STOR445 - Midterm '#1
Please be neat and Show all your work to get partial credit. W’rite your name on each page.
1 Let X be a continuous random variable with probab
MAXIM is a collection of MATLAB programs (m-files) intended to be used with the
book `Introduction to Modeling and Analysis of Stochastic Systems (Second Edition)'
by V G Kulkarni. These files were created by using MA
Lifetime Fitness Final Exam Review
The LFIT final will be given on Sakai
Come to Fetzer Gym A on the LAST day of class during your regular class time.
Bring your computer and make sure your battery is fully charged before the exam (no outlets will
(Please turn in your solutions for Questions 1, 2, and 4 only.)
1. Suppose that X is a Poisson random variable with parameter 5. Let Y = min(X, 5).
Determine the following:
(a) The probability mass function of X
(b) The probability mas
Simple Linear Regression
Regression analysis is "a statistical methodology that utilizes the relation between two or more
quantitative variables so that one variable [the dependent or response variable] can be predicted
from the other, or
Diagnostics & Remedies in Simple Regression
1. Residual Analysis & the Healthy Regression
1. Residual Plot of the Healthy Regression
Residual analysis is a set of diagnostic methods for investigating the appropriateness of a
regression model based on the
Matrix Representation of the Regression Model
1. Introduction to Matrices
These notes cover the following:
1. properties of, and operations on, matrices and vectors
2. matrix representation of the linear regression model, both simple and multiple
Multiple Linear Regression
1. The Multiple Regression Model in General
1. Multiple Regression Model with p - 1 Independent Variables
The multiple linear regression model with p - 1 independent variables can be written
Yi = 0 + 1 Xi,1 + 2 Xi,2 + + p-1 Xi,p
1. Nature of Heteroscedasticity
Heteroscedasticity refers to unequal variances of the error i for different observations. It may be
visually revealed by a "funnel shape" in the plot of the residuals ei against the estimates Yi or
Outlying & Influential Observations
1. Added-Variable Plots for Functional Form & Outlying Observations
1. Uses of Added-Variable Plots
Added-variables plots are also called partial regression plots and adjusted variable plots.
A partial regression plots
Polynomial Regression & Interactions
1. Polynomial Regression with One Predictor Variable
1. Formulation of the Model
A nonlinear relationship between y and x can often be approximately represented within the
general linear model as a polynomial function
There are two model selection procedures we will consider:
all-possible regressions procedures identify "good" subsets of the pool of potential
independent variables among all possible subsets of the variables, where "good" may be
Categorical Independent Variables
1. Models without Interactions
An indicator (or binary variable) is a variable that can have only two values, 0 or 1.
Indicator variables are used to represent categorical (or nominal or qualitative) variables.
*Multiple Linear Regression SAS Code;
EXAMPLE DATASET: The example dataset has been expanded to include more
and more observations.
case = id
pubs = # of publications
time = years since phd
cits = # of citations
salary = salary