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Take Home Exam 1 Example - Brand Loyalty 1

Take Home Exam 1 Example - Brand Loyalty 1 - c ‘n...

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Unformatted text preview: c ‘n Lhmngdummhgflmm; This analysis examines a dataset of the top 100 Best Global Brands according to Interbrand. The data was combined from a variety of sources. The objective is to determine if the amount of media coverage attained by a company, advertising expenditures, and brand loyalty are related to it 3 brand value. This information is used to determine whether media penetration, advertising 1/ ; expenditure or brand loyalty is most correlated with brand value, and to predict brand value. Also, the descriptive statistics are used to show the distribution of brand values for US brands versus non-US brands. Ultimately the reliability and generalizability are determined. 111;"v3'i: Table 1: Descritive Statistics for To. Global Brands . . Lead Ad Media Headline . - Brand Value Expenditure Brand Loyalty Penetration Mentions Fijéilgifrf’: Text Mentions _———-a—a-a M 38015.50 m_—-_—— 1351.00 m 205699.00 m— Ila-m III. Statistical Analysis: Question 1. Figure 1: Histogram for US Brand Values Figure 2: Histogram for Non—US Brands 20': l W m; 16% 144: l E 12 3 10 i S u. 3 l s Ar?» 4 - w 2 J a 0 Q ........ _° _ . ........ Wm ........... o w _ w . Q o ~°° “9° o°°°~s>°§~§°°$°°~a°° a°°°¢°°°§°°e°°°§°°a°§é°§e°§e9° «9&0 e" #9 o°°y°°¢°°°w§fie°°$°° £13 and? 3° $134? f 9%? 8“ Band Value Brand Value c *w.‘ ‘ NJ Question 2. Figure 3: Histogram for Brand Loyalty Figure 4: Normal Model for Brand Loyalty 14 T 12 .. 10 ” g 3 mm... L”) = z (148 Emmi logallj) if ....... 0 Q 0 Q Q 0 woo-'ooo no woo-ooo-o-o‘ 993519»: gawpbsfig‘: 3319 605:1? we we we we we we we a swat-had ox-x-v’vvvvs- ‘ ~- 9 e o a c e c e so°°99999999§°9 I i BrandLoyalty if ‘Zo' "la- 0 lo- 1ir 3a- *5 Question 3. Table 2: Correlation Matrix of To a Global Brands ——-”-_—— E__EE———_—— _:-—-3—m_———— _-l_l-E—__- m—_—— m—m-m-m— Figure 5: Media Penetration vs Brand Value 80000 70000 60000 50000 40000 ' 30000 ‘ 20000 10000 0 Brand Value 0 100000 200000 300000 400000 500000 600000 700000 Media Penetration M Mé ““1. Figure 6: Plot of Res'duals W 8 Estimated Regression Line: M5 m (a): .m (w) . 0 0., ‘ 129013.71 ' / Question 4. Residuals (Brand Value) Media Penetration IV. Discus ion f Res lts: / / Question 1: Accordin 0 Figure 1, the distribution of US Brand Values is unimodal and sk d right. The median is 8344 nd the IQR is 15 012/1“ here are three extraordinary values (outliefiheich, afier investigation, account for Microsoft, IBM, and CocaCola, three of the US’s highest earning brands. +3 According to Figure 2, the distribution of Non-US Brand Values is unimodal and skewed right. The /____ median is 6155-41de the IQR is 7057. There are no outliers. The values for each dataset meet the Quantitative Data Condition, therefore a histogram and numeric summaries are appropriate. Because the datasets are not symmetric, reporting the standard deviation was not appropriate. Question 2: A Brand Loyalty score of 148 is not justifiably a “really good” score according to the Figure 4 (Normal Model for Brand Loyalty), where the corresponding z-score for the brand loyalty score is plotted. A score of 148 is only 1.13 standard deviations from the mean with 13% of all other reported brands scoring higher Brand Loyalty. Although 87% of all other reported brands scored lower than this particular brand, a score of 148 is not higher than the expected value, thus disqualifying the brand from characterizing their score as “really good”, where a “really good” score is indicated as significantly higher 3 than the expected value or at least in the top-10 percentile of all brands. The Normal Mode] is appropriate and the findings are reliable because the Nearly Normal Condition is met. The distribution of data is both symmetric and unimodal as shown in Figure 3, the Histogram for Brand