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2…Launching Fruit Flavoured Soft Drinks at Fresh Cola (B)

2…Launching Fruit Flavoured Soft Drinks at Fresh Cola (B)

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7.2 Launching Fruit Flavoured Soft Drinks at Fresh Cola (B)

189

7.2.5 Experiment-4
The file freshcola4.xls reports data for each individual on purchase likelihood for
the brand he/she was exposed to (reported as 1 for Bravo, 2 for Delight and 3 for
Cool) under the experiment, along with information on the store type where
interviewed (reported as 1 for drug store, 2 for supermarket, 3 for hypermarket and
4 for kirana store). The data need to be analysed to answer the above query.
Analysis Results (Fresh Cola: Experiment-4)

This table shows treatment (Store type
and Brands) representations and
sample size in each category
Between-Subjects Factors
Value Label

Store Type

Brands

N

1

Drug Store

60

2

Super Market

60

3

Hyper Market

60

4

Kirana Store

60

1

Bravo

80

2

Delight

80

3

Cool

80

This table shows mean value of
dependent variable in each cell (12
different cells) and total mean values

Descriptive Statistics
Dependent Variable: Likelihood of Purchase
Store Type

Drug Store

Super Market

Hyper Market

Kirana Store

Total

Brands

Mean

Std. Deviation

N

Bravo

90.75

5.711

20

Delight

38.45

5.491

20

Cool

19.60

5.862

20

Total

49.60

30.863

60

Bravo

63.20

5.415

20

Delight

89.45

4.696

20

Cool

41.45

4.489

20

Total

64.70

20.364

60

Bravo

39.70

4.680

20

Delight

61.90

4.364

20

Cool

90.15

6.072

20

Total

63.92

21.413

60

Bravo

21.00

4.801

20

Delight

18.85

5.060

20

Cool

55.05

6.778

20

Total

31.63

17.609

60

Bravo

53.66

26.766

80

Delight

52.16

26.978

80

Cool

51.56

26.412

80

Total

52.46

26.622

240

190

7 Experimental Analysis of Variance (ANOVA)

Levene's Test of Equality of Error Variances

This indicates that the assumption of homogeneity
of variances is followed. Because Levene's
test is insignificant, we know that the variances
are significantly equal across groups. This test
follows a regression approach to test the
homogeneity across groups.

a

Dependent Variable: Likelihood of Purchase
F

df1

df2

.801

11

Sig.
228

.639

Tests the null hypothesis that the error variance of the
dependent variable is equal across groups.
a. Design: Intercept + Treatment_1 + Treatment_2 +
Treatment_1 * Treatment_2
Tests of Between-Subjects Effects
Dependent Variable: Likelihood of Purchase
Source

Type III Sum of

df

Mean Square

F

Sig.

Squares
Corrected Model
Intercept

162911.012

Partial Eta
Squared

a

11

14810.092

521.044

.000

.962

660555.337

1

660555.337

23239.431

.000

.990

Treatment_1

43380.146

3

14460.049

508.728

.000

.870

Treatment_2

187.200

2

93.600

3.293

.039

.028

119343.667

6

19890.611

699.785

.000

.948

Error

6480.650

228

28.424

Total

829947.000

240

Corrected Total

169391.662

239

Treatment_1 * Treatment_2

Partial
Eta
Squared
indicates how much of the
variance
in
Purchase
likelihood
can
be
Predicted
from
each
independent variables

a. R Squared = .962 (Adjusted R Squared = .960)

R Squared is the variance explained by all the independent
variables to the dependent variable.
Rule of Thumb: by Cohen (1988)
For eta: small = .10, medium = .24, and large = .31;
for R squared: small = .10, medium =.36, and large = .51.

Shows the interaction effect is statistically significant.
When the interaction is statistically significant, you should
analyze the "simple effects" (differences between means
for one variable at each particular level of the other
variable). If interaction is significant, giving inferences
using main effect (due to treatments) is somewhat
misleading

7.2 Launching Fruit Flavoured Soft Drinks at Fresh Cola (B)

191

If you find a significant interaction, you should examine the profile plots of
cell mean to visualize the differential effects. If there is a significant
interaction, the lines on the profile plot will not be parallel. In this case, the
plot indicates that brand Bravo’s purchase likelihood is high in Drug store,
compared to super market, hyper market and Kirana stores. Brand Delight’s
purchase likelihood is very high when it’s there in Super market, compared
to other three stores. Brand Cool’s likelihood of purchase is high in Hyper
market compared to other stores. In all these three brands are shown least
likelihood preference when they are in Kirana stores This interpretation,
based on a visual inspection of the plots, needs to be checked with
inferential statistics.

192

7 Experimental Analysis of Variance (ANOVA)
How to Analyse Two Way Factorial ANOVA Results

Interaction of the treatments is statistically
significant
Yes

No

Examine the interaction effect first and then analyze the
"simple effects" (differences between means for one
variable at each particular level of the other variable).








Check the main effect separately
for each treatment

Compute a new variable using
Transform=>Compute in SPSS.
This new variable is a categorical variable which
represents the levels (each cell as a level). In this
example, we will get 12 different cells. So 12
different levels.
Run One-way ANOVA, in which purchase
likelihood as dependent variable and the newly
created variable as independent variable.
Do the Contrast Test using SPSS
Examine the simple main effects using the
contrast results.

One-Way ANOVA and Contrast Test Results
The overall F is significant at
p<.001

ANOVA
Likelihood of Purchase
Sum of Squares
Between Groups
Within Groups
Total

df

Mean Square

162911.013

11

14810.092

6480.650

228

28.424

169391.663

239

F

Sig.

521.044

.000

Contrast Coefficients
Contrast

Twelve new cell codes
1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

1

1

-1

0

0

0

0

0

0

0

0

0

0

2

1

0

-1

0

0

0

0

0

0

0

0

0

Contrast Tests
Contrast
Assume equal variances

Value of Contrast

Std. Error

t

1

27.55

1.686

16.341

df

Sig. (2-tailed)
228

.000

2

51.05

1.686

30.280

228

.000

Does not assume equal

1

27.55

1.760

15.654

37.893

.000

variances

2

51.05

1.651

30.918

36.587

.000

Likelihood of Purchase

Contrast 1 looks at the difference
Between codes 1 and 2 (Brand Bravo in
Drug store and Brand Bravo in Super
Market)

7.2 Launching Fruit Flavoured Soft Drinks at Fresh Cola (B)

193

7.2.6 Questions for Discussion
1. Suggest appropriate analysis tool for each of the experiments to draw meaningful conclusions on the queries. Recall that Varghese has to report to the
Chairman, Mr. Kutty on these at the Board meeting scheduled for October
2012.

Chapter 8

Multiple Regression

8.1 Introduction
Multiple regression analysis is one of the dependence technique in which the
researcher can analyze the relationship between a single-dependent (criterion)
variable and several independent variables. In multiple regression analysis, we use
independent variables whose values are known or fixed (non-stochastic) to predict
the single-dependent variable whose values are random (stochastic). In multiple
regression analysis, our dependent and independent variables are metric in nature;
however, in some situations, it is possible to use non-metric data as independent
variable (as dummy variable).
Gujarati and Sangeetha (2008) defined regression as:
‘It is concerned with the study of the dependence of one variable, the dependent
variable, on one or more other variables, the explanatory variables, with a view to
estimating and/or predicting the (population) mean or average value of the former
in terms of the known or fixed (in repeated sampling) value of the later’.

8.2 Important Assumptions of Multiple Regression
1. Linearity—the relationship between the predictors and the outcome variable
should be linear
2. Normality—the errors should be normally distributed—technically normality is
necessary only for the t-tests to be valid, estimation of the coefficients (errors
are identically and independently distributed
3. Homogeneity of variance (homoscedasticity)—the error variance should be
constant
4. Independence (no autocorrelation)—the errors associated with one observation
are not correlated with errors of any other observation
5. There is no multicollinearity or perfect correlation between independent
variables.
S. Sreejesh et al., Business Research Methods,
DOI: 10.1007/978-3-319-00539-3_8,
Ó Springer International Publishing Switzerland 2014

195

196

8 Multiple Regression

Additionally, there are issues that can arise during the analysis that, while
strictly speaking, are not assumptions of regression, are none the less, of great
concern to regression analysis. These are
1. Outliers; it is an observation whose dependent variable value is unusual given
its values on the predictor variable (independent variable).
2. Leverage; an observation with an extreme value on a predictor variable is called
a point with high leverage.
3. Influence; an observation is said to be influential if removing the observation
substantially changes the estimate of coefficients. Influence can be thought of as
the product of leverage and outliers.

8.3 Multiple Regression Model with Three Independent
Variables
One of the well-known supermarket chains (ABC group) in the country has
adopted an aggressive marketing decision particularly to increase the sales of its
own private brands in the last 19 months. Recently, the company decided to
investigate its product sales in the last 19 months. In the last 19 months, the
company has invested lot of money in three strategic areas: Advertisement,
marketing (excluding advertisement and distribution) and its distribution network.
The company decided to do a multiple regression analysis to predict the impact of
advertisement, marketing, and distribution expenses on its sales (Table 8.1a).

8.4 Multiple Regression Equation
A multiple regression equation with three independent variables is given below:
Yt ¼ b1 þ b2 x2t þ b3 x3t þ b4 x4t þ u0t

ð1Þ

Salest ¼ b1 ðconstantÞ þ b2 ðAdvertisement Ex:Þt þ b3 ðMarketing Ex:Þt
þ b4 ðDistribution Ex:Þt
þ u0t

ð2Þ

Here, Yt is the value of the dependent variable (here it is sales) on time period t,
b1 is the intercept or average value of dependent variable when all the independent
variables are absent. b2 b3 ; and b4 ; are the slope of sales (partial regression
coefficients) with respect independent variables like advertisement expenses,
marketing expenses, and distribution expenses holding other variables constant.
For example, the coefficient value b2 implies that one unit change (increase or