This essay explores the correlation between a company’s logo color, its industry sector, and its market capitalization. By developing a linear regression model, we visualize and interpret these relationships. Building a dataset and visualizations in Wolfram Language facilitated the interpretation of correlations. The analysis successfully quantifies the impact of logo color and industry sector on market capitalization, shedding light on branding’s influence on financial performance. However, the findings do not successfully explain all determinants of market value. Future research will examine additional factors influencing a company’s market capitalization to provide a more holistic understanding.
Introduction
Introduction
Customers often remember a company by its distinctive logo, sparking my curiosity about how various logo designs influence a company’s success. This curiosity drove my research. Initially, gathering data posed a challenge, as datasets of companies’ logo colors are rare. Using Wolfram’s tools, I created a custom dataset and analyzed the correlation between logo characteristics and market capitalization. This analysis raised additional questions, as it became clear that I did not fully grasp all the factors affecting market capitalization. Consequently, I expanded my research to investigate the influence of a company’s industry sector on market capitalization. By integrating this new information, I constructed a linear regression model incorporating both factors, yielding more comprehensive conclusions about their combined impact. This research can potentially influence marketing decision within businesses, and allow companies to better understand factors affecting their success.
Creating the dataset
Despite Wolfram Language’s extensive built-in entities, a dedicated function for automatically determining the colors of company logos remains absent. Therefore, I created a dataset including each company’s name, market capitalization, and the specific colors featured in their logos. This dataset serves as the foundation for subsequent analysis, particularly in constructing a linear regression model that correlates logo colors with company market capitalization.
Dataset including: company names and their market capitalization
Dataset including: company names and their market capitalization
sp500Data loads the Market Capitalization and Name data for each company of the S&P 500 from Wolfram’s entity data, and then sp500Dataset turns the data into a dataset for better visualization:
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sp500Data=EntityValue,{"Name","MarketCap"};
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sp500Dataset=Dataset[AssociationThread[{"Name of Firm", "Market Capitalization"}->#]&/@ sp500Data]
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The next step was to add each company’s respective logo image to this dataset as a new column.
Dataset including : company name, market capitalization, and logo images
Dataset including : company name, market capitalization, and logo images
sp500Names creates a list of each name of the 500 companies from the S&P 500, and then those names are used to list all of those companies’ logos from Wolfram Alpha:
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sp500Names=Normal[sp500Dataset[All, "Name of Firm"]];
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firmLogos=;
logoDataset is an updated dataset that appends an image of each company’s respective logo under a new column, “Logo”:
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logoDataset=Dataset[Table[Append[Part[Normal[sp500Dataset],i],"Logo"->Part[firmLogos,i]],{i,Length[firmLogos]}]]
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The issue I faced was the absence of associated logos for several companies in the previous dataset, logoDataset. This resulted in blank entries under the “Logo” column for those companies, as there were no images to attach. To address this, the dataset was refined by removing observations of companies with invalid or missing logos. Consequently, these entries were excluded from the updated dataset, ensuring all remaining entries have valid logos associated with them.
badLogos identifies and lists any logos from all the companies that do not have the head of an image:
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badLogos=DeleteCases[firmLogos,_Image];
This creates an updated dataset without invalid images using the function matchesAnyPart to check that if any invalid logos are included in any row, the entire row is removed:
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matchesAnyPart[row_Association,badLogos_List]:=AnyTrue[Values[row],MatchQ[#,Alternatives@@badLogos]&]
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associationLogoDataset=Table[Append[Part[Normal[sp500Dataset],i],"Logo"->Part[firmLogos,i]],{i,Length[firmLogos]}];
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filteredLogoData=Dataset[Select[associationLogoDataset,!matchesAnyPart[#,badLogos]&]]
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Dataset including: company names, market capitalization, logo image, and logo’s main color.
Dataset including: company names, market capitalization, logo image, and logo’s main color.
The next step was to add what each company’s logo’s main color is to the dataset.
The images in the previous dataset, filteredLogoDataset, are formatted into a list, and then DominantColors are applied to each image to get the top 4 most used colors in each image:
A key issue with dominantColorOfLogos was that white or transparent backgrounds frequently appeared as the dominant color, as they constituted large elements of the images. Since the focus is on the actual logo colors, these background colors were irrelevant. To address this, numerous functions were developed to accurately identify the true dominant color of each company’s logo, excluding the background.
