Lecture 11
Residual Analysis (III)
-Assessing Independence
Assessing the Assumption That the
Disturbances are Independent
If the disturbances are independent, the
residuals should not display any patterns.
One such pattern was the curvature in the
resid
Chapter 3
Simple Regression Analysis
(Part 1)
Using Simple Regression to Describe a
Relationship
Regression analysis is a statistical technique
used to describe relationships among variables.
The simplest case is one where a dependent
variable y may be
Lecture 15
One-Way Analysis of Variance
ANOVA
Analysis of variance was a term used in
regression to describe how we split the
variation in our sample into "explained"
and "unexplained" parts.
In this chapter we will look at some other
ANOVA procedures w
Lecture 5
Multiple Regression Analysis (Part II)
Comparing Two Regression Model
Comparing Two Regression Models
So far we have looked at two types of
hypothesis tests. One was about the
overall fit:
H0: 1 = 2 = = K = 0
The other was about individual terms
Lecture 14
Variable Selection
Introduction
One of the primary tasks in this course is
to choose which variables to include in the
regression equation: The F test for overall
fit, the partial F test , and t test.
Variable selection technique can also be
Autumn 2016
JSIS 200A. States and Capitalism:
The Origins of the Modern Global System
Anand A. Yang (aay@uw.edu)
Tel. 206-543-4902, 308C Smith
Office Hours: M 11-12.15
and by appointment
Teaching Assistants (TA Office: Thomson Hall)
Esra Bakkalbasioglu (e
Lecture 13
Forecasting Methods for Time Series Data
Introduction
Time-series data are data gathered on a single
unit (person, firm, etc.) over a sequence of time
periods.
These time periods may be years, months or
any other measure of time.
Here we ass
Lecture 8
Residual Analysis (I)
-Assessing Linearity Assumption-
The multiple linear regression model is
yi = 0 + 1 x1i + 2 x2i + L + k xki + ei
Certain assumptions were made about how
the errors ei behaved.
Do those assumptions appear reasonable.
Assumpt
Lecture 12
Regression with Indicator Variables
Using and Interpreting Indicator Variables
Indicator or dummy variables are a special type of variable
Indicator variables take on two values: one and zero. These values
are used to indicate if an observation
Lecture 7
Fitting Curves to Data
Background
Multiple linear regression model was presented as:
yi = 0 + 1 x1i + 2 x2i + L + k xki + ei
where we assumed linear relationships between
y and the x variables.
In case that linear relation doesnt hold, we need
c
Lecture 3
Simple Regression Analysis
(Part 2)
Estimating the Conditional Mean of y
Given x.
At xm = 40 , the quantity we are estimating is:
y| x = 40 = 0 + 1 40
Our best guess of this is just the point on the
regression line:
y m = b 0 + b1 40
Standard E
Lecture 9
Residual Analysis (II)
-Assessing Constant Variance-
Constant variance
Assumptions states that the errors i should
have the same variance everywhere.
This implies that if residuals are plotted against
an explanatory variable, the scatter shoul
Lecture 4
Multiple Regression Analysis
(Part 1)
Multiple Regression Analysis
For two independent variables, the general
form of the multiple regression equation is:
Yi = 0 + 1 X1i + 2 X2i + i
X1i and X2i are the i-th observation of
independent variables
Two-Way ANOVA
In this situation, there are two factors or
explanatory variables.
For example, suppose a company is going
to experiment with two price levels and
three types of advertising.
Now a "treatment" is considered a priceadvertising combination,
Lecture 10
Residual Analysis (III)
-Assessing Normality
-Influential Observations
Assessing the Assumption That the
Disturbances are Normally Distributed
There are many tools available to check the
assumption that the disturbances are normally
distributed
Lecture 6
Time Series Regression
-Lagged Explanatory Variables
Lagged Variables as Explanatory Variables
in Time-Series Regression
When using time series data in a regression, the
relationship between y and x may be concurrent or x
may serve as a leading
Family of regression models
Outcome variable determines choice of model
Outcome
Continuous
Survival
Categorical
Model
Linear regression
Cox model
Logistic regression
Uses
Estimate force of association between outcome and
covariates (Factor)
Control o
Lecture 13
Regression with Interaction Variable
Some important facts about Indicator variables:
Always pick one reference category first.
The coefficients of indicator variables are not really slopes , but
are intercept adjuster.
Dont forget to use partia