling extensions that illustrate more advanced regression techniques, including logistic regression, Poisson regression, discrete choice models, multilevel models, Bayesian modeling, and time series and forecasting. New to this edition are more exercises, simplification of tedious topics (such as checking regression assumptions and model building), elimination of repetition, and inclusion of additional topics (such as variable selection methods, further regression diagnostic tests, and autocorrelation tests)"-- Provided by publisher."

"Analisis regresi merupakan salah satu metode yang paling sering digunakan dalam menganalisis data. Pada aplikasinya, seringkali proses analisis dihadapkan dengan masalah keterurutan. Pada tahun 1972 Richard E. Barlow memperkenalkan metode Regresi Isotonik sebagai salah satu metode analisis data yang mempertimbangkan keterurutan. Metode regresi ini digunakan ketika penelitian berhadapan dengan asumsi bahwa ketika nilai variabel independen bertambah, maka nilai variabel dependen juga bertambah. Dengan adanya asumsi ini, maka digunakan fungsi isotonik, yaitu fungsi yang mempertahankan keterurutan naik, untuk menemukan model yang sesuai. Tujuan dari metode Regresi Isotonik adalah menemukan fungsi g* yang merupakan anggota kelas fungsi isotonik dan memiliki jarak kuadrat minimum terhadap fungsi yang diperoleh dari data pengamatan. Dengan menggunakan prinsip dasar Cumulative Sum Diagram dan Greatest Convex Minorant, g* bisa diperoleh, dimana g* adalah fungsi tangga. Seiring berkembangnya teori pendekatan, interpolasi polinomial juga semakin berkembang dan bisa digunakan untuk smoothing fungsi tangga yang diperoleh dari metode Regresi Isotonik. Fungsi hasil smoothing ini dinamakan Smooth Isotonic Regression. Dalam skripsi ini akan dibahas bagaimana cara memodelkan hubungan antara dua variabel menggunakan metode Regresi Isotonik dan Smooth Isotonic Regression.

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Regression analysis is a method in statistics that often used to analyze data. On the application in real world problem, the analysis process is often confronted an order restriction. In 1972, Richard E. Barlow introduced a method named Isotonic Regression as a method that concerns on the order restriction. This method is used when the analysis confront an assumption that the dependent variable value will increase as the independent variable value increase. With this assumption, the regression model is constructed from isotonic function that preserves the order of the variable.

The objective of this method is to find a function g* that has minimum distance to the observation data function and g* is element of class of isotonic function . Using the Cumulative Sum Diagram and Greatest Convex Minorant, appropriate g* can be found and g* is a step function. Polynomial interpolation as the development of approximation theory can be used as a smoothing function to the step function from isotonic regression. This smooth function named Smooth Isotonic Regression. In this paper, these two methods will be explained."

"Masalah yang sering terjadi dalam penelitian adalah adanya missing value padahal data yang lengkap diperlukan untuk mendapatkan hasil analisis yang menggambarkan populasi. Dalam pengolahan data, missing value sering terjadi pada analisis regresi. Analisis regresi merupakan suatu model prediksi dengan melihat hubungan antara variabel respon dan variabel prediktor. Missing value dalam analisis regresi dapat ditemukan baik pada variabel respon maupun variabel prediktor. Penelitian ini membahas imputasi missing value yang terjadi pada kedua variabel tesebut dengan menggunakan imputasi regresi. Algoritma Expectation Maximization (EM) merupakan metode penaksiran parameter regresi dengan menggunakan metode Maximum Likelihood Estimaton (MLE) pada data yang memiliki missing value. Untuk menyeimbangkan hasil taksiran parameter model regresi untuk setiap variabel, dilakukan proses penyeimbangan (balance process) untuk mendapatkan hasil taksiran parameter yang konvergen. Simulasi taksiran nilai variabel respon dan prediktor yang hilang dilakukan pada berbagai variasi persentase missingness. Metode penaksiran parameter regresi dengan menggunakan algoritma EM, dapat menghasilkan model yang menjelaskan data sebesar 87% hingga terjadi missing sebanyak 60%.

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The problem that often occurs in research is the existence of missing values even though complete data is needed to obtain the results of analysis that describe the population. In processing data, missing values often occur in regression analysis. Regression analysis is a prediction model by looking at the relationship between response variables and predictor variables. Missing values in regression analysis can be found in both the response variable and predictor variable. This study discusses the imputation of missing values that occur in both variables using regression imputation. The Expectation Maximization (EM) algorithm is a method of estimating regression parameters using the Maximum Likelihood Estimaton (MLE) method on data that has missing value. To balance the estimated parameters of the regression model for each variable, a balance process is performed to obtain the results of the convergent parameter estimates. The estimated simulation of the value of the response variable and missing predictor was carried out in various variations in the percentage of missingness. The method of estimating regression parameters using the EM algorithm, can produce a model that explains the data by 87% until there is missing as much as 60%."

"Premi murni merupakan salah satu elemen penting untuk perusahaan asuransi. Penetapan premi murni yang sesuai dengan risiko kerugian dari calon pemegang polis menjadi salah satu faktor utama agar perusahaan tetap berjalan dan mampu berkompetisi dalam industri. Premi murni dapat ditentukan dengan menghitung ekspetasi dari besar klaim agregat yang dibagi dengan durasi kontrak asuransi. Namun, perlu diketahui bahwa premi murni juga dapat dipengaruhi oleh berbagai faktor risiko seperti umur, jenis kelamin, dan jenis pekerjaan dari nasabah. Salah satu metode untuk mengatasi masalah ini yaitu dengan membuat model regresi menggunakan generalized linear model Distribusi yang cocok untuk memodelkan premi murni adalah distribusi Compound Poisson-Gamma yang merupakan bagian dari distribusi Tweedie. Distribusi Tweedie merupakan distribusi yang mengeneralisasi distribusi lain yang termasuk ke dalam exponential dispersion family. Tujuan dari penelitian ini adalah untuk memodelkan premi murni menggunakan generalized linear model dengan asumsi respons berdistribusi Tweedie atau disebut regresi Tweedie. Dengan mengaplikasikan model ini pada data asuransi kecelakaan kendaraan didapat bahwa regresi Tweedie mampu menjelaskan premi murni dengan baik.

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Pure premium is one of the essential elements for insurance companies. Calculate the appropriate pure premium based on the potential policyholder's risk of loss is crucial to ensure the company's operations and competitiveness in the industry. Pure premiums can be determined by calculating the expectations of large aggregate claims divided by the duration of the insurance contract. However, it should be noted that pure premiums can also be influenced by various risk factors such as age, gender, and the type of employment of the client. One method to address this issue is by creating a regression model using a generalized linear model. The suitable distribution to model of pure premium is the Compound Poisson-Gamma distribution, which is a part of the Tweedie distribution. Tweedie distribution generalizes other distributions that fall under the exponential dispersion models. The objective of this research is to model pure premium using a generalized linear model with assumption that the response follows a Tweedie distribution, known as Tweedie regression. The application of Tweedie regression model to automobile accident insurance data yielded promising results in explaining the pure premium."

"Statistik; Statistik matematika; Indication"

"This volume offers a thorough treatment of the 'grand universe' of linear and weakly nonlinear regression models, from an algebraic view as well as a stochastic one. It includes examples and test computations, and a bibliography with over 2000 references."