Quant: Regression and Correlations

Top management of a large company has told you that they really would like to be able to determine what the impact of years of service at their company has on workers’ productivity levels, and they would like to be able to predict potential productivity based upon years of service. The company has data on all of its employees and has been using a valid productivity measure that assesses each employee’s productivity. You have told management that there is a possible way to do that.

Through a regression analysis, it should be possible to predict the potential productivity based upon years of service, depending on two factors: (1) that the productivity assessment tool is valid and reliable (Creswell, 2014) and (2) we have a large enough sample size to conduct our analysis and be able to draw statistical inference of the population based on the sample data which has been collected (Huck, 2011). Assuming these two conditions are met, then regression analysis could be made on the data to create a prediction formula. Regression formulas are useful for summarizing the relationship between the variables in question (Huck, 2011). There are multiple types of regression all of them are tests of prediction: Linear, Multiple, Log-Linear, Quadratic, Cubic, etc. (Huck, 2011; Schumacker, 2014).  The linear regression is the most well-known because it uses basic algebra, a straight line, and the Pearson correlation coefficient to aid in stating the regression’s prediction strength (Huck, 2011; Schumacker, 2014).  The linear regression formula is: y = a + bx + e, where y is the dependent variable (in this case the productivity measure), x is the independent variable (years of service), a (the intercept) and b (the regression weight) are a constants that are to be defined through the regression analysis, and e is the regression prediction error (Field, 2013; Schumacker, 2014).  The sum of the errors should be equal to zero (Schumacker, 2014).

Linear regression models try to describe the relationship between one dependent and one independent variable, which are measured at the ratios or interval level (Schumacker, 2014).  However, other regression models are tested to find the best regression fit over the data.  Even though these are different regression tests, the goal for each regression model is to try to describe the current relationship between the dependent variable and the independent variable(s) and for predicting.  Multiple regression is used when there are multiple independent variables (Huck, 2011; Schumacker, 2014). Log-Linear Regression is using a categorical or continuously independent variable (Schumacker, 2014). Quadratic and Cubic regressions use a quadratic and cubic formula to help predict trends that are quadratic or cubic in nature respectively (Field, 2013).  When modeling predict potential productivity based upon years of service the regression with the strongest correlation will be used as it is that regression formula that explains the variance between the variables the best.   However, just because the regression formula can predict some or most of the variance between the variables, it will never imply causation (Field, 2013).

Correlations help define the strength of the regression formula in defining the relationships between the variables, and can vary in value from -1 to +1.  The closer the correlation coefficient is to -1 or +1; it informs the researcher that the regression formula is a good predictor of the variance between the variables.  The closer the correlation coefficient is to zero, indicates that there is hardly any relationship between the variable (Field, 2013; Huck, 2011; Schumacker, 2014).  A negative correlation could show that as the years of service increases the productivity measured is decreased, which could be caused by apathy or some other factor that has yet to be measured.  A positive correlation could show that as the years of service increases the productivity also measured increases, which could also be influenced by other factors that are not directly related to the years of service.  Thus, correlation doesn’t imply causation, but can help determine the percentage of the variances between the variables by the regression formula result, when the correlation value is squared (r2) (Field, 2013).

References

  • Creswell, J. W. (2014) Research design: Qualitative, quantitative and mixed method approaches (4th ed.). California, SAGE Publications, Inc. VitalBook file.
  • Field, A. (2013) Discovering Statistics Using IBM SPSS Statistics (4th ed.). UK: Sage Publications Ltd. VitalBook file.
  • Huck, S. W. (2011) Reading Statistics and Research (6th ed.). Pearson Learning Solutions. VitalBook file.
  • Schumacker, R. E. (2014) Learning statistics using R. California, SAGE Publications, Inc, VitalBook file.

Business Intelligence: Data Mining

When you think about business intelligence (BI), the first thing that probably comes to mind is data. However, all of those BI solutions use technology. This post discusses how does the data mining approach and concept flow to BI solutions and the enterprise level of an organization’s information technology (IT) effort.

Data mining is just a subset of the knowledge discovery process (or concept flow of Business Intelligence), where data mining provides the algorithms/math that aid in developing actionable data-driven results (Fayyad, Piatetsky-Shapiro, & Smyth, 1996). It should be noted that success has much to do with the events that lead to the main event as it does with the main event.  Incorporating data mining processes into Business Intelligence, one must understand the business task/question behind the problem, properly process all the required data, analyze the data, evaluate and validate the data while analyzing the data, apply the results, and finally learn from the experience (Ahlemeyer-Stubbe & Coleman, 2014). Conolly and Begg (2014), stated that there are four operations of data mining: predictive modeling, database segmentation, link analysis, and deviation detection.  Fayyad et al. (1996), classifies data mining operations by their outcomes: prediction and descriptive.

It is crucial to understand the business task/question behind the problem you are trying to solve.  The reason why is because some types of business applications are associated with particular operations like marketing strategies use database segmentation (Conolly & Begg, 2014).  However, any of the data mining operations can be implemented for any business application, and many business applications can use multiple operations.  Customer profiling can use database segmentation first and then use predictive modeling next (Conolly & Begg, 2014). By thinking outside of the box about which combination of operations and algorithms to use, rather than using previously used operations and algorithms to help meet the business objectives, it could generate even better results (Minelli, Chambers, & Dhiraj, 2013).

A consolidated list (Ahlemeyer-Stubbe & Coleman, 2014; Berson, Smith, & Thearling 1999; Conolly & Begg, 2014; Fayyad et al., 1996) of the different types of data mining operations, algorithms and purposes are listed below.

