This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: SSC306 I. Introduction to the Problem:
This analysis examines data collected on the top 100 Global Brands identiﬁed by Interbrand. To determine if the amount of media coverage attained by a company, its advertising expenditures and brand loyalty are related to its
brand value, variables such as brand value, ad expenditures, brand loyalty, media penetration, and brand mentions
are studied in the analysis. The brand value data was collected from Interbrand’s published report of the top 100
Global Brands, and the corresponding data was combined from a variety of sources. Some data is unavailable for
several brands, particularly ad expenditure data, due to various reasons. Ultimately, the reliability and
generalizability of this analysis will be determined. II. Descriptive Statistics: Count Median Q1
QB ” Min.
Max.
Mean IQR Range SD Table 0.1: Descriptive Statistics Brand Media Lead Par. Mentions Text
Mentions Headline
Value Penetration Mentions _ 98 98 98 _
9198.00
M
mm Brand III. Statistical Analysis:
Question 1. Frequency N
O H
LI'I H
O OUI Figure 1.1: Brand Value for US Brands Figure 1.2: Brand Value for nonUS Brands u—ninN
OLI‘O new”; Frequency 5 ‘7‘ _ IFrequency 0 WWWWWWVV IFrequency
OOOOOOOOOOOOOOOOO
§§§§§§§§§§§§§§§§§ a°°e°°¢°°°¢°°°so°°$°°§°¢°°§°°°§°° HHNNNmmvvvnmwww l BrandValue V” .1, BrandValue \/
Ch: 544—4 Ch: 4555.25
Q1: 90455.5 Qas ll3l4—l.‘l‘5 Question 2. s, ? Fig; 2.1: The Normal Model for Brand Loyalty Figure 2.1: Brand Loyanv / / ‘ I Frequency 24.15 17.52 59.19 100.86143.53184.20 225.87
'3 "R —\ O l 2 5
Question 3. Table 3.1: Correlation Matrix Brand Ad Media Lead
Value Exnditure Penetration Lo a Headline Parrah Text Brand Value 1.000 — —_— 1.000 Media mum— m— 0.263 Lead
Pararah 0.534 0.321 0.991 0.165
0.519 0.305 0.981 0.132 0.916 m Question 4.
Figure 3.1 Brand Value vs. Media Penetration Figure 4.1: Residual Plot 80000 , ,, ,, ........h..... H. (Residuals vs. Media Penetration) 70000 we 7 ~ .7 r 50000 60000 ~ 0 r to ' ~ 50000 ~
% 50000 L w ’ e e w VI 40000 e o
E 40000 f r. r r. V 30000 ~ 0 l/
g 30000 ~07 20000 O 7 O O V V OBrand Value
20000 t.. 9 w "9.77 «mm imwﬂw e Residuals .,. z
10000  . O o .9
Q Q
9. . Q . , . ,
. 0 ¢ ,
~ 0 1 400000 500000 600000 700000
’ e e o e 0
10000 7 7.7777177777777777
oﬁfyff. 10000
0 200000 400000 600000 800000 40000 ‘
30000 1
Media Penetration Media Penetration b‘: (\% b‘: , 53q(ia4ai.48 i2i45ﬂ5— 080365253) IV Discussion ofResults : 557 be + o OBW‘edm penei’mdnon l/ Question}; The histograms demonstrated in ﬁgure 1.1 and ﬁgure 1.2 are similar in shape as they are both
unimodal and skewed to the right/ The nonUS histogram has an outlier‘tﬁnote around 3400, while the US
histogram has extreme outliers/around 5900 and 6600. The US histogram also appears to have a gap in data from
about 1600 to 2000, making what could be twq groups of data without the extreme outliers. The center of the
brand values is bestdescn'bed by the median’since both histograms are skewed to the right. US brands have a
median of 8344, 6d the nonus brands 6 £55:The spread of the brand values is best deyibed by the 101? and the
range: US Brands have an IQR of 15012 and a range of 63329, and nonus brands 7057 and 32541 respectively.
