A Correlation Analysis tells us if there is a relationship between two variables. It does not necessarily mean there is a cause and effect relationship, it can sometimes be a coincidence or due to a third “lurking” variable which has not been include in the analysis.

Types of Correlation

  • Positive correlation means that higher values of one measurement are associated with higher values of the other one
  • Negative correlation means that higher values of one measurement are associated with lower values of the other one

Correlation Coefficients

  • The Pearson correlation coefficient “r”, tell the strength and direction of the relationship.
  • The Coefficient of determination “R2”, is the square of the Pearson coefficient. It tells how much variation in the response variable “Y”, can be explained by the independent variable “X”.
  • The coefficient “r” can be negative or positive from -1 to +1, but “R2” is always positive.
  • r >0.65 or <-0.65 is considered strong relationship

Correlation Analysis Interpretation

It is important always to make a scatterplot of your data, since there could be a strong nonlinear relationship between variables. For example below graph have r = 0.

Correlation Analysis Diagram

Simple Linear Regression

  • Regression measures the strength of relationship between independent variable(s), (also called predictors, or regressors) and a dependent variable (also called a response variable)
  • For simple and multiple linear regression, the dependent variable must be continuous
  • Regression analysis allows to develop a mathematical model to predict the value of an output variable as a function of an input variable, i.e., Y = f (X)

How Regression Analysis Works

  • Regression works by fitting a line which minimises the sum of the squares of the errors between the data points and the line. This line is called the line of least squares or line of best fit.
  • The residual errors, or “residuals” are an indication of how good the model is for prediction

Correlation Study Diagram 02

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Correlation Analysis