Coefficient Correlation and Linear Regression terms

• bivariate data

  • data that involve two variables
  • the purpose of the analysis is to describe relationships

  ex.

  1. IQ dcores ang math scores
  2. age of a person and weight
  3. age of a car and its price
• correlation analysis

  • a statistical method used to determine whether a relationship between two variables exists
• FRANCIS GALTON

  • in the late 19th century, an english statistician and polymath created a statistical concept of the correlation coefficient after examining height and forearm measurements
  • he demonstrated applications of correlation coefficient in the study of genetics, psychology, and anthropology
• scatter plots

  • the relationship between two variables may be visualized using this
• population linear correlation coefficient

  • denoted by ρ (read as rho)
  • a measure of the extent to which two quantitative variables x&y tend to move together
  • this coefficient measures the degree of association between x&y
• ρ

  • given by the ratio of the covariance of x&y to the product of the standard deviations of x&y
• pearson sample product moment correlation coefficient

  • point estimator of ρ
  • named after Carl earson (1857 to 1936)
• Carl Pearson

  • an english statistician who studied various correlation coefficients and other significant statistical concepts
• pearson's r

  • can be interpreted by the STRENGTH and DIRECTION of the relationship
• the strength of the relationship between two variables is indicated by the closeness of the points to the trend line
• direction of correlation can be classified as positive, negative or zero
• ±1 = perfect

  ±0.90 to < ±1 = very strong

  ±0.70 to < ±0.90 = strong

  ±0.50 to < ±0.70 = moderate

  ±0.30 to < ±0.50 = weak

  >0 to < ±0.30 = very weak

  0 = no correlation
• the more far apart the points are on a linear line, the weaker their relationship (vice versa)