McGill University
Advanced Business Statistics
MGSC-372
MGSC 372
Lognormal Distribution
The Lognormal Distribution
A continuous random variable X follows a lognormal distribution if its
natural logarithm, ln(X), follows a normal distribution.
The lognorma

McGill University
Advanced Business Statistics
MGSC-372
Simple Linear Regression
Simple Linear Regression
Simple linear regression analysis is used to analyze the nature of
the relationship between two variables.
The dependent variable is designated by Y

ANOVA
McGill University
Advanced Business Statistics
MGSC-372
Read: Business Statistics (A Second Course),
2nd Custom Edition for McGill University
Chapter 11
ANOVA
ANOVA is a statistical test of significance for the equality
of several (2 or more) popula

Contrasts and Problems on ANOVA
The data sets are available through the
ANOVA section of myCourses.
See myCourses ANOVA Problems for
dataset Problem 11.25
Problem 11.28
See myCourses ANOVA Problems for
dataset Problem 11.36
Contrasts
A contrast is a comb

McGill University
Advanced Business Statistics
MGSC-372
Box-Jenkins Analysis
Autocorrelation - ACF
Partial Autocorrelation - PACF
ARIMA Models
ARIMA = Autoregressive Integrated Moving
Average
AR = Autoregressive
I = Integrated
MA = Moving Average
Steps to

McGill University
Advanced Business Statistics
MGSC-372
Checking ANOVA Assumptions
Completely Randomized Design
Detecting Nonnormal Populations
1. For each treatment construct a histogram, normal
probability plot, or other graphical display that will
dete

McGill University
Advanced Business Statistics
MGSC-372
Time Series Classical Decomposition,
Census II, X-12 ARIMA Methods
Decomposition Models
Time series
a sequence of observations collected from a process at
fixed (and usually equally spaced) points i

McGill University
Advanced Business Statistics
MGSC-372
Residual Analysis
Using residuals to detect
departure from assumptions
Definition of Residual vs. Error Term in
Model
Error term in a true multiple regression model
i yi E ( y )
yi 0 1 x1 . k xk
R

McGill University
Advanced Business Statistics
MGSC-372
Good or Bad Forecasts!
"Computers in the future may weigh no more than 1.5 tons."
Popular Mechanics, forecasting the relentless march of
science, 1949
"I think there is a world market for maybe fiv

McGill University
Advanced Business Statistics
MGSC-372
Variable Screening Methods
Stepwise Regression
All-Possible-Regressions (Best subsets)
Stepwise Regression
Variables are entered into the model in order of
significance (based on -values or F-values)

Estimation
Least Squares
Maximum Likelihood
Introduction to Least Squares Estimation (LSE)
Example: Estimate the mean of a distribution based on a sample of n
values x1 , x2, x3, , xn.
Let = the population mean
Then the Least Squares estimate of is the va

Return to Regression EXAMPLE
The VP of Sales for a large department store chain wishes to investigate the
relationship between store profits Y per day (in $1,000) and advertising expenditures
per month (X in $1,000). The following data has been determined

Full and Reduced (Nested) Models
Testing a Hypothesis
For example, assume we have a (Reduced) model
E (Y ) 0 1 X1 2 X 2 3 X 3
(R)
H: = = 0
and we are considering the (Full) model
E(Y ) 0 1 X1 2 X 2 3 X 3 4 X 4 5 X 5 (F) H: at least one of , 0
To test whet

McGill University
Advanced Business Statistics
MGSC-372
Regression Pitfalls
Identify and correct potential
problems in Multiple Regression
Observational vs Experimental Data
Observational Data:
Values of the independent variable are uncontrolled.
Experime

McGill University
Advanced Business Statistics
MGSC-372
Review
Normal Distribution
The Normal Distribution
aka
The Gaussian Distribution
The Normal Distribution
y
1
f ( x)
e
2
1 x
2
2
x
Areas under the Normal Distribution curve
-3
-2 -
68%
95%
99.7%
+

McGill University
Advanced Business Statistics
MGSC-372
Review
Binomial Distribution
The Binomial Distribution
Bernoulli Process
Characteristics of the Bernoulli Process
1.
The experiment consists of a fixed number (n) of repeated trials.
2.
Each trial ha

McGill University
Advanced Business Statistics
MGSC-372
Residual Analysis II
More on outliers
As we saw, an outlier may be due to an error in
measurement or data entry.
When an outlier is not due to an error but represents
an accurate value, we have to in