Take Home Exam 1 Example - Brand Loyalty 2

Take Home Exam 1 Example - Brand Loyalty 2 - SSC306 I...

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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 non-US Brands u—ni-nN OLI‘O new”; Frequency 5 ‘7‘ _ IFrequency 0 WWW-WWWVV IFrequency OOOOOOOOOOOOOOOOO §§§§§§§§§§§§§§§§§ a°°e°°¢°°°¢°°°so°°$°°§°¢°°§°°°§°° HHNNNmmvvv-nmwww 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 non-US 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 non-us 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 non-us 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 non-US brands (35942). Thus, US brands have a wider range of brand values and a larger center than non-US brands, which is mostly due to its extreme outliers. The US brand value distribution would be much more similar to non-US 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 above-averagei/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 x-axis. 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. ...
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This note was uploaded on 11/12/2010 for the course SSC 57531 taught by Professor Collins during the Fall '10 term at University of Texas.

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Take Home Exam 1 Example - Brand Loyalty 2 - SSC306 I...

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