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Ashley Quintilone
Marketing Tools and Applications Spring 2018 Final To understand the image of Fort Worth in order to attract and retain creative young professionals Q1 Data Examining In order to decide the usefulness of the data, diagnostic tests should be run to assess whether normality is present or if any outliers will damage the relationships between variables. Although the Kolmogorov-‐Smirnov and Shapiro-‐Wilk tests can be used to check normality, the Central Limit Theorem confirms that normality is present when reaching over 30 responses. The dataset has a total of 534 responses indicating I can move on. The survey question I determined to be most indicative of the “image” of Fort Worth is Q19: “What is your perception of Fort Worth on these city characteristics?” The twelve variable characteristics included: Public Education, Higher Education, Employment Opportunities, Safety, Environmentally-‐Friendly, Public Transportation, Social Diversity, Developed Downtown Core, Nightlife, Cultural Amenities, Parks and Recreation, and Cost of Living. The variables are metric. Respondents evaluated the variables on a 1-‐5 scale: (1) Very Bad, (2) Bad, (3) Neither Good nor Bad, (4) Good and (5) Very Good. The scale acts as an indicator of what attributes should become focal points moving forward. The cities analyzed include Fort Worth, Kansas City and Atlanta. Looking at the descriptives below, I could determine that the min was -‐3.99 and fell outside of the 3.5 standard deviations above or below the mean. This indicated that outliers are present.
Using univariate detection, I found that Q19 presented no threatening outliers to the dataset. All outliers fell within the normal scale of 1-‐5. The comparison variable Q16 indicated that only 4 outliers were present. Again, this is not a concern moving forward to analysis. Excluding this data from the dataset would compromise the integrity and originality. I can confirm that 60 of the 534 recorded observations are missing. This falls a bit higher than the 5-‐10% missing value range we like to stay inside, but we can attribute the this to skip logic
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and incomplete questions during the survey. Rather than estimate the missing values through imputation or substitution, I chose to keep the values in their original forms to maintain the integrity of the data. Due to assumptions varying in each analysis, linearity, independence, and multicollinearity will be assessed in later sections. I can conclude that each variable is within its valid range in terms of outliers, frequencies, and means. The Director of VisionFW should have no concern about the variables or observations in the dataset.
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Q2 Multiple Regression Research Question / Objectives In order to understand what influences the likelihood a YP recommends his/her city to friends, multiple regression is conducted. Analysis will show which factors among the perceptions of home city influence their recommendations. Analysis Plan All variables are metric and scaled. Regression requires 1 dependent variable, the recommendation, represented by Q16_2 in the survey. The outcome variable is answered on a 1-‐7 scale of how likely they are to recommend to a friend: (1) Very Unlikely, (2) Unlikely, (3) Somewhat Unlikely, (4) Undecided, (5) Somewhat Likely, (6) Likely and (7) Very Likely. The independent variables are the twelve attributes in Q19_1-‐12: Public Education, Higher Education, Employment Opportunities, Safety, Environmentally-‐Friendly, Public Transportation, Social Diversity, Developed Downtown Core, Nightlife, Cultural Amenities, Parks and Recreation, and Cost of Living. Respondents evaluate the variables on a 1-‐5 scale: (1) Very Bad, (2) Bad, (3) Neither Good nor Bad, (4) Good and (5) Very Good.
Every independent variable should have at least 15 observations when running regression. This dataset has 534 respondents, giving it enough power to identify the influence of variables and making it representative of the population.
Model Assumptions The errors should be homoscedastic. The errors for the perception variables should all have the same variance, resulting in a formation of two parallel lines on the residual value plot. As indicated below, the plot is predicted by the residuals and shows that the variances are somewhat equal. This confirms homoscedasticity.
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No multicollinearity is present. According to the Coefficients Table, all the variables present a Variation Inflation Factor, VIF, of less than 10. This confirms that the perception factors do not relate to one another and the x’s are fixed and independent. Normality can be tested by the Shapiro-‐Wilk test. All relevant variables had significance levels less than 0.05, concluding that the data is not normal. However, due to the Central Limit Theorem, we can assume normality because the mean of all samples from the population should be proportionate with the mean of the population. Independence of errors can be conducted through both confirmatory and step-‐wise methods. I chose to utilize the step-‐wise method, giving me a Durbin-‐Watson value of 2.169. Ideally, the Durbin-‐Watson should be equal to 2.169 is within the appropriate range, indicating independence between errors.
To test linearity, the correlations table should be assessed. The null is that there is no correlation, with the alternative being there is. The significance values are all less than 0.05, represented by the stars in the Pearson Correlation row. Because the Pearson Correlation is positive for each attribute, we can confirm there is a positive linear correlation between perceptions and recommendations. Public transportation is the only variable that is not significant at a 0.01 level, but still falls within the 0.05.
