EDA-Lesson 5

• Scatter Plot

  • Explains the correlation between two attributes or variables
  • Represents how closely the two variables are connected
• Simple Linear Regression


  • Single regressor variable or predictor variable x and a dependent or response variable Y
  • Random errors corresponding to different observations are assumed to be uncorrelated random variables
  • Regression model may be thought of as an empirical model
• Correlation vs. Causation

  • Correlation indicates a statistical relationship between two variables
  • Causation is a cause-and-effect relationship between variables
• What does it mean when errors are normally distributed?

  • It means that the distribution of the errors, or residuals, follows a normal distribution
• Deterministic Relationship


  • A model that predicts a variable perfectly
• Scatter plots

  • Present the relationship between two variables in a data-set
  • Represent data points on a two-dimensional plane or on a Cartesian system
  • Independent variable or attribute on the X-axis, dependent variable on the Y-axis
  • Also known as scatter graphs or scatter diagrams
  • Effective in revealing the joint variability of x and y or the nature of relationship between them
• Types of Correlation

  • Positive Correlation
  • Negative Correlation
  • No Correlation
• Regression Analysis


  • Collection of statistical tools used to model and explore relationships between variables that are related in a non-deterministic manner
  • Used when the relationship between variables is not deterministic
• Correlation Does Not Imply Causation
• Errors being normally distributed means

  • The distribution of errors follows a normal distribution
  • Discrepancies between observed values and values predicted by a statistical model are symmetrically distributed around the mean
  • Most errors cluster near the mean with fewer errors occurring further away in both positive and negative directions
  • Simplifies calculations and allows for the application of many statistical tests
• Method of Least Squares

  • Criterion for estimating the regression coefficients
  • Used to estimate the parameters of a system by minimizing the sum of the squares of the differences between the observed values and the fitted or predicted values from the system
• Normal distribution in statistical models


  • Simplifies calculations and allows for the application of many statistical tests and procedures that rely on the assumption of normality
• Possible Interpretations of ρ

  • When ρ is equal to zero, there is no correlation
  • When ρ = 1, there is a perfect, positive, linear relationship
  • When ρ = -1, there is a perfect, negative, linear relationship
  • When ρ is between 0 and 1 in absolute value, it reflects the relative strength of the linear relationship
• Correlation


  The degree of linear association between two random variables X and Y
• Coefficient of Determination


  Denoted by r^2, a descriptive measure of the strength of the regression relationship, a measure of how well the regression line fits the data
• r^2 is often used to judge the adequacy of a regression model. Its value tells that the model accounts for r2×% of the variability in the data
• Correlation coefficient

  Indicated by ρ, the population (true) correlation coefficient, estimated by r, the sample correlation coefficient or Pearson product-moment correlation coefficient
• Errors in a statistical model

  • Cluster symmetrically around the mean, with most errors near the mean and fewer errors further away in both positive and negative directions
• Good linear fit


  • Defined by how well it represents the relationship between the independent variable and the dependent variable
• Ordinarily, we do not use r^2 for inference about ρ^2
• Sample Correlation Coefficient


  The estimate of ρ, also referred to as the Pearson product-moment correlation coefficient