Regression Analysis(RA)is a statistical forecasting model that is
concerned with describing and evaluating theip between a given
variable (usually called the dependent variable, denoted as Y) and one or
more other variable (usually known as thent/exploratory
variable, denoted as X) .
RA can predict the outcome of a given key business indicator (dependent
Simple Linear Regression variablebased on the interactions of other related business drivers
(independent /exploratory variables)
Analyzes the relationship between two variables, X and Y.
The eatonship an bedessced asa uncconofa nearrstaghttne))in
equation simple linear regression
Chapter 13 Y Y=- +- X lnearegresson lnein
1. For elementary school children, it is possible to predict
a students reading ability level by measuring the height Learning Objectives
of the student. One X to predict Y
Reading_ability = f(height) 1. How to use regression analysis to predict
the value of a dependent variable
2. If we assume the value of an automobile decreases by a
constant amount each year after its purchase, and for based on an independent variable
each mile it is driven, the following linear function would 2. The meanin g of the reg gression
predict its value (the dependent variable on the left side coefficients, b and b
of the equal sign) as a function of the two independent o
variables which are age and miles: 3. To make inferences about the slope and
MORE than One X to predict Y
Car_value = f(age, miles) correlation coefficient
where Car_value, the dependent variable, is the value 4. To estimate mean values and predict
of the car, age is the age of the car, and miles is the individual values
number of miles that the car has been driven.
Dependent Variable (Notation: Y)
The variable you wish to predict Example
Independent Variable (Notation: X) For elementary school children, it is possible
Variable used to make the prediction
Simple Linear Regression to predict a students reading ability level
A single numerical independent variable X is used to predict the by measuring the height of the student.
numerical dependent variable Y
In the regression terms, we could say that
Use sevveall independent variables to predict a numerical for elementary school children
dependent variable Y.
-therre is aa diirecttrellattonnshhip bbettweeeen aa
students height and reading ability level
One variable X Called the independent or explanatory
can be used explain (forecast, predict.)
to - a students reading level ability can be
a second Y Called the dependent or response variable explained (forecasted) by the students
When changes in the variable X leads to predictable change in the variable Y
then we say X can be used to explain Y
Simple Linear Regression
Does this mean that we should conclude Regression analysis allows you to identify the type off
that taller children are better readers?
relatonnship that exists between a dependent variable
NO! (X) and an independent variable (Y)
The simplest relationship is the straight line or linear
Since for the elementary school children relationship
height is usually a good predictor of age Y Y See Figure 13.2 page 579
types of relationshipsferent
a ge is a ggood predicp tor of grade level g
and finally reading level will be strongly related .
to grade level . .
. -o . .
So while height may allow us to predict reading . . .
level for elementary school students we should . . . .
not conclude that we should stretch out the Slope=1 . .
students to make them better readers.
Positive (Direct) Linear RelationNegative (Inverse) Linear
TYPES OF RELATIONSHIPS Recall that when the graph of y versus x tends to be in the straight line, we
Regression analysis allows you to identype offeatonsshpip say that there is a linear relationship
that exists between a dependent variable (X) and an independent y To predict the straight-line (linear) model
variable (Y) .
The simplest relationship is the straight line or linear relationship .
Rule of Thumb concepts . . Slope=1
X Y ,Y XType of