This is applied to dominantColorOfLogos and states that if the first dominant color is white, then it will show the second dominant color instead as the new number 1 dominant color:
Additionally, these functions were created to remove the transparent colors from droppedWhiteColors.
The function isLowOpacity checks if the color has an opacity lower than 0.95:
The function findFirstNonTransparent finds the first non-transparent color, and returns an empty list if there is no non-transparent color found:
This applies the two functions, isLowOpacity and findFirstNonTransparent, to droppedWhiteColors to ultimately get a refined list of colors without white or transparent as dominant colors:
Although removing transparent and white as dominant colors improved accuracy, grayscale colors still frequently appeared as the dominant color despite not being representative of the logo color. To address this, I wrote various functions and applied them to refinedColorList to determine the most accurate dominant color for each company logo.
This function classifies all the colors as either black, white, or color:
This function determines if there is a non grayscale color in the list, then output that color, but if there are only grayscale colors, output the most dominant out of them:
This function applies determineColor to every color in both a sublist and in a single list, as the color list includes both nested and singular lists:
This applies these functions to output only the dominant color from each company’s logo without white or transparent:
This flattens oneColor one level to get rid of the lists inside of the lists to output one large list, and also shows the invalid colors as “nothing”:
It was observed that some company logos failed to return any valid dominant colors, resulting in blank entries in the dataset. Consequently, when integrating the filteredColor data with the existing filteredLogoData dataset, rows with invalid color entries had to be excluded.
This adds the colors, filteredColor, to their respective company in the previous dataset:
This identifies and removes rows labeled as “Nothing,” representing invalid colors. Subsequently, it generates a formatted dataset of company names, market capitalization, logo images, and primary logo colors:
Dataset including: company names, market capitalization, logo image, logo’ s specific main color, and color classification.
Dataset including: company names, market capitalization, logo image, logo’ s specific main color, and color classification.
The subsequent step involved categorizing the various colors into general color groups. To achieve this, I developed multiple functions to calculate and utilize the Euclidean distance of RGB values, identifying the closest color match. The outcome was an additional column in the dataset, indicating the generalized color for each company’s logo.
This extracts all the colors from the “Color” column in the dataset, logoAndColorDataset:
This classifies the ranges of the desired colors in the RGBColor range:
This function calculates the Euclidean distance between two colors, which will be used to find the closest color match to rainbowColors:
This function checks if a color is gray, and then classifies the color as Black if it is gray:
The function classifyRainbowColor classifies a color based on closest match to rainbowColors, which is applied to the dataset colors, resulting in a list of color names that are correlated to each logo’s color:
The final result of these functions is an updated dataset with the added column of “Color Name” which includes the classified colors:
Visualizing the data
Upon acquiring the dataset, the next crucial step involved data visualization and interpretation. Visualizing the data is essential to uncovering patterns and relationships between logo colors and company market capitalization. This process could not only answer my initial questions, but it could also guide further exploration.
It is important to note that the data retrieved from Wolfram’s entity database changes on a daily basis. This leads to slightly different statistics every day, such as slightly different number of companies with each color logo, or slightly different amount of companies in each sector. This changes are minimal, and does not change the overall trend of the data, and my conclusions are still relevant even with these slight changes.
Histogram showing: number of companies by logo color classification
Histogram showing: number of companies by logo color classification
I first wanted to investigate how many companies use each color for their logo. To address this, a histogram was utilized, illustrating the distribution of companies based on their logos’ predominant colors.
histogramColors defines the categories of the histogram, or the x value, which is also the general colors of the logos:
This involves counting the frequency of each color from the pre-existing list, classifiedColors. These counts serve as the y-values in the histogram, representing the number of companies associated with each specific color:
This allows the bars of the histogram to correlate with their color:
This sorts the data to the proper format for a histogram, and then outputs the histogram:
Interpretations
Interpretations
Based on this visualization, it became evident that blue is the most prevalent color in company logos, followed by black, which also appears frequently. Conversely, orange, yellow, and purple are the least utilized, each represented by fewer than 25 companies. It could be hypothesized that blue has benefits to a company’s market capitalization, since blue is the most used color by companies. This is not a good enough analysis to fully support that idea. While this distribution shows potential benefits of blue in relation to market capitalization, it is important to note that correlation does not imply causation.
