3/17/2011
1
Simple Linear Regression
Chapter 13
Page 578
Regression Analysis
•Regression Analysis(RA) is a statistical forecasting model that is
concerned with describing and evaluating the relationshipbetween a given
variable (usually called the dependent variable, denoted as Y) and one or
more other variable (usually known as the independent/exploratory
variable, denoted as X) .
•RA can predict the outcome of a given key business indicator (dependent
variable) based on the interactions of other related business drivers
(independent /exploratory variables)
•Analyzes the relationship between two variables, X and Y.
can be described as afunction of alinear (
•

equation <called linear regression> “simple linear regression”
Y=Eo+E1X
Eo
E1
linear regression linelinear regression lineY
X
intercept
slope
Example
1. For elementary school children, it is possible to predict
a student’s reading ability level by measuring the height
of the student.
Reading_ability= f(height) <Simple Linear Regression>
2. If we assume the value of an automobile decreases by a
constant amount each year after its purchase, and for
each mile it is driven, the following linear function would
One X to predict Y
predict its value (the dependent variable on the left side
of the equal sign) as a function of the two independent
variables which are age and miles:
Car_value = f(age, miles) <Multiple Linear Regression>
where Car_value, the dependent variable, is the value
of the car, age is the age of the car, and miles is the
number of miles that the car has been driven.
MORE than One X to predict Y
Learning Objectives
1. How to use regression analysis to predict
the value of a dependent variable
based on an independent variable
2. The meanin
of the re
ression
coefficients, boand b
3. To make inferences about the slope and
correlation coefficient
4. To estimate mean values and predict
individual values
•Dependent Variable (Notation: Y)
–The variable you wish to predict
•Independent Variable (Notation: X)
–Variable used to make the prediction
•Simple Linear Regression
–A singlesingle numerical independent variable X is used to predict the
numerical dependent variable Y
•Multiple Regression
–Use severalseveral independent variables to predict a numerical
de
endent variable Y.
One variable XCalled the independent or explanatory
variable
can be used
to
“explain” (forecast, predict….)
a second
variable
YCalled the dependent or response variable
When changes in the variable X leads to predictable change in the variable Y
then we say “X can be used to explain Y”
Example
For elementary school children, it is possible
to predict a student’s reading ability level
by measuring the height of the student.
In the regression terms, we could say that
for elementary school children
“
there isadirect relationship between a

student’s height and reading ability level”
or
 “a student’s reading level ability can be
explained (forecasted) by the student’s
height”
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