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Assess Model Fit In order to assess model-‐fit, I ran both a confirmatory and a step-‐wise model. Under the confirmatory model, The ANOVA table indicated the results of the f-‐test. The f-‐test determines if at least one x has an influence over y, or if one perception factor has influence over recommendations. The significance value for the confirmatory model is less than 0.05, confirming there is at least one variable with influence over recommendation of a city. the model summary table confirms that 31.8% of the variation for or against city recommendations can be explained by the model. The adjusted R2 indicates that 29.8% of the variation in recommendations can be explained by the model adjusted for the number of x’s. The model fits.
For the purpose of cleaner data, I chose to rerun the dataset using the step-‐wise method. This method lets the model decide by significance which variables are preserved or disposed of. If the x has no effect on the y then the variable is not included. The ANOVA table again depicts the results of the f-‐test. The step-‐wise model shows F (4,437) = 47.756. The significance is less than 0.05, showing that at least one city perception factor has influence on recommendations.
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The step-‐wise model indicates that 30.6% of the variance in perceptions of home cities can be explained by four factors: safety, developed downtown core, higher education, and parks and recreation. This is not as high as I would like it to be, but for the purposes of predicting rather than explaining I will continue.
The adjusted R2 takes into consideration the variables that aren’t significant in this model. The adjusted R2 is lower than the R2 by 0.006, indicating that a lower percentage of variables have a predictive power in this model. Interpretation In order to determine the variables that are influential over a YP recommending his/her city to friends, I utilized the Coefficient Table. Using the step-‐wise model, I concluded that safety, developed downtown core, higher education, and parks and recreation are significant to recommendations. Increasing or decreasing the perceptions of these attributes by one unit will influence the likelihood of a person recommending it.
Recommendation (hat) = 1.691 + 0.323 SAFETY + 0.326 DEVELOPED DOWNTOWN CORE + 0.279 HIGHER EDUCATION
+ 0.156 PARKS AND RECREATION
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*If you increase safety in city by one unit, the likeliness a person will recommend the said city will increase by 0.323. *If you increase developed downtown core in city by one unit, the likeliness a person will recommend the said city will increase by 0.326. *If you increase higher education in city by one unit, the likeliness a person will recommend the said city will increase by 0.279. *If you increase parks and recreation in city by one unit, the likeliness a person will recommend the said city will increase by 0.156. Part A Recommendations The multiple regression analysis confirmed that the director should focus on safety, developed downtown core, higher education and parks and recreation perceptions to increase how likely a young professional is to recommend his/her home city. A developed downtown core often relates to the shopping, dining, and entertainment the city has to offer. I recommend that the director encourage more publicity for city attractions. The city website is a useful way to showcase to young professionals by tailoring to their interests. By implementing links and blogs to local bars and eateries on various forms of media, young professional’s will develop more positive perceptions of a city’s downtown core. To increase safety perceptions, the director should work alongside the police department to promote success stories in the community. Publicity of neighborhood transgression and hate crimes can hinder the perception of safety in large cities like Fort Worth, Kansas City and Atlanta. By promoting positivity and increasing security presence in large metropolitan areas, young professional recommendations will likely increase. Perceptions of higher education can be promoted by making local colleges more engaging to young professionals. Partnering with local universities, the director can work to promote furthering education. The director can also encourage young professionals to attend university-‐hosted seminars, sports games or community events to develop positive cognizance with the schools. Lastly, if resource permitting, parks and recreation perceptions should be recognized. Young professionals today are more active and health conscious than in the past, giving opportunity to utilize parks and recreational areas for their interests. I recommend revamping parks around the downtown areas to include basic fitness machines. Making parks more pet-‐friendly would also work to drive perceptions up. Developed downtown core carries the most weight, therefore should be the focal point when implementing changes. Safety and higher education follow behind developed downtown core, with parks and recreation being the least influential to young professional recommendations.
Ashley Quintilone
Part B Kansas City In order to assess recommendations for Kansas City only, an additional multiple regression analysis must be computed. The sample size for this regression decreases from 534 to 180, still proving enough power to be representative of the population. Despite this change, all other assumptions remain accurate. Rerunning the data with a selection variable through step-‐wise, the Coefficients Table concludes that safety and social diversity are significant to Kansas City recommendations. Increasing or decreasing the perceptions of these attributes by one unit will influence the likelihood of a person recommending it.
Recommendation (hat)= 1.866 + 0.528 SAFETY + 0.468 SOCIAL DIVERSITY
*If you increase safety in Kansas City by one unit, the likeliness a person will recommend Kansas City to a friend will increase by 0.528. *If you increase social diversity in Kansas City by one unit, the likeliness a person will recommend Kansas City to a friend will increase by 0.468. Recommendations When looking at Kansas City alone, safety and social diversity become the two perception attributes. The director should focus on safety first to maximize likelihood of a young professional recommending his/her city. Safety perceptions can be increased in Kansas City by increasing patrol around frequent crime areas like Seventh to 18th street and Grandview Boulevard to Pacific Avenue. Kansas City already funds “Project Art” in hopes of decreasing crime
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rates. I recommend publicizing the program more overtly to the public. This would work towards developing positive association between young professionals and safety. To increase social diversity perceptions, the director should focus on public areas like markets, playground and parks. Utilizing areas that border different communities is the most effective way to target social diversity. By fostering a program that encourages cultural representation, safety among ethnicities and mutual respect for cultures, young professionals will build stronger perceptions of Kansas City’s social diversity.
