bivariate statistical measures

bivariate statistical measures

1. correlation

   • The correlation between two variables seeks to determine the degree of relationship that exists between them
     • strong correlation
       • The correlation will be stronger the closer the points are to the line
     • weak correlation
       • The correlation will be weak the further apart the points are on the line.
     • null correlation
       • Null correlation occurs when there is no dependency of any kind between the variables.
   • correlation coefficient
     • The correlation coefficient is the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis.
       • For two variables, the formula compares the distance of each data point from the mean of the variable and uses this comparison to tell us how well the relationship between the variables fits an imaginary line drawn between the data.

2. regression

   • In statistics, regression analysis is a statistical process for estimating relationships between variables. It includes many techniques for the modeling and analysis of various variables, when the focus is on the relationship between a dependent variable and one or more independent variables.
     • Simple linear regression model
       • Simple linear regression analysis is the most widely used and the simplest of all. It is about studying the effect of an independent variable on a single dependent variable.
         • formula
           • y = B0 + B1 x + ε
     • Multiple linear regression model
       • In the case of multiple linear regression, we find ourselves with a model that simply has more than one independent variable.
         • formula
           • Y = 0 + B1*X1 + B2*X2 + … + Bn*Xn + ε
     • Nonlinear regression model
       • There are occasions in which the relationship that can occur between independent variables and the dependent variable does not have a linear development, but instead has, for example, an exponential growth.
         • exponential regression
           • y = a.bx
             • log y = log(a.bx) = log a + x log b
         • potential regression
           • y = a. xb
             • log y = log a + b log x
         • parabolic regression
           • y* = a0+a1x+a2 x2

3. coefficient of determination

   • The coefficient of determination is the proportion of the total variance of the variable explained by the regression

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