correlation regression relationship analysis 1233772232553257 1

8/8/2019 Correlation Regression Relationship Analysis 1233772232553257 1

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PPT 18-1

Correlation/Regression

RELATIONSHIP ANALYSIS



PPT 18-2

Learning Objectives

The meanings and uses of regression andcorrelation analyses

Calculate regressions and correlation Basics of multivariate statistical analysis

techniques



PPT 18-3

Statistics Not Always Black and

White How does the story relate to marketing

research?

Explain the meaning of this statementfrom the story: ´Statistical fallacies bythemselves might create a certain amountof random mischief. But the big problemis that statistics which seem to confirm thedogmas of the intelligentsia are seizedupon and trumpeted throughout

academia and the media, with little or no´ µ



PPT 18-4

Relationship Analysis

The examination of the associationbetween two or more variables. Inmarketing, some of the more apparentrelationships include associations betweenadvertising and sales, company size and

advertising budget, supply and demandfor products, and customer satisfaction andcustomer loyalty.



PPT 18-5

Scatter Diagrams

Two related variables, called bivariate data,plotted as points on a graph.

Each point on the diagram represents a pair ofvalues, one based on the X scale (independentvariable) and the other based on the Y scale

(dependent variable). Making a scatter diagram usually is the initial

step in investigating the relationship betweentwo variables, because the diagram shows

visually the shape and degree of closeness of the



PPT 18-6

Simple Regression Analysis

Refers to statistical techniques formeasuring the relationship between a

dependent variable and one or moreindependent variables. The relationshipbetween two variables is characterized byhow they vary together. Given pairs of X

and Y variables, regression analysismeasures the direction (positive or negative)and rate of change (slope) in Y as X changes,

or vice versa. Using the values of the



PPT 18-7

Regression Analysis Requires Two

Operations Derive an equation, called the regression

equation, and a line representing the

equation to describe the shape of therelationship between the variables. Theregression line is the line drawn through ascatter diagram that ´best fitsµ the data

points and accurately describes therelationship between the two variables.The equation and its line may be linear or

curvilinear.



PPT 18-8

Correlation Analysis

Statistical techniques for measuring thecloseness of the relationship between

variables. It measures the degree to which changesin one variable are associated withchanges in another.

It can only indicate the degree ofassociation or covariance betweenvariables. Covariance is a measure of the

extent to which two variables are related.



PPT 18-9

Correlation Analysis -

continued Regression and correlation analysis maybe either simple or multiple. Simple

analysis uses only two variables, onedependent and one independent.Multiple analysis deals with three or morevariables, one dependent and two or more

independent.



PPT 18-10

Regression Equation and Line

Researchers estimate the regression lineusing the following equation:

Y = F0+ F1Xi + II

F0 = the Y intercept when X equals zero

F1 = the slope of the regression line, which is

the increase or decrease in Y for each changeof one unit of X

Xi = a given value of the independentvariable

=



PPT 18-11

Regression Equation and Line -

continuedThe model involves parameters that areunknown ( F 0 and F1) but can be estimated

from sample data. The error term, Ii,referred to as ´eta,µ is also unobservable,but can be estimated from sample data.



PPT 18-12

The Lack Of Precision Can Be Due To

Complexity of most marketing and otherbusiness problems

The functional form of the relationship between

the dependent and independent variables maydiffer from the one selected

Measurement of the variables may be imperfect

Data are typically available only at an aggregatelevel

Data are based on human behavior, so the errorterm in the model may account for a ´randomµ

component in behavior



PPT 18-13

Least-Squares Method

A statistical technique that fits a straightline to a scatter diagram by using the

shortest vertical distances of all the pointsfrom the straight line.

The equation derived by this method willyield a regression line that best fits the

data.



Regression coefficients are the values thatrepresent the effect of the individualindependent variables on the dependentvariable.



PPT 18-14

Standard Deviation of

RegressionThe standard deviation of the Y values fromthe regression line (Y c). This is also calledthe standard error of estimate, since it canbe used to measure the error of theestimates of individual Y values based onthe regression line.



PPT 18-15

Total Deviation

Total deviation = Unexplained deviation +Explained deviation

The terms ´explainedµ and ´unexplainedµare used here to indicate whether or not aportion of the total deviation is reduced bythe introduction of the X values incomputing Y

cvalues. When these values

are summed and squared individually, they



PPT 18-16

Coefficient of Determination (r 2)

The strength of association or degree ofcloseness of the relationship between twovariables measured by a relative value. Itdemonstrates how well the regression linefits the scattered points.

It indicates the amount of variation in the

dependent variable that is explained bythe variation in the independent variableand vice versa.