Ashley Quintilone
Q3 Logistic Regression Part A Findings / Recommendations Research Question / Objectives The objective of this research is to understand what influences the likelihood a YP recommends his/her city to friends. The goal of this logistic regression is to assess what city attributes influences the probability of recommending or not recommending. Analysis Plan Using the discrete and binary variable “Recommendation” as the dependent, respondents are given the options “yes” or “no” to whether they would recommend a city. The independent variables are the twelve attributes in Q19_1-‐12: Public Education, Higher Education, Employment Opportunities, Safety, Environmentally-‐Friendly, Public Transportation, Social Diversity, Developed Downtown Core, Nightlife, Cultural Amenities, Parks and Recreation, and Cost of Living. Respondents evaluate the variables on a 1-‐5 scale: (1) Very Bad, (2) Bad, (3) Neither Good nor Bad, (4) Good and (5) Very Good. Every independent variable should have at least 15 observations when running logistic regression. This dataset has 534 respondents with 96 missing cases. 438 cases carry enough power to identify the influence of variables. APPENDIX A I chose to run both a confirmatory and step-‐wise model for this logistic regression. In order to foster congruency between the regressions, I decided to make recommendations based on a forward-‐Wald step-‐wise model. Step-‐wise reduces the number of predictor variables based on what the data decides is significant or not. This will make recommendations and comparing results more veracious. Model Assumptions Through a pairwise correlation of x’s, I visually assessed the model for collinearity. No multicollinearity is present. In logistic regression, errors cannot be normal. No normality is presented in this model. The model needs to be gauged for incomplete information of independent variables, complete separation between variables and overdispersion. With 438 useful cases, there is enough data on each variable. The recommend variable and the twelve city attributes are completely separated. This is vital to logistic regression because a y that can perfectly predict an x or
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numerous x’s results in perfect prediction, essentially making it inconsequential to run the model. Because there are enough independent observations, overdispersion is not an issue. Assess Model Fit The fit test and likelihood ratio must be assessed when running logistic regression. Using the Omnibus Tests of Model Coefficients table, the chi-‐square column identifies whether the independent variables have influence on the dependent variables in the model.
Chi-‐squared4= 125.798 This is an indicator of how much unexplained information there is after the model has been fitted. The four depicts how many x’s are being represented in the test.
Deviance = -‐2(125.798)
Deviance tests the model overall and ensures that it follows a chi-‐square distribution. Because the significance level is less than 0.05, the null is rejected. At least one of the independent variables in the model has influence on the “Recommend” variable.
The Model Summary table is then used to evaluate the Nagelkerke R Square. APPENDIX B
Nagelkerke R2 = 0.336 This confirms that 33.6% of the variation in probability of recommending his/her city can be explained by their perceptions of the twelve city attributes. This percentage is not as high as I would like, but because the goal is explaining and not predicting I will continue.
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The HITT Ratio is utilized to determine if perceptions are a good indicator of whether young professionals will recommend his/her city to friends. Using Step 4 of the Classification Table, the HITT ratio, CMAX and CPRO are determined.
Not Recommend
PREDICTED
Recommend PREDICTED
Not Recommend OBSERVED
215 40 255
Recommend OBSERVED
77 106 183
292 146 438
HITT Ratio= 73.3% CMAX= 0.582 CPRO= 0.513
1.25CMAX= 0.7275= 72.75% 1.25 CPRO= 0.64125= 64.13%
73.3 HITT RATIO > 0.7275 CMAX
The ratios work to assess if the model is predicting well. Because HITT ratio is greater than the CMAX, the highest proportion of the two observed groups, I am confident that this model can predict well. Overall, perceptions of cities attributes are a good indicator of whether or not young professionals will recommend his/her city to friends.
Ashley Quintilone
Interpretation The Variables in the Equation table is used to determine which attributes are significant under logistic regression. The attributes Higher Education, Safety, Developed Downtown Core and Nightlife have a significance level less than 0.05, confirming they are influential on predicting the probability of young professionals recommending his/her city to a friend.
P(RECOMMEND) = 1
1+e-‐(-‐9.733 + 0.457 (HIGHER EDUCATION) + 0.569 (SAFETY) + 0.840 (DEVELOPED DOWNTOWN CORE) + 0.445 (NIGHTLIFE))
There is no marginal effect in PRECOMMEND. Therefore, there is no way to determine which attributes are more important. Because the betas are all positive, however, increasing perceptions of Higher Education, Safety, Developed Downtown Core, and Nightlife will increase the probability of a young professional recommending his/her city to a friend.
Recommendations The logistic regression model reflects that perceptions of higher education, safety, developed downtown core, and nightlife can positively increase the probability that young professionals recommend his/her city to friends. To increase perceptions of higher education, the director should partner with local universities to promote higher education to young professionals. Specifically, advocating for graduate programs in popular metropolitan areas would work towards building more positive perceptions.
