Correlation and linear regression
Correlation and linear regression
The terms correlation and regression are related but are not synonymous. Correlation is used to test for association between variables (e.g. whether salary and IQ are related). Once correlation between two variables has been shown regression can be used to predict values of other dependent variables from independent variables. Regression is not used unless two variables have firstly been shown to correlate.Correlation
The degree of correlation is summarised by the correlation coefficient (r). This indicates how closely the points lie to a line drawn through the plotted data. In parametric data this is called Pearson's correlation coefficient and can take any value between -1 to +1.
For example
- r = 1 - strong positive correlation (e.g. systolic blood pressure always increases with age)
- r = 0 - no correlation (e.g. there is no correlation between systolic blood pressure and age)
- r = - 1 - strong negative correlation (e.g. systolic blood pressure always decreases with age)
Whilst correlation coefficients give information about how one variable may increase or decrease as another variable increases they do not give information about how much the variable will change. They also do not provide information on cause and effect.
Correlation is summarised when using parametric variables by Pearson's correlation coefficient (represented by a small r). In the situation of non parametric variables, Spearman's correlation coefficient is used. Spearman's correlation coefficient is usually represented by the Greek letter p (rho), or by rs.
In the case of dichotomous variables logistic regression is used. Linear (or simple linear) regression is used when looking for association between two continuous variables, and multiple regression is used when looking for association between more than two continuous variables.
Linear regression
In contrast to the correlation coefficient, linear regression may be used to predict how much one variable changes when a second variable is changed. A regression equation may be formed, y = a + bx, where
- y = the variable being calculated
- a = the intercept value, when x = 0
- b = the slope of the line or regression coefficient. Simply put, how much y changes for a given change in x
- x = the second variable
+PassMedicine Notes
The terms correlation and regression are related but are not synonymous. Correlation is used to test for association between variables (e.g. whether salary and IQ are related). Once correlation between two variables has been shown regression can be used to predict values of other dependent variables from independent variables. Regression is not used unless two variables have firstly been shown to correlate.
Correlation
The degree of correlation is summarised by the correlation coefficient (r). This indicates how closely the points lie to a line drawn through the plotted data. In parametric data this is called Pearson's correlation coefficient and can take any value between -1 to +1.
For example- r = 1 - strong positive correlation (e.g. systolic blood pressure always increases with age)
- r = 0 - no correlation (e.g. there is no correlation between systolic blood pressure and age)
- r = - 1 - strong negative correlation (e.g. systolic blood pressure always decreases with age)
Whilst correlation coefficients give information about how one variable may increase or decrease as another variable increases they do not give information about how much the variable will change. They also do not provide information on cause and effect.
Correlation is summarised when using parametric variables by Pearson's correlation coefficient (represented by a small r). In the situation of non parametric variables, Spearman's correlation coefficient is used. Spearman's correlation coefficient is usually represented by the Greek letter p (rho), or by rs.
In the case of dichotomous variables logistic regression is used. Linear (or simple linear) regression is used when looking for association between two continuous variables, and multiple regression is used when looking for association between more than two continuous variables.
Linear regression
In contrast to the correlation coefficient, linear regression may be used to predict how much one variable changes when a second variable is changed. A regression equation may be formed, y = a + bx, where- y = the variable being calculated
- a = the intercept value, when x = 0
- b = the slope of the line or regression coefficient. Simply put, how much y changes for a given change in x
- x = the second variable