  • Prediction – “What could happen?”
    • Classification – data is classified into different predefined classes
      • C4.5
      • Chi-Square Automatic Interaction Detection (CHAID)
      • Support Vector Machines
      • Decision Trees
      • Neural Networks (also called Neural Nets)
      • Naïve Bayes
      • Classification and Regression Trees (CART)
      • Bayesian Network
      • Rough Set Theory
      • AdaBoost
    • Regression (Value Prediction) – data is mapped to a prediction formula
      • Linear Regression
      • Logistic Regression
      • Nonlinear Regression
      • Multiple linear regression
      • Discriminant Analysis
      • Log-Linear Regression
      • Poisson Regression
    • Anomaly Detection (Deviation Detection) – identifies significant changes in the data
      • Statistics (outliers)
  • Descriptive – “What has happened?”
    • Clustering (database segmentation) – identifies a set of categories to describe the data
      • Nearest Neighbor
      • K-Nearest Neighbor
      • Expectation-Maximization (EM)
      • K-means
      • Principle Component Analysis
      • Kolmogorov-Smirnov Test
      • Kohonen Networks
      • Self-Organizing Maps
      • Quartile Range Test
      • Polar Ordination
      • Hierarchical Analysis
    • Association Rule Learning (Link Analysis) – builds a model that describes the data dependencies
      • Apriori
      • Sequential Pattern Analysis
      • Similar Time Sequence
      • PageRank
    • Summarization – smaller description of the data
      • Basic probability
      • Histograms
      • Summary Statistics (max, min, mean, median, mode, variance, ANOVA)
  • Prescriptive – “What should we do?” (an extension of predictive analytics)
    • Optimization
      • Decision Analysis

Finally, Ahlemeyer-Stubbe and Coleman (2014) stated that even though there are a ton of versatile data mining software available that would do any of the abovementioned operations and algorithms; a good data mining software would be deployable across different environments and include tools for data prep and transformation.

References

Big Data Analytics: R

R has proven to be the most effective software tool for analyzing big data. This post will be quick discuss of my evaluation of this tool and its relevance in the big data arena, with respects to text mining.

R is a powerful statistical tool that can aid in data mining.  Thus, it has huge relevance in the big data arena.  Focusing on my project, I have found that R has a text mining package [tm()].

Patal and Donga (2015) and Fayyad, Piatetsky-Shapiro, & Smyth, (1996) say that the main techniques in Data Mining are: anomaly detection (outlier/change/deviation detection), association rule learning (relationships between the variables), clustering (grouping data that are similar to another), classification (taking a known structure to new data), regressions (find a function to describe the data), and summarization (visualizations, reports, dashboards). Whereas, According to Ghosh, Roy, & Bandyopadhyay (2012), the main types of Text Mining techniques are: text categorization (assign text/documents with pre-defined categories), text-clustering (group similar text/documents together), concept mining (discovering concept/logic based ideas), Information retrieval (finding the relevant documents per the query), and information extraction (id key phrases and relationships within the text). Meanwhile, Agrawal and Batra (2013) add: summarization (compressed representation of the input), assessing document similarity (similarities between different documents), document retrieval (id and grabbing the most relevant documents), to the list of text mining techniques.

We use the “library(tm)” to aid in transforming text, stem words, build a term-document matrix, etc. mostly for preprocessing the data (RStudio pubs, n.d.). Based on RStudio pubs (n.d.) some text preprocessing steps and code are as follows:

  • To remove punctuation:

docs <- tm_map(docs, removePunctuation)

  • To remove special characters:

for(j in seq(docs))      {        docs[[j]] <- gsub(“/”, ” “, docs[[j]])        docs[[j]] <- gsub(“@”, ” “, docs[[j]])        docs[[j]] <- gsub(“\\|”, ” “, docs[[j]])     }

  • To remove numbers:

docs <- tm_map(docs, removeNumbers)

  • Convert to lowercase:

docs <- tm_map(docs, tolower)

  • Removing “stopwords”/common words

docs <- tm_map(docs, removeWords, stopwords(“english”))

  • Removing particular words

docs <- tm_map(docs, removeWords, c(“department”, “email”))

  • Combining words that should stay together

for (j in seq(docs)){docs[[j]] <- gsub(“qualitative research”, “QDA”, docs[[j]])docs[[j]] <- gsub(“qualitative studies”, “QDA”, docs[[j]])docs[[j]] <- gsub(“qualitative analysis”, “QDA”, docs[[j]])docs[[j]] <- gsub(“research methods”, “research_methods”, docs[[j]])}

  • Removing coming word endings

library(SnowballC)   docs <- tm_map(docs, stemDocument)

Text mining algorithms could consist of but are not limited to (Zhao, 2013):

  • Summarization:
    • Word clouds use “library (wordcloud)”
    • Word frequencies
  • Regressions
    • Term correlations use “library (ggplot2) use functions findAssocs”
    • Plot word frequencies Term correlations use “library (ggplot2)”
  • Classification models:
    • Decision Tree “library (party)” or “library (rpart)”
  • Association models:
    • Apriori use “library (arules)”
  • Clustering models:
    • K-mean clustering use “library (fpc)”
    • K-medoids clustering use “library(fpc)”
    • Hierarchical clustering use “library(cluster)”
    • Density-based clustering use “library (fpc)”

As we can see, there are current libraries, functions, etc. to help with data preprocessing, data mining, and data visualization when it comes to text mining with R and RStudio.

Resources: