MATHM | Correlation Analysis

• Measures the existence of relationship and association between two or more variables.

  Correlation Analysis
• The goal of a correlation analysis is to see the strength and the nature / direction of the relationship between two variables.
• can be used to predict the changes that will happen on the other variable.

  Independent Variable
• Usually expressed by the symbol "x"

  Independent Variable
• variable where the values are expected to change as a result of changes in the values of the other variable (independent variable),.

  Dependent Variable
• Usually expressed by the symbol "y"

  Dependent Variable
• is the diagram of the correlation analysis.

  Scatter Plot
• is a type of plot or mathematical diagram using Cartesian Coordinates to display values for typically two variables for a set of data.

  Scatter Plot
• Two variables are positively correlated if the values of the two variables both increase or both decrease
• Two variables are negatively correlated if the values of one variable increase while the values of the other decrease and vice versa.
• Two variables are not correlated, or they have zero correlation if one variable neither increases nor decreases while the other increases or decreases.
• Positive Correlation

  
• Negative Correlation

  
• No Correlation

  
• Degrees of Correlation: None

  
• Degrees of Correlation: Low

  
• Degrees of Correlation: High

  
• Degrees of Correlation: Perfect

  
• shows DIRECT relationship between X and Y variables

  Positive Linear Correlation
• Example:

  • Income and Expenses
  • Age and Weight

  Positive Linear Correlation
• shows INVERSE relationship between X and Y variables

  Negative Linear Correlation
• Example:

  • Academic Performance and Usage time of Cellphone
  • Quantity of Food Servings and the Prices of Ingredients

  Negative Linear Correlation
• • a statistic showing the degree of relation between two variables
  • denoted by "r"
  • its value denotes the strength of association
  • its value ranges from -1.00 to 1.00

  Coefficient of Correlation
• Value of r: 1.00

  Perfect Correlation
• Value of r: 0.81 to 0.99

  Very High Correlation
• Value of r: 0.71 to 0.80

  High Correlation
• Value of r: 0.41 to 0.70

  Moderate Correlation
• Value of r: 0.21 to 40

  Slight / Low Correlation
• Value of r: 0.01 to 0.20

  Negligible Correlation
• Value of r: 0

  No Correlation
• Use when:

  1. the relationship is linear
  2. both variables are quantitative
  3. normally distributed
  4. have no outliers

  Pearson R
• When the entries in as set of data are ranks

  Spearman Rank