Ashley Quintilone
The director can also encourage young professionals to attend university-‐hosted seminars, sports games or community events to develop positive cognizance with the schools. Safety perceptions can be fixed by working alongside the police department to develop a program that fosters community commitment to public safety. Promoting success stories, increasing law enforcement presence, and keeping hostile crimes out of the press will develop a sense of security. Working towards creating proactive publicity through media on topics such as safety tactics will grab the attention of young professionals. Perceptions of a developed downtown core can be increased by advertising the shopping, dining, and entertainment the city has to offer. Focusing on places that cater to young professional’s interests, such as sports, games or outside patio’s, would be most beneficial to increasing their perceptions. Utilizing the city website, social media platforms and local events, young professionals can progress a more positive perception of a city’s developed downtown core. The perceptions of nightlife are built around the personal experiences of young professionals. I recommend working with city authorities to potentially amend noise ordinances. Encouraging restaurant and bars to operate later into the evening would be beneficial to bringing in business after work. Increasing accessible transportation, like train-‐stops, bus-‐stops, Uber pick-‐up zones or overnight parking garages, in areas with nightlife districts, cultivate both safety and practicality. Lastly, working with high-‐frequented bars and clubs to streamline wait times would promote a more positive perception of nightlife for young professionals. Focusing on any of these four attributes will increase the probability young professionals recommend his/her city to friends.
Ashley Quintilone
Part B Multiple Regression vs Logistic Regression The multiple regression analysis confirmed that the director should focus on safety, developed downtown core, higher education and parks and recreation perceptions to increase how likely a young professional is to recommend his/her home city. Developed downtown core carries the most weight in this model, therefore should be the focal point if implementing changes based off this strategy. Safety and higher education follow behind developed downtown core, with parks and recreation being the least influential to a young professional recommendation. Recommendation MULTIPLE REGRESSION (hat) = 1.691 + 0.323 SAFETY + 0.326 DEVELOPED DOWNTOWN CORE +
0.279 HIGHER EDUCATION + 0.156 PARKS AND RECREATION
The logistic regression model reflects that perceptions of higher education, safety, developed downtown core, and nightlife can positively increase the probability that young professionals recommend his/her city to friends. Unlike multiple regression, logistic regression has no marginal effect and cannot determine which variable is most important. PLOGIT(RECOMMEND) = 1
1+e-‐(-‐9.733 + 0.457 (HIGHER ED) + 0.569 (SAFETY) + 0.840 (DEVELOPED DT CORE) + 0.445 (NIGHTLIFE))
Both multiple regression and logistic regression found that safety, developed downtown core and higher education are significant when young professionals recommend his/her city to friends. Multiple regression concluded that parks and recreation was the fourth and final attribute. Parks and recreation also held the least weight in terms of influencing whether a young professional would recommend his/her city to a friend. Logistic regression, however, found nightlife to be the fourth and final significant attribute. Recommendations for enhancing perceptions towards parks and recreation differ greatly from those benefitting nightlife. For this reason, I recommend following the multiple regression analysis model for recommendations and implementations. The multiple regression model confirms which attributes are the most influential, by weight, to a young professional recommending his/her city. This will be more resourceful for the director when making modifications to the city then having to focus on four variables equally. Nightlife can arguably fit in as an alcove to developed downtown core, working synonymously in perceptions as adjustments are made. Additionally, parks and recreation is a much easier attribute to revise perceptions of than nightlife. That being said, I recommend following the multiple regression model and focusing first and foremost on developed downtown core. The developed downtown core is the shopping, dining, and entertainment experiences the city can use to cater to young professionals. Promoting eateries with trendy menus, patio music, and games will engage the young professional
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demographic. Publicizing city attractions on the city’s website and social platforms will progress a more positive perception of the developed downtown core. With the lasting resources, I recommend developing a community-‐outreach that fosters commitment to public safety. Publicizing success stories, increasing law enforcement presence, and keeping hostile crimes out of the press will develop a sense of security. Once safety perceptions have been enhanced, higher education can be promoted by making local universities more engaging to the city’s young professionals. I recommend partnering with local universities to promote higher education, specifically graduate programs, in congested metropolitan areas. Encouraging young professionals to attend university-‐hosted seminars, sports games or community events will develop positive cognizance between the young professionals and the schools. If developed downtown core, safety and higher education are all accounted for, I recommend actuating young professionals to utilize parks and recreational areas by tailoring to their interests. Parks are often associated with families and children. By advertising parks as a place to work-‐out, hangout or spend an afternoon reading a book, young professionals would develop preferred perceptions of what already exists.
Ashley Quintilone
Q4 Factor Analysis Part A Research Question / Objectives Factor analysis is an interdependence technique implemented to reduce data for variable summarization. The objective of exploratory factor analysis is to develop the twelve city attributes in Q19_1-‐12 into factors. Utilizing Principal Components Analysis, the goal is to minimalize loss of data by determining an appropriate number of factors to explain the maximum amount of total variance in the computed correlation mix. PCA will transform the twelve city attributes into a set of linear components to simplify and abridge the data. Analysis Plan Data was collected from 534 young professionals: 183 from Fort Worth, 180 from Kansas City and 171 from Atlanta. The sample size is sufficient and representative of the population APPENDIX D.