While the minimum for both histograms are about the same, the maximum for US brands (66667) is almost
double that of nonUS brands (35942). Thus, US brands have a wider range of brand values and a larger center than nonUS brands, which is mostly due to its extreme outliers. The US brand value distribution would be much
more similar to nonUS brands if it were conﬁgured without its extreme outliers. The mode for both US and non
US brands values falls between 4000 and 8000. These histograms are an appropriate model of the distribution of
brand values and are reliable because both variables are quantitative. V/ Question 2: In order to determine if a brand loyalty score of 148 is really good, the standard normal model is
used in ﬁgure 2.1 to demonstrate what brand loyalty values are considered normal. The value 148 falls about 1
standard deviation above the mean, indicating that it is aboveaveragei/Since anything outside of 3 standard
deviations is considered unusual, a score above 225.87 would be extremely good brand loyalty. Thus, the brands’
initial feeling that it has really good brand loyalty is not correct/ With a score of 148 the brand has good brand
loyalty, but it could improve to have really good brand loyalty by reaching to 2 or 3 standar deviations above the
mean. The normal model is appropriate and reliable for this data because the assumptions of normal distribution
are met. As demonstrated in ﬁgure 2.1, the histogram’s distribution of brand loyalty is unimodal and roughly
symmetric. Question 3: The correlation matrix in table 3.1 shows that media penetration/is the most correlated with brand
value because its correlation coefﬁcient is the closet to +/ 1, which corresponds to a strong linear association.
The scatterplot in ﬁgure 3.1 shows a positive direction that is fairly linear‘ifi form and moderatelyﬁong in
strength. There are a cluster of points near the intersection of the x and y axis that extends along the xaxis. There
are some outliers‘vvith high leverage and several with high residuals. The correlation matrix is appropriate and
reliable since the assumptions — the quantitative variable condition, the straight enough condition, and the outlier
condition — are met. The variables are quantitative, and it’s assumed that the correlations between the variables
are linear with no extreme outliers, which would be checked with scatterplots. ‘/ / Question 4: By using an estimated regression line (shown in statistical analysis #4), b (1 value can be predicted
for a brand with a media penetrations of 50,000: 5576.32 + .05(50,000) = 8076.32. e accuracy of this
prediction can be checked by looking at the residuals plot in ﬁgure 4.1, which shows a negative residual around
50,000 meaning that the predicted value is an overestimate. The residuals plot shows a pattern and changing
spread, which violates the Equal variance assumption of correlation and warrants caution about the conclusions
made from the correlation. While the residuals plot fails to meet the right assumptions for correlation, it is still
appropriate and reliable because it demonstrates the error of the estimated regression liner/The estimated
regression line yields a larger coefﬁcient for brand value (55 76.32) than the residuals plot (5460.23) because the
estimated regression line is based on descriptive table statistics while the residuals plot is based only on viable
pairs of data."l‘hus, there is error in the estimated regression line, particularly the inﬂated coefﬁcient for brand
value. This error is due to the two cases that have no media penetration values to correspond with their brand
values. The error is reﬂected in the residuals plot as many of the points are negative and indicate that the
predicted brand values (are an overestimate. About 28% of the variation in brand value can be accounted for by
media penetration. l/ There is very little generalizability in the results of this analysis because the data are not random but collected
from the top 100 global brands according to interbrand. The results are hard to generalize to a larger population
because the sample is a speciﬁc group of brands. It would be incorrect to extrapolate the results from this analysis
to other brands not in Interbrand’s top 100. However, the results found for the sample in this analysis are
appropriate because all the proper assumptions were met for most questions, and when the assumptions were not met caution was noted about the reliability of the results. Bonus: Does using brand loyalty and media penetration to predict brand value with multiple regression lead to a
more accountable prediction? The multiple regression line for predicting brand value by media penetration and brand loyaty: /\ Brand Loyalty = l49.05 + .05 Media Penetration + 58%Brand Loyalty \/ R square is not a reliable value for predicting the/ percentage of variation in brand value because no matter what
variable you add, this number always increases. In order to determine what percentage of brand value is
accounted for by media penetration and brand loyalty the adjusted R square must be examined. About 30% of
brand loyalty is accounted for by media penetration and brand loyalty. By looking at r square for media
penetration in question 4, it can be argued that only 2 % of the variability in brand value is accounted for by
brand loyalty. This percentage is not high enough to consider brand loyalty a signiﬁcant variable in predicting
brand value, but it could be argued that media penetration is signiﬁcant to predicting brand value since it is
accountable for 28% of its variation. These results indicate a lurking variable or variables that most likely account
for a larger percentage of the variability in brand value, and would therefore be a better predictor of brand value.
Overall the prediction is a little more accountable with brand loyalty factored in, but not signiﬁcantly enough to use the multiple regression equation with high conﬁdence. ...
View
Full
Document
 Fall '10
 COLLINS

Click to edit the document details