This finding is intriguing and informative, but it does not directly address the impact of logo color on market capitalization. Further analysis is required to support any claims regarding the impact of logo colors on market performance. I believed that visualization of the correlation between logo color and market capitalization would be the next most helpful in my research.
Scatter Plot showing: the general colors of logos vs the market capital of each company
Scatter Plot showing: the general colors of logos vs the market capital of each company
A scatter plot seemed to be the most insightful method for comparing the relationship between logo colors and the corresponding market capitalization of each company. This graphical approach allowed for a visual examination of how different colors correlate with varying levels of market value across the dataset. By plotting logo colors on one axis and market capitalization on the other, patterns and outliers became more apparent, providing a nuanced perspective on correlations between color and financial performance.
This creates a new dataset by extracting the columns for name, market capitalization, and color logo of each company:
This produces a list of lists, each with the number color and their market capitalization:
The colors used are defined, and then each are given a number to correlate with them:
This uses the coloredData to create a scatter plot that shows each company’s logo categorized into their respective color on the x axis. The y axis is their respective market capitalization:
Interpretations
Interpretations
The scatter plot illustrates the market capitalizations of companies categorized by the primary color of their logos. This scatter plot indicates that companies with red and blue logos tend to exhibit higher market capitalizations, while purple and pink logos are associated with lower market capitalizations. This observation could support the hypothesis that blue and red logos may contribute to greater market success. Additionally, this reinforces the previous histogram analysis that blue, in particular, appears to be the most advantageous color for enhancing a company’s market capitalization.
The clustering of data points within each color category also provides valuable information. Red and blue logos not only show high market capitalizations but also a larger number of companies within these high ranges, indicating a trend rather than isolated cases. In contrast, the fewer data points for purple and pink logos in higher market capitalization ranges highlight their lesser association with top market performers.
The companies with black logos exhibit a wide range of market capitalizations, with some reaching high values, though not as consistently as the red and blue categories. This variability suggests that while black can be associated with high market capitalizations, its impact is less predictable compared to red and blue.
Overall, the scatter plot underscores the significance of logo color in market performance, with red and blue logos standing out as potentially influential factors in achieving higher market capitalizations. This reinforces the notion that strategic color choices in branding could play a crucial role in a company’s market success.
However, I understood that it is crucial to recognize that while this scatter plot offers valuable insights, it does not provide conclusive evidence of causation. Further statistical analysis, such as regression modeling, was necessary to accurately assess the strength and significance of this factor.
Logo Color Linear Regression
Logo Color Linear Regression
Linear regression was used to understand the amount of correlation there is between company logo colors and their market capitalization. The P-Value was specifically used to understand this.
This extracts the market capitalization and logo color for every company, from colorClassificationDataset. Market capitalization is expressed in billions to allow easier visualization:
Dummy variables are used in linear regression to represent categorical data with numerical values, typically 0 and 1. They allow the model to include categorical predictors, enabling it to understand the impact of different categories on the dependent variable. By converting categorical variables into a series of binary variables, dummy variables allow the inclusion of non-numeric data in regression analysis.
colorToDummy creates dummy variables, and dataWithDummies joins together the dummy variables and market capitalization of each company:
A parameter table in linear regression displays the estimated coefficients for each predictor variable, along with their probability value, or P-Value. It helps to interpret the relationship between each independent variable and the dependent variable. This table is essential for understanding a model’s predictive accuracy and for making informed decisions based on the regression analysis.
This creates and shows the colorModel parameter table which shows many statistical values correlated to each colors best line of fit based off of the data, dataWithDummies:
Using the estimates from the parameter table, I created a plot of all the colors lines, and emphasized the points at x=0 and x=1:
R-squared in linear regression indicates the model’ s goodness of fit, with values ranging from 0 to 1, where higher values represent better explanatory power. The R-squared represents a percent of variation that explained by the data. R - squared helps assess how well the model captures the variability of the data.
