Machine Learning – Mathematical Concepts for Linear Regression Models

This article represents some of the key mathematics & statistics concepts that one may need to learn in order to work with linear regression models. Understanding following concepts would help in some of the following manners in relation with evaluating linear regression models:

• Interpreting coefficients
• Evaluating the regression model
• Comparing multiple regression models and choosing the best out of them

Please feel free to comment/suggest if I missed to mention one or more important points. Also, sorry for the typos.

• Statistical hypothesis testing
• Probability distributions
• Quantitative data analysis
• Plots

Key Mathematics & Statistics Topics for Linear Regression Models

• Statistical Hypothesis Testing: One would need to understand concepts around with statistical hypothesis testing and the related topics. Following are some of the related topics that would be useful to understand for having better understanding of different machine learning techniques and related models created using those algorithm. Understanding following concepts is key to understanding the evaluation techniques for various machine learning models including linear regression, logistic regression etc.
  • Null hypothesis, Alternate hypothesis
  • Type I & Type II error
  • Region of acceptance, Statistical significance, P-value
  • Standard error

  A good starting point could be Wikipedia page on statistical hypothesis testing There are multiple Youtube videos on hypothesis testing and the ones from Khan Academy (hypothesis testing) that could prove helpful in understanding these concepts.

• Probability Distributions: It would be good to understand the concepts around some of the following continuous probability distributions:
  • Normal Distribution
  • Z-Distribution
  • Student’s T-Distribution
  • F-Distribution
• Quantitative Data Analysis: Following are some of the concepts that would be helpful in analysing the data when working with regression model:
  • Mean, median, variance
  • Quantiles concepts
  • Correlation
  • Covariance
  • Multicollinearility
• Plots: It would be good idea to understand nuances around some of the following plots which will come handy while working on regression models:
  • Scatterplots
  • Density plot
  • Histogram