The young professionals record their perceptions of the twelve city attributes: Public Education, Higher Education, Employment Opportunities, Safety, Environmentally-‐Friendly, Public Transportation, Social Diversity, Developed Downtown Core, Nightlife, Cultural Amenities, Parks and Recreation, and Cost of Living. Respondents evaluate the variables on a 1-‐5 scale: (1) Very Bad, (2) Bad, (3) Neither Good nor Bad, (4) Good and (5) Very Good. Variables are both metric and interval. Model Assumptions No multicollinearity and correlation are essential for factor analysis. Using the correlations among the variables as model inputs, factor analysis recognizes interrelated variables and groups them together. The Bartlett’s Test of Sphericity determines whether the correlation among variables is sufficient to proceed. The significance is less than 0.05, so we reject the null. Correlation is present. The Kaiser-‐Meyer-‐Olkin Measure of Sampling Adequacy, MSA, test determines if variable in the dataset can be predicted from one another. MSA is greater than 0.5. APPENDIX E
MSA = 0.830 0.830 > 0.5
The data set has sufficient correlation and no multicollinearity. All other assumptions are met.
Ashley Quintilone
Assess Model Fit To assess the Principal Component Analysis, the Total Variance Explained table shows the components created to maximize variance in the fewest number of factors. Using the VERIMAX orthogonal rotation technique, three uncorrelated factors are created.
Analyzing a screen plot or following the latent root criterion will determine the ideal number of factors for maximal variance. APPENDIX F The Eigenvalues for the factors are all greater than one, confirming that three factors are optimal for summary. Factor 1 explains 34.865% of variance, Factor 2 explains 11.744% of variance, and Factor 3 explains 10.175% of variance. Collectively, the three factors can explain 56.784% of all factor variance. Interpretation To determine what variables a factor is inclusive of, the Rotated Component Matrix table is utilized. Any variable with a factor loading greater than |0.4| is represented in that component, or factor. The factors are a weighted linear combination of the select city attributes. The orthogonal rotation ensures that each factor is made up of different variables. The attributes with the largest weight, in terms of absolute value, are the biggest contributor to the factor. The following factors were derived from the following table:
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FACTOR 1: Culturally Versatile Developed Downtown Core, Social Diversity, Nightlife, Public Transportation, Cultural Amenities,
Parks and Recreation
Culturally Versatile = 0.720 DEVELOPED DOWNTOWN CORE + 0.699 SOCIAL DIVERSITY + 0.675 NIGHTLIFE + 0.632PUBLIC TRANSPORTATION + 0.621 CULTURAL AMENITIES + 0.445 PARKS AND RECREATION
FACTOR 2: Social Responsibility Public Education, Environmentally-‐Friendly, Higher Education, Safety
Social Responsibility = 0.834 PUBLIC EDUCATION+ 0.757 ENVIRONMENTALLY-‐FRIENDLY + 0.622 HIGHER EDUCATION +
0.604 SAFETY
FACTOR 3: Standard of Living Cost of Living, Employment
Standard of living = 0.745 COST OF LIVING + 0.437 EMPLOYMENT
To test reliability, each factor must be computed separately. The Cronbach’s Alpha measures the correlations among the designated variables, determining if the factor is producing appropriate summarization. The alpha ranges from zero, indicating no reliability, to one, complete reliability. The Cronbach’s Alpha should be greater than 0.7 to substantiate the integrity of the factor.
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Culturally Versatile = 0.764
0.76 > 0.7
Social Responsibility = 0.762 0.76 > 0.7
Standard of Living = 0.483
0.48 < 0.7 The Culturally Versatile and Social Responsibility factors both express sufficient reliability. The Standard of Living factor, however, has a low reliability statistic. I would not recommend moving forward with this factor in terms of recommendations.
Ashley Quintilone
Part B Two-‐Factor / Perceptual Map To summarize the city attributes in the most simplistic way, I ran a two-‐factor orthogonal analysis on Q19_1-‐12. This forced the model to develop only two factors, allowing the opportunity to plot them on a 90-‐degree perceptual map.