This displays the RSquared value of the logo color linear regression:
Interpretations
Interpretations
The plot of “Logo Colors and Expected Estimate Market Capitalization” shows the lines of best fit of each color. The color line with the most gentle slope shows that its color has the largest affect on market capitalization. In general, it seems that red is normally the most impactful or one of the most impactful. The colors with the gentle slopes are expected and predicted to have higher market capitalization. This supports the scatter plots data of red seemingly being one of the most beneficial colors for a company’s market capitalization. Surprisingly, after running this numerous times, blue does not seem to be the most beneficial in this plot, even though the histogram and scatter plot support the idea that blue is the most beneficial to market capitalization.
As previously explained, the RSquared Value ranges from 0 to 1, with the higher the better. The RSquared of approximately 0.03 means that only 3% of a company’s market capitalization is explained by logo color. It can therefore be concluded that a company’s logo color does not explain a lot of the market capitalization. It can also indicate that other factors not included in the model may explain most of the variance.
I was not satisfied with the R-Squared score being only around 0.03, indicating that logo color alone explains a minimal percentage of a company’s market capitalization. To delve deeper, I explored the influence of a company’s industry sector. Industry sectors play a crucial role due to varying market conditions and consumer perceptions. By categorizing companies based on their industry sectors and analyzing the relationship between logo color and market capitalization within each sector, I aim to uncover whether certain colors hold more significance in specific industries. This approach will provide a better understanding of how logo color interacts with industry dynamics to influence market capitalization, potentially revealing information that this initial analysis overlooked.
Company Sector Linear Regression
Company Sector Linear Regression
After understanding the correlation between a company’s logo color and its market capitalization, a possible extension for further understanding was how a company’s sector impacts its market capitalization.
This loads the name and sector of S&P500’s companies from Wolfram’s entities, and lists all the unique sectors:
This creates a list of associations between a company and sector, and then appends a new column to colorClassificationDataset of each company’s sector, resulting in a dataset including the following: name of firm, market capitalization, logo color name, and sector:
This drops the logo color name column from sectorAndColorDataset, resulting in a dataset with the following: name of firm, market capitalization, and sector:
Acquiring this dataset, the market capitalization and sector for every company is extracted and normalized from sectorDataset. Market capitalization is expressed in billions to allow easier visualization.
sectorToDummy creates dummy variables from the names of all the sectors, and sectorDataWithDummies joins together the dummy variables and market capitalization of each company:
This creates and shows the sectorModel parameter table which shows many statistical values correlated to each sectors best line of fit based off of the data, sectordataWithDummies:
This shows the rSquared value:
Interpretations
Interpretations
As previously explained, the R-squared Value ranges from 0 to 1, with the higher the better. The R-squared value of approximately 0.1 suggests that sector accounts for about 10% of the variation in a company’s market capitalization, indicating a modest but noticeable impact. While this value still implies that a significant portion of market capitalization remains unexplained by sector alone, it signifies a stronger relationship compared the model with only logo color, as it can be noticed that it had an R-squared score around 0.03. The findings suggest that, while other factors beyond sector play substantial roles in determining market capitalization, the choice of sector does contribute measurably. This insight underscores the importance of considering multiple factors comprehensively when evaluating the strategies and market outcomes of companies.
I sought to explore the correlation between logo color, company sector, and market capitalization to uncover nuanced insights into branding strategies across industries. By integrating logo color with company sector data, I aimed to discern whether certain colors yield differential impacts on market capitalization within specific sectors. While logo color alone may explain a modest proportion of market capitalization variability, the combined influence of color and sector could provide a more comprehensive understanding. Ultimately, this investigation underscores the importance of holistic analyses that consider both visual identity and industry context in market outcomes.
Company Sector and Color Linear Regression
Company Sector and Color Linear Regression
To find more answers, I created a linear regression comparing both logo colors and company sector to market capitalization.
This combines dummy data from both sectors and colors into one list for linear regression:
This creates and shows the colorsAndSectorsModel parameter table which shows many statistical values correlated to each sectors best line of fit based off of the data, sectordataWithDummies:
This shows the RSquared value:
Interpretations
Interpretations
The R-squared value of approximately 0.13 indicates that logo color and sector together explain approximately 13% of the variation in a company’s market capitalization. This finding suggests a notable influence of both visual branding and industry context on market outcomes, showing their combined explanatory power. While other factors beyond logo color and sector account for the majority of market capitalization variability, the identified 13% underscores the significance of branding strategies tailored to specific industry dynamics. This understanding could enable businesses to leverage not only their visual identity but also sector-specific preferences and competitive landscapes to optimize market positioning and enhance shareholder value.
