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General Linear Model

The general linear model is a flexible generalization of ordinary linear regression that allows for response variables that have other than a normal distribution. It generalizes linear regression by allowing the linear model to be related to the response variable through a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.

General linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models. These models include linear regression, logistic regression and Poisson regression. The proposed an iteratively reweighted least squares method for maximum likelihood estimation of the model parameters. Maximum-likelihood estimation remains popular and is the default method on many statistical computing packages. Other approaches have been developed which include Bayesian approaches and least squares fit to variance stabilized responses.

In a generalized linear model, each outcome of the dependent variables, Y, is assumed to be generated from a particular distribution in the exponential family, a large range of probability distributions that includes the normal, binomial, Poisson and gamma distributions. The mean of the distribution depends on the independent variables.

A point of confusion with the general linear models has to do with the distinction between the general linear models. The general linear model may be viewed as a case of the generalized linear model with identity link. As most exact results of interest are obtain only for the general linear model, the general linear model has undergone a somewhat longer historical development. 

RUGS Corporation produces three types of rugs

The RUGS Corporation produces three types of rugs, which it sells to large carpet stores. The production of each rug requires two machine operations, weaving and binding, followed by assembly, which includes inspection and packaging. All three rug types require 0.4 hour of assembly time, but the machining operations have diffe

Statistics: Maximize the number of customers for Island Water Sports

Island Water Sports is a business that provides rental equipment and instruction for a variety of water sports in a resort town. On one particular morning, a decision must be made of how many Wildlife Raft Trips and how many Group Sailing Lessons should be scheduled. Each Wildlife Raft Trip requires one captain and one crew pe

Seasonally Adjusted Forecast

From the given data develop a seasonally adjusted forecast for 2006. (Use a linear trend line model to develop a forecast estimate for 2006.) Year Quarter Ice cream sales (gal) 2003 1 350 2 510 3

Exponential Forecast - Simple and Trend (Holt's), Seasonal Forecast

The management of American Auto Parts is having a meeting to plan the operating budgets for next year. The Senior Vice-President of Sales, Mr. Tom Tremellon, knows that a large portion of the company's income is derived from sales of their 1-year, 3-year, and lifetime batteries. He has asked you, Manager of Production, to prepar

Statistics linear programming for jeweler: how many pins; how many necklaces

A jeweler and her apprentice make silver pins and necklaces by hand. Each week they have 80 hours of labor and 36 ounces of silver available. It requires 8 hours of labor and 2 ounces of silver to make a pin and 10 hour of labor and 6 ounces of silver to make a necklace. Each pin also contain a small gem of of some kind. The de

Statistics: Dreskin Development Co construction of two apartment complexes.

See attached file for clarity. The Dreskin Development Company is building two apartment complexes. It must decide how many units to construct in each complex subject to labor and material constraints. The profit generated for each apartment in the first complex is estimated at $900, for each apartment in the second complex,

Integer programming, goal programming and nonlinear programming

An airline owns an aging fleet of Boeing 737 jet airplanes. It is considering a major purchase of up to 17 new Boeing model 757 and 767 jets. The decision must take into account numerous cost and capability factors, including the following: (1) the airline can finance up to $1.6 billion in purchases; (2) each Boeing 757 will cos

LP problem

The solution of the problem has to be detailed and the values have to be computed by hand, without using excel or some other software program! Thompson Distributors packages and distributes industrial supplies. A standard shipment can be packaged in one of 3 types of containers: A, K, T. A single class A container yields a

Linear Programming Assignment Example ...

Biggio's Department Store has six employees available to assign to four departments in the store: home furnishings, china, appliances, and jewelry. Most of the six employees have worked in each of the four departments on several occasions in the past and have demonstrated that they perfrom better in some departments than in othe

Linear Programming: Material/Labour Min-Maxing

A. Maximize Z = 4x1 + 3x2 Subject to Material 6x1 + 4x2 < 48 lb Labor 4x1 + 8x2 < 80 hr x1, x2 > 0 b. Maximize Z = 2x1 + 10x2 Subject to Durability 10x1 + 4x2 > 40 wk Strength 1x1 + 6x2 > 24 psi Time 1x1 + 2x2 < 14 hr x1, x2 > 0 c. Maximiz

Investment Decision Problem

The Heinlien and Krampf Brokerage has just been instructed by one its clients to invest $250,000 for her money obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but also has her own ideas about the distribution of the funds being invested. In particular, she


In the cash now lottery game there are 10 finalists who submitted entry tickets on time. From these 10 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the second prize is one hundred thousands dollars, and the third prize is ten thousand dollars. Use the permutations rule to determine th

Set of data that can be modeled as a polynomial function

Details: Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. If we compare gas mileage at two different speeds, V1 and V2, the gas required varies as (V1/V2), raised to the third power, (V1/V2)3. Rational functions are also usefu

Solve a Linear Programming Problem using Excel

AC's take 3 hours of wiring and 2 hours of drilling. Fans take 2 hours of wiring and 1 hour of drilling. 240 hours of wiring and 140 hours of drilling are available during production cycle. Each AC sold yields $25 profit and each fan yields $15 profit.At least 20 ACs should be made and no more than 80 fans should be made. What i

LPP: Blending problem calculations

A drink company plans to make new drink consisiting of a mixture of fruit juice and soda: each ounce of juice contains 0.25mg of sugar and 3mg of VitaminC and costs 3p to produce. each ounce of soda contains 0.5mg of sugar and 1mg of Vitamin C and costs 1p to produce. the drink is to be sold in 10 ounce bottles and must conta

Media Selection and TV Ads

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper ads. Information about each medium is shown below. Medium Cost Per Ad # Reached Exposure Quality TV 500 10000 30 Radio 200 3000 40 Newspaper 400 5000 25 If the number of TV ads cannot exc

Descriptive Statistics

The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. The company operates one "8 hour" shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup is limited to maximum produ

integer linear program

(See attached file for full problem description) --- The following table is a list of all of the stocks that you have in your stock portfolio. The original purchase price, current price and your best guess for the "anticipated" price (one year into the future) is given below: Share Price ($) Stock # Shares Owned Purch

Developing Constraints for Lindo

Reliable Investment Corporation is in the process of determining its investment strategy for the next three years. Currently (time t = 0), $100,000,000 is available for investment. The cash flow associated with investing $1 in each of the available investment alternatives (A - E) is given in the table below: (See attached fi