The Total Variance Table concludes that both factors have sufficient Eigenvalues for summary. I recognize that “Component 3” has an Eigenvalue > 1, however, for the purpose of simplifying the data, I will continue with two factors. By doing so, the factors can be mapped in a clear and easily understood way. Factor 1 explains 34.865% of variance and Factor 2 explains 11.744% of variance. Both factors collectively explain 46.609% of all variable variance. The following factors were derived from the Rotated Component Matrix: APPENDIX H
FACTOR 1: Amenability Public Education, Safety, Environmentally-‐friendly, Higher Education, Parks and Recreation,
Employment
Amenability = 0.771 PUBLIC EDUCATION + 0.738 SAFETY + 0.726 ENVIRONMENTALLY-‐FRIENDLY+ 0.677 HIGHER EDUCATION + 0.524 PARKS AND RECREATION+ 0.471 EMPLOYMENT
FACTOR 2: Versatility Developed Downtown Core, Cultural Amenities, Nightlife, Social Diversity, Public Transportation
Versatility = 0.728 DEVELOPED DOWNTOWN CORE + 0.726 CULTURAL AMENITIES + 0.694 NIGHTLIFE + 0.658 SOCIAL
DIVERSITY + 0.521 PUBLIC TRANSPORTATION
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To develop a perceptual map based on the factors Amenability and Versatility, I analyzed the means for each city. This allows me to identify where Fort Worth, Kansas City and Atlanta fall on the perceptual map. Because there is no ideal vector, I will not compute an additional linear regression.
The Report above indicates the mean factor-‐scores of Fort Worth, Kansas City and Atlanta in terms of Amenability and Versatility. In the perceptual map below, the means of each city are plotted. By putting them next to each other, it becomes much more evident how the cities are ranked on these factors comparatively. Although no ideal vector is computed, it is likely that quadrant 1 is the optimal quadrant based off previous analysis.
Perceptual Map
Low Versatility
High Versatility
Low Amen
ability
High Am
enability
(Amenability, Versatility) Fort Worth ( -‐0.2154, 0.1297) Kansas City (-‐0.4276, -‐0.1344)
Atlanta (0.5934, 0.0169)
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Recommendations
Fort Worth, Kansas City and Atlanta all have room to improve their versatility and amenability. Fort Worth ranks highest in versatility, but fall short to Atlanta in amenabilities. Catering to young professional’s perceptions on attributes in Amenability should become the focal point moving forward. Fort Worth needs to foster stronger young professional perceptions on educational systems, safety and being environmentally-‐friendly. It is apparent that Fort Worth lacks recognition in characteristics pertaining to security. Young professionals are looking for stability in a city. Both public education and higher education in Fort Worth are extremely competitive. Promoting this and capitalizing on it will develop the positive recognizance to push Fort Worth Amenability up. Developing community-‐outreach programs that foster commitment to public safety would help young professionals feel more at ease. Increasing law enforcement presence, and keeping hostile crimes out of the press will develop the stronger sense of security needed to increase Amenability in Fort Worth. Lastly, environmentally-‐friendliness has become a new factor of importance country wide. Subtle implementations such as recycling cans, or encouraging businesses to utilize sustainable resources, perceptions would improve. Fort Worth’s downtown, cultural amenities and nightlife compete well against Kansas City and Atlanta. Although there is still room for improvement, I recommend staying committed to bettering Fort Worth’s sustainable environment. The downtown scene will continue to evolve, but cultural and social amenities should be continually manipulated to cater to young professionals in the upcoming years. Focusing on increasing Amenability and Versatility, Fort Worth should strive to make a clear division from Kansas City and Atlanta. Doing so would help to retain the young professionals already in Fort Worth and procure those in neighboring cities.
Ashley Quintilone
Q5 Cluster Analysis Factor Analysis – Atlanta Young Professionals Only Research Question / Objectives The objective of factor analysis is to reduce data for variable summarization. Exploratory factor analysis will develop the twelve city attributes in Q14_1-‐12 into factors. To summarize the city attributes in the most simplistic way, a two-‐factor orthogonal analysis will force the model to develop only two factors, allowing the opportunity to utilize the factors for a cluster analysis. The factor analysis will simplify and abridge the data for Atlanta respondents specifically. Analysis Plan Data was collected from 171 young professionals in Atlanta. The sample size is sufficient for this analysis. APPENDIX I
The young professionals are asked to evaluate how important twelve different city characteristics are when deciding where to live. The characteristics include: Public Education, Higher Education, Employment Opportunities, Safety, Environmentally-‐Friendly, Public Transportation, Social Diversity, Developed Downtown Core, Nightlife, Cultural Amenities, Parks and Recreation, and Cost of Living. Respondents evaluate the variables on a 1-‐5 scale: (1) Not at all Important, (2) Very Important, (3) Neither Important nor Unimportant, (4) Very Important and (5) Extremely important. Variables are both metric and interval. Model Assumptions The Bartlett’s Test of Sphericity determines whether the correlation among variables is sufficient to proceed. The significance is less than 0.05, so we reject the null. Correlation is present. The KMO-‐MSA test determines if variable in the dataset can be predicted from one another. MSA is greater than 0.5. The data set has sufficient correlation and no multicollinearity. All assumptions are met.
MSA = 0.793 0.793 > 0.5
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Assess Model Fit The Total Variance Explained table depicts the forced two-‐factors computed. The factors are based on what young professionals in Atlanta identified as important city attributes. Using the VERIMAX orthogonal rotation technique, the Eigenvalues for both factors are greater than one. The factors are sufficient for summary.