It is defined as the ratio of the explained



PPT 18-17

Coefficient of Determination (r 2) -

continued

When r 2 is close to 1, the Y values are veryclose to the regression line. When r 2 isclose to 0, the Y values are not close to theregression line.

r 2 is always a positive number. It cannot

tell whether the relationship between thetwo variables is positive or negative.



PPT 18-18

Correlation Coefficient

The square root of r 2, is frequentlycomputed to indicate the direction of therelationship in addition to indicating thedegree of the relationship.

It is the correlation between the observedand predicted values of the dependent

variable.



Since the range of r 2 is from 0 to 1, thecoefficient of correlation r will vary withinthe range of from 0 to s 1.

The + sign of r will mean a negativecorrelation. The sign of r is the same asthe sign of b (the slope) in the regression

equation.



PPT 18-19

Calculating Regressions Using

Computers To run the calculations using SPSS

² Click on ´Statisticsµ

² Then click on ´Regressionµ and ´Linearµ² These commands designate the statistical test

to be run

To run calculations using Excel

² Click on ´Toolsµ and ´Data Analysisµ

² Then click on ´Regression.µ



PPT 18-20

Multiple Regression Analysis

This test will determine the association orrelationship between dependent andindependent variables.

In multiple regression analysis, more thantwo variables are included in theexamination. While the dependent

variables is still represented by Y , theindependent variables are represented byX

1, X

2, X

3, . . . and so on



Since with multiple regression we aredealing with more than one independentvariable, we refer to the associationbetween the dependent and independentvariables as the coefficient of multipledetermination, denoted by.



PPT 18-21

Calculating Multiple Regression UsingComputers

To perform the computations using SPSSfor Windows

² Click on ´Statisticsµ

² Then click on ´Regressionµ and ´Linearµ

² These commands designate the statistical testto be run

To run the calculations using Excel² Click on ´Toolsµ and ´Data Analysisµ

² Then click on ´Regression.µ



PPT 18-22

Forecasting Using Time Series

Analysis Numerical variables that are calculated,measured, or observed sequentially on aregular chronological basis are called timeseries

A time series representing anorganization·s is the result of interactions

of many changing forces The forces can be business, economic,

political, and social influences as well as

the forces of nature.



PPT 18-23

Time Series Patterns Or

Components Secular trends - direction of a time series

movement over a long period of time usually

represented by a straight line or a smoothcurve.

Seasonal variation - repeating periodicmovement of a time series



PPT 18-24

Two Popular Forecasting

Techniques Trend Analysis - Used when historical data is

plotted or extrapolated to project some

outcome in the future. Exponential Smoothing -Type of weighted

average forecasting technique that assigns

heavier weights to recent data and lighterweights to less recent data. When forecasting,the more recent data are more likely to bebetter predictors of the near future than areearlier eriods.



PPT 18-25

Multivariate Statistical Analysis

y Any simultaneous analysis of more than twovariables.

y Many times, multivariate techniques are a

means of performing in one analysis what usedto take multiple analyses using univariatetechniques (analysis of single-variabledistributions).

y Common multivariate techniques:multiplediscriminant analysis,multidimensional scaling, factor analysis, cluster analysis and conjoint

analysis.



PPT 18-27

Multiple Discriminant Analysis(MDA)

- continued Intent of this technique is two-fold:

(1) to understand group differences

(2) to predict the likelihood that a variable willbelong to a particular group, based on severalindependent variables.

Linear combination is known as the

discriminant function An important function of discriminant

analysis is to create a classification matrix,

which shows the number of correctly and



PPT 18-28

Factor Analysis

Groups attributes that are alike.

Used to examine interrelationships among

many variables and to explain thesevariables in terms of their commonunderlying and unobservable dimensions(called ´factorsµ).

Factor analysis can be used to reduce theinformation contained in several originalvariables into a smaller, more manageable,

set of variables while losing as little



PPT 18-31

Conjoint Analysis

Provides information about the relativeimportance respondents place onindividual attributes when choosing frommultiple brands.

Built on the assumption that consumersmake complex decisions based not on one

factor at a time but on several factors´jointlyµ (thus the term ´conjointµ).



PPT 18-32

Net Impact

The Internet

² Will not help researchers with statisticalanalyses.

² Will lend qualitative support for the researchfindings obtained from the quantitativeanalyses.

² Can inform researchers about advancementsmade in statistical analyses through publishedmanuscripts, discussion groups, and chatgroups

² Researchers also use electronic mail



PPT 18-33

Decision Time!

If correlation analysis is a popular and informativestatistical method, why should researchers botherusing the somewhat intimidating multivariatestatistical techniques? Do you feel there is really much

to gain from these methods?

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