Final Thoughts
Conclusions
Conclusions
To better understand the P-values and estimates, I made manipulative interfaces to be able to change these values and see which categories have what specific values. It is noted that these functions take into account absolute values.
The function identifyEstimatesLargerThanAbsoluteValue identifies which colors or sectors have the same or higher estimate than a certain value:
The function is formed into an interface where there is an option choose between sectors, colors, or both. It shows where the estimate can be changed to show which category is equal or higher than that number:
The function identifyEstimatesWithSignificance identifies which colors or sectors have the same or lower P-Value than a certain value:
The function is formed into an interface where there is an option choose between sectors, colors, or both . It shows where the P - value can be changed to show which category is equal or higher than that number :
After looking through all the P-values, I noticed that the majority of time all the logo colors have a P-Value lower than most of the sectors. Initially, I thought this suggested that logo color may have a more significant association with market capitalization than the industry sector itself. A lower P-value typically indicates stronger evidence against the null hypothesis (that there is no relationship), suggesting that variations in logo color are more reliably linked to differences in market capitalization compared to differences across industry sectors. However, the R-Squared value of logo colors is also very low. Together, a high p-value and a low R-squared value suggest that the variable logo color does not significantly explain variations in market capitalization in the current model. This could imply that color is not strong predictors of market value in isolation, or that other unaccounted factors have a more substantial influence on market outcomes. In practical terms, it shows the complexity of assessing logo color impacts on market performance, encouraging further exploration into additional variables to capture these relationships more accurately.
Studying the estimates, I noticed that most of the time Media and Entertainment is the highest or one of the highest. This suggests that media and entertainment impacts the market capitalization the most, and companies in that sector will benefit the most. Additionally, out of all the sectors, media and entertainment has the lowest P-value most of the time. This supports the hypothesis that media and entertainment is very beneficial for companies, as it will increase their market capitalization the most.
Referencing the previous histogram and scatter plot, it could be hypothesized that many companies choose logos with red and blue, as it increases the market capitalization. Color psychology research also states that the color red increases a person’s hunger and excitement, which could also partially explain the large use of the color red.
Applications and Future Improvements
Applications and Future Improvements
Exploring extensions to the analysis could provide deeper insights into the complex factors influencing market capitalization beyond logo color and sector alone. One avenue for further investigation involves expanding the dataset to include additional variables that might better capture the drivers of market outcomes, such as brand reputation metrics, consumer sentiment indices, or competitive positioning measures. By broadening the scope of analysis, we can assess whether these variables enhance the predictive power of models.
Furthermore, an extension of a temporal analysis could illuminate how these relationships evolve over time, offering insights into the dynamic nature of branding strategies and sectoral influences on market performance.
By studying the effects of logo color and sector, businesses apply these findings in to refine their branding strategies to better align with market dynamics and consumer preferences. Academically, studying the correlation between logo color and sector provides insights into consumer psychology and perception, shedding light on how visual cues influence market behavior and brand valuation. This knowledge contributes to broader research in marketing and behavioral economics, deepening our understanding of the complex factors shaping market dynamics. From a practical standpoint, businesses can leverage this understanding to strategically optimize their branding efforts. By choosing colors that resonate with their target audience and aligning their visual identity with sector-specific expectations, companies can enhance brand recognition, customer engagement, and ultimately, market competitiveness. Furthermore, understanding sector-specific influences allows businesses to tailor their strategies more effectively, navigating industry nuances and capitalizing on market trends to achieve sustained growth and profitability. In essence, learning about the correlation of color and sector in market capitalization equips both researchers and practitioners with valuable insights to inform strategic decision-making and drive business success in competitive markets.
CITE THIS NOTEBOOK
CITE THIS NOTEBOOK
Impact of logo colors and industry sector on company market capitalization
by Iris Li
Wolfram Community, STAFF PICKS, July 11, 2024
https://community.wolfram.com/groups/-/m/t/3212373
by Iris Li
Wolfram Community, STAFF PICKS, July 11, 2024
https://community.wolfram.com/groups/-/m/t/3212373