Factor 1 explains 36.675% of variance, while Factor 2 explains 12.680% of variance. Collectively, the two factors can explain 49.355% of all factor variance. Interpretation Using a forced two-‐factor orthogonal technique, two factors were computed. The Rotated Component Matrix table is utilized to find which variables are included in the factors. Any variable with a factor loading less than |0.4| is not represented in that factor. The factors are a weighted linear combination of the select city attributes. The orthogonal rotation ensures that each factor is made up of different variables. The attributes with the largest weight, in terms of absolute value, are the biggest contributor to the factor. The following factors were derived from The Rotated Component Matrix. APPENDIX J
FACTOR 1 = Social Grace Social Grace = 0.759 DEVELOPED DOWNTOWN CORE + 0.749 NIGHTLIFE + 0.733 CULTURAL AMENITIES + 0.642 PUBLIC
TRANSPORTATION + 0.591 PARKS AND RECREATION + 0.538 ENVIRONMENTALLY-‐FRIENDLY + 0.50 SOCIAL DIVERSITY
FACTOR 2 = Indispensables
Indispensables = 0.838 PUBLIC EDUCATION + 0.745 HIGHER EDUCATION + 0.540 EMPLOYMENT + 0.512 SAFETY
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Both factors must be tested for reliability. The Cronbach’s Alpha measures the correlations among the designated variables, determining if the factor is producing appropriate summarization. The Cronbach’s Alpha should be greater than 0.7 to substantiate the integrity of the factor.
Social Grace = 0.805
0.81 > 0.7
Indispensables = 0.680 0.68 < 0.7
Social Grace shows sufficient reliability but Indispensables falls below the 0.7 threshold. Indispensables has a low reliability statistic in terms of how well the variables are being represented. That being said, the sample size is large enough to assume representation so I will continue on. Part A Cluster Analysis Research Question / Objectives The objective of cluster analysis is to divide a set of objects into 2 or more groups based on the objects’ similarity to a set of specified characteristics, the factors. Using the factors Social Grace and Indispensables, a cluster analysis will segment the Atlanta young professionals into summary attitudes about the twelve city attributes they deem important. The goal of this analysis is to determine where the young professionals in Atlanta fall within the clusters based on their factor scores. The objects within the segments will be homogeneous, but different across. The variables are distributed to the mutually exclusive groups based on similarities to the set of city attributes.
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Analysis Plan There are 171 young professionals from Atlanta in this sample. Because the goal is grouping, power is not necessary for this analysis. Variables represent the characteristics on the axis. Variable forms are relevant to how similarity among the observations is measured. Similarity is assessed as distance among the observations. The proximity in distance will assess how similar two objects are. The variables are metric so similarity will be assessed through Euclidean. The distance among observations is sensitive to scaling, reiterating why observations must be standardized and relevant to analysis. A two-‐factor orthogonal technique was utilized to ensure standardization between the twelve city characteristics: Public Education, Higher Education, Employment Opportunities, Safety, Environmentally-‐Friendly, Public Transportation, Social Diversity, Developed Downtown Core, Nightlife, Cultural Amenities, Parks and Recreation, and Cost of Living. Outliers should be recognized, being aware of their power over cluster forming. It is important to look for outlying observations on specific variables and characteristics. Without distinction, they can influence how the clusters form or where the new cluster will fall. Model Assumptions Because factor analysis was run to derive Social Grace and Indispensables with this dataset, it is not essential to check for multicollinearity, normality or linearity. To preserve the latency of no multicollinearity, the orthogonally rotated factor scores should be utilized moving forward. The model should be representative of the population. Assess Model Fit Cluster analysis uses an algorithm when forming clusters. If executed correctly, clusters should be compact, mutually exclusive and as far apart as possible. To do so, I chose to utilize Ward’s agglomerative method. An agglomerative method begins with each seed being independent of one another. It works to unify them progressively until one large cluster is left. Cluster analysis can be run both hierarchically or non-‐hierarchically. For the purpose of seeking the most accurate results, I will run both. Non-‐hierarchal assigns objects to clusters once a predetermined number of clusters is specified. All objects within a fixed distance are united into one cluster. Objects may be reassigned to different cluster as new seeds are added. Each seed integration leads to rinsing and repeating. Hierarchical is a must faster method, but is not competent for analyzing large samples. I will be utilizing hierarchal to determine how many clusters would be most beneficial to the data set. I will then use non-‐hierarchal to provide more depth to the clusters chosen. The goal is to
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determine where the biggest leap occurs on the Agglomeration Schedule. APPENDIX K Running the non-‐hierarchal will determine the final number of clusters. The factors Social Grace and Indispensables serve as the axis for plotting. The Final Cluster Centers table gives the midpoint of the clusters. It also reveals how many young professionals in Atlanta fall within each cluster.
Cluster Analysis Map
High Social G
race Low Social G
race
Indispensables Surplus
Indispensables Deficiency
PARTY IN THE USA
UMBRELLA
SINGLE LADIES
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Part B Profiling and Segmentation The Cluster Analysis Map depicts the market segmentation of young professionals in Atlanta. The clusters are created based on recorded importance of factors Social Grace and Indispensables. The cluster centers and case totals determined the location and size represented on the map.
