Bivariate measures of regression and correlation

Bivariate measures of regression and correlation

1. regression problems

   • -Inhomogeneous variance -Relation not linear -Correlation errors

2. regression analysis

   • Study the relationship between two quantitative variants
     • Statistical technique used to derive an equation that relates a criterion variable to one or more predictor variables.
     • It studies the strength of the association through a measure of association called the consequence coefficient.

3. bivariate statistical measures

   • R2 determination coefficient
     • -Simple linear correlation -Positive correlation and negative connections -Description Diagram -Regression -Simple regression

4. Some formulas: Linear regression y=a+bx Logarithmic y=a+bl n(x) Exponential y=ac(bx) Quadratic y=a+bx+Cx 2

5. Simple regression method

   • If Y˄ since it is rarely the same, no matter how good the regression model is, the quantity “-e Y-y˄” is called residual error.
   • We find a very simple linear function of X, which allows approximation by - y˄=b0+ b1X.

6. linear regression

   • Person Linear Correlation Coefficient
     • If the points have a tendency to line up
     • R is useful to determine if there is a linear relationship between two variables, but it will not work for (quadratic, logarithmic)
     • It has the same sign as S(X,Y)

7. correlation

   • analysis of two quantitative variables.
     • They can be represented by a scatterplot
       • The coordinates on the Cartesian axes are the values ​​that the two values ​​take for the observation.
         • Taking into account the dependent and independent variables
   • Mutual relationship, measures and indicates the degree and values ​​of a variable when related to another variable.
     • Correlation: measures closeness
       • r =0: no connections, r= 1: perfect positive connections, 0<r1, perfect negative connections, 1<r<0: negative connections.
         • The simple linear determination coefficient is named like this, because it is a particularization of the ratio of connections, exactly of the determination coefficient.
           • The correlation does not distinguish between the response variables.
   • positive linear correlation
     • It has a median value, because not all the points are included in the line, null: not all are associated, positive linear, strong: all the values ​​are on the line, strong negative linear: the graph does not show the vertex, non-linear strong parabolic: meets the sense of the parabola line.