Loyalty, verifying the previous conjecture. Question 3: According to Table 2 (Correlation Matrix) Med enetration is most correlated with Brand Value, with a linear association of. 53. A linear association between the quantitative variables 15 assumed, however this assumption cannot be assessed because this analysis did not call for a linear relationship to be shown between the variables. The Quantitative Variables Condition 1s met, however the Straight + 5' Enough Condition and Outlier Condition are only slightly justified, indicated by Figure 5, and make this correlation data less reliable. Figure 5 contains a scatterplot illustrating the association between Media Penetration and Brand Value. The scatterplot has a positive direction but is weak, has only a slight linear pattern and contains several straggling points. Question 4. 28. 09% of the variation in brand value can be accounted for by media penetration (or R= .2809) The application of a simple regression line shows that one comma Brand Value of 7994. 97 for a brand that has a Media Penetration of 50, 000. In other words, brand value(50, 000)— — 7994.97 (y= 5444.971 + 0. 051x 15 the estimated regression line). The Quantitative Variables Condition 15 met and there are no major outliers. Although the Straight Enough Condition 15 nearly met when looking at Figure 5, the Equal Variance Assumption is not met after checking Figure 6, the plot of residuals. A regression model is, therefore, not appropriate; there is a distinct pattern to residual plot, indicating an unusual spread in the data. This decreases reliability in using the regression line to predict values. 1L 7 There is a moderate amount of generalizability in the results of this analysis, as the data represents a diverse sample taken from a global population. The results reflect an analysis covering a report of the top brands according to Interbrand, however, limiting the generalizability to companies within a particular brand value range. Thus, the results would be generalizable within only a sector of global brands. In predicting brand value based on media penetration, it is important to remember that causation cannot be determined by linear regression, so no assumptions can be made regarding these variables as you investigate brands of increasingly lower brand value. Furthermore, the regression model applied to brand value and media penetration lacks reliability. It would be interesting to explore the possible lurkers or compounding factors that effect the variance not accounted for by the predictor variable. ~ Bonus: Find the estimated regression line for predicting Media Penetration using Lead Paragraph Mentions. Create a scatterplot and residual plot for these two variables. Use the regression line to predict +5 Media Penetration for a brand that has Lead Paragraph Mentions of 70,000. Figure 7: Lead Mentions vs Media Figure 8: Plot of Residuals . i Penetration 1 80000 9 700000 50000 T 0 500000 *— t—w E. I ’g o. 5 mm f 0 Q * ‘ 4°°°°° ”V 0 o ’ ! E ‘5 o ‘ 9 7:, 3°°°°° 6"? E. 0 13000 {$0000 $1.00 M 50001 60000 70000. 30000 E 200000 1 ’9 .2 : ........ m.....;_ms._ ..... . ......................................... 100000 i i “000°“ 3" o E W "v . 4 a 00000 ' 0 10000 20000 30000 40000 50000 60000 70000 80000 5 430000 -_ Lead Mentions f Lead Mentions The estimated regression line for predicting Media Penetration using Lead Paragraph Mentions 1s y= 4502. 663 + 8. 405x. Therefore, The predicted Media Penetration for a brand with 70, 000 Lead Paragraph Mentions 15 592852. 66. While Figure 7 appears to meet all conditions- quantitative variable condition, straight enough condition and outlier condition (should the one major outlier be arguably removed)- Figure 8 (Plot of Residuals) illustrates that the Equal Variance Assumption is not met. The regression model is, therefore, not appropriate. This decreases the reliability of using the regression line to predict values. ...
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