Summary Of Business Analytics Course Presentationdr Hemang ✓ Solved

This document summarizes a business analytics course presentation by Dr. Hemang Subramanian, detailing various statistical methods and machine learning techniques used in analytics.

Regression Equation

The linear regression equation is expressed as:

Y = bX + a

Where:

  • Y = dependent variable

  • X = independent variable

  • a = constant (value of Y when X = 0)

  • b = slope of the regression line

The standard regression equation also includes an error term:

Y = α + βX + ε

Where:

  • Y = dependent variables (Matrix)

  • α = constant term

  • β = slope or regression coefficient

  • X = independent variable (Matrix)

  • ε = error term

Panel Regressions

A panel regression refers to repeated observations over time about an individual. For instance:

  • Obsid = 1, dvar1_1, time 1, ivar1_1_2, ivar2_1_1, …

  • Obsid = 1, dvar2_1, time 2, ivar1_2_2, ivar2_2_2, …

Panel data is advantageous for analyzing the dynamics of change over time and individual behavior.

Logistic Regression

Logistic regression is used when the dependent variable is dichotomous (binary), such as true/false or yes/no.

The generalized linear model can be expressed as:

g(E(y)) = α + βx1 + γx2

Where g() is the link function, E(y) is the mean of the target variable, and α, β, γ are predictors with their coefficients. An example of logistic regression might predict if customers will buy a magazine based on age, represented as:

p = exp(β0 + β(Age))

Probit Regression

The probit function is the inverse cumulative distribution function associated with the standard normal distribution and is used in binary response variables. For instance, predicting the choice of food for different sizes of alligators can utilize probit regression.

Multinomial Logistic Regression

In multinomial logistic models, choices among various alternatives can be analyzed. For instance, students might choose between general, vocational, and academic programs based on their scores.

The model helps in understanding relative choice probabilities informed by predictors like socioeconomic status.

Clustering Techniques

Clustering is vital for grouping data to apply targeted marketing strategies or identify behavioral patterns.

Some clustering methods include:

  • K-means clustering

  • Hierarchical clustering

Hierarchical clustering does not require a pre-specified number of clusters and provides a dendrogram representation.

Bayesian Classifier

The Naïve Bayesian Classifier employs Bayes' theorem to update the probability of hypotheses as more evidence becomes available. The probability relationship is expressed as:

P(H/E) = [P(E/H)/P(E)] x P(H)

This method is particularly effective in scenarios where new data continually influences predictions.

Conclusion

In summary, the business analytics presentation by Dr. Hemang Subramanian provides a comprehensive overview of various regression analyses, machine learning techniques, and statistical models vital for understanding complex data and making informed decisions in business analytics.

References

  • 1. Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. SAGE Publications.

  • 2. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning. Springer.

  • 3. Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer.

  • 4. Agresti, A. (2018). Statistics (5th ed.). Pearson.

  • 5. Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.

  • 6. Kleinbaum, D. G., & Klein, M. (2010). Logistic Regression: A Self-Learning Text. Springer.

  • 7. Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.

  • 8. Ripley, B. D. (2007). Pattern Recognition and Neural Networks. Cambridge University Press.

  • 9. Siegel, A. F. (2016). Practical Business Statistics. Academic Press.

  • 10. Kuhn, M., & Johnson, K. (2013). Applied Predictive Modeling. Springer.