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