“Party in the USA” Miley Cyrus (0.84697, 0.00478)
The Party in the USA cluster follows the wise influence of Miley Cyrus, letting the “butterfly’s fly away” for any city that exhibits high Social Grace. These young professionals value a city for its developed downtown core, exciting nightlife and diverse amenity opportunities. This group is invested in the social scene, looking to live anywhere they can hang out and mingle with likeminded people. This group is less influenced by a cities Indispensables. Education and employment opportunities are not as important in comparison to the various social attributes.
“Umbrella” Rihanna (-‐0.70845, 0.55381)
As Bad Girl RiRi preaches, the essentials are all you need to be happy. This segment of young professionals prefer to be under an “umbrella” of security. They are less concerned with a city’s nightlife, but value the notion of stability. These young professionals are influenced predominately by Indispensables. The Umbrella cluster is responsive to strong education systems, prospective employment opportunities, and safety.
“Single Ladies” Beyoncé (-‐0.4230, -‐1.79126)
The Single Ladies cluster of young professionals embody the soul and spirit of our Queen B. As she sings in her Grammy Award Winning, 2010 Song of the Year: Single Ladies, “I’m doing my own little thing.” These young professionals find Social Grace and Indispensables irrelevant and influential when deciding where to live. Social, educational and professional attributes do not work for or against cities, inconspicuous to where they live now. The motives influencing where these young professionals live are likely unparalleled to the twelve attributes used to develop the model.
*Formal apology for the ear worms*
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Appendix
a. Logistic Regression Included Cases
b. Logistic Regression Model Summary
c. CMAX and CPRO Logistic Regression
CMAX= MAX (255/438, 183/438) =0.42 OR 0.582
=0.582
CPRO= (0.582)2 + (1-‐0.582)2 =0.513
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d. Factor Analysis Sample Size
10 * (number of variables) = ideal sample size for population generalization 10 * 12 city attributes = 120
534 > 120
e. Factor Analysis Tests for Correlation
f. Scree Plot (PCA Factors)
The Scree Plot indicates a plateau forming between values 2 and 3. With assistance from the Eigenvalues test, I can conclude that three is the optimal number of factors for maximized summarization.
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g. Screen Plot (Forced Two-‐factor)
This Scree Plot indicates a forced plateau between values 1 and 2.
h. Rotated Component Matrix (Forced Two-‐factor)
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i. Atlanta-‐ Factor Analysis Sample Size
10 * (number of variables) = ideal sample size for pop. generalization 10 * 12 city attributes = 120
171 > 120
j. Atlanta-‐ Rotated Component Matrix
k. Agglomeration Schedule
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Not at all Important (1)
Very Unimportant
(2)
Neither Important nor Unimportant
(3)
Very Important (4)
Extremely Important (5)
Public Education (1) m m m m m
Higher Education (2) m m m m m
Employment opportunities in a
wide range of fields (3)
m m m m m
Safety (e.g., crime rate, street
lights) (4) m m m m m
Environmentally-friendly (e.g., air
quality, recycling) (5)
m m m m m
Public transportation (e.g., access,
availability) (6)
m m m m m
Social diversity (e.g., ethnic,
socio-economic) (7)
m m m m m
Q14 How important are the following city characteristics to you in deciding where to live?
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Developed Downtown Core
(8) m m m m m
Nightlife (e.g., restaurants, clubs, live music) (9)
m m m m m
Cultural Amenities (e.g.,
museums, symphony, ballet) (10)
m m m m m
Parks and Recreation (11) m m m m m
Cost of Living (12) m m m m m
Other (13) m m m m m
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Q16 How likely are you to:
Very
Unlikely (1)
Unlikely (2)
Somewhat Unlikely (3)
Undecided (4)
Somewhat Likely (5) Likely (6) Very
Likely (7)
Stay in Fort Worth if
offered an opportunity in another
city (1)
m m m m m m m
Recommend Fort Worth to friends
(2)
m m m m m m m
Come back to Fort
Worth if you ever left
(3)
m m m m m m m
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Very Bad (1) Bad (2) Neither Good nor Bad (3) Good (4) Very Good (5)
Public Education (1) m m m m m
Higher Education (2) m m m m m
Employment opportunities in a
wide range of fields (3)
m m m m m
Safety (e.g., crime rate, street
lights) (4) m m m m m
Environmentally-friendly (e.g., air
quality, recycling) (5)
m m m m m
Public transportation (e.g., access,
availability) (6)
m m m m m
Social diversity (e.g., ethnic,
socio-economic) (7)
m m m m m
Developed Downtown Core
(8) m m m m m
Q19 What is your perception of Fort Worth on these city characteristics?
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Nightlife (e.g., restaurants, clubs, live music) (9)
m m m m m
Cultural Amenities (e.g.,
museums, symphony, ballet) (10)
m m m m m
Parks and Recreation (11) m m m m m
Cost of Living (12) m m m m m
Other (13) m m m m m