SOCI CH 12

• Correlation


  A summary statistic measuring the degree and direction of linear relationship between two interval-ratio variables

  
• Correlation


  • Measures the degree of association between two variables
  • Has two components: direction (positive or negative) and magnitude (strength)

  
• Interpretation of Correlation


  • Strong negative (-1.00 to -0.50)
  • Moderate negative (-0.49 to -0.30)
  • Weak negative (-0.29 to -0.10)
  • Weak positive (0.10 to 0.29)
  • Moderate positive (0.30 to 0.49)
  • Strong positive (0.50 to 1.00)
• Requirements for using Pearson's Correlation Coefficient (r):
• Correlation vs Regression


  Correlation analysis measures the strength of the association (linear relationship) between two variables, but does not imply causation. Regression analysis is used to predict the value of a dependent variable based on the value of at least one independent variable, and to explain the impact of changes in an independent variable on the dependent variable.
• Bivariate Linear Regression Model


  Relationship between X and Y is described by a linear function: Y = a + b(X), where a is the Y-intercept and b is the slope of the regression line.

  
• The coefficients a and b, and other regression results, will be found using SPSS.
• Interpretation of the Slope (b)


  b measures the estimated change in the average value of Y as a result of a one-unit change in X.
• Interpretation of the Intercept (a)

  a is the estimated average value of Y when the value of X is zero (if X = 0 is in the range of observed X values).
• The predicted price for a house with 2000 square feet is $318,250.
• Coefficient of Determination (R^2)


  R^2 tells us how accurate a prediction the regression model is. It is the total variation in the dependent variable that is explained by variation in the independent variable.

  
• 58.08% of the variation in house prices is explained by variation in square feet.
• Independent variable is the cause

  • it is goes first then dependent goes second