01.2) The correlation between the dependent and independent variables with the effects of one or more additional variables removed from both sides of the equation.
The degree of association between two variables with one or more additional variables “held constant†statistically. {r AB|C = (r AB – r AC * r BC) / [SQRT (1 – r 2 AC) * SQRT (1 – r 2 BC)]} EX: SES (socioeconomic status), insurance coverage, and oral health are all related in America. It is possible to calculate the effect of insurance on oral health partial ling out or “holding constant†the effects of SES if the correlations among all three variables is known. [See correlation coefficient, spurious correlation
a correlation between two variables when the effects of one or more related variables are removed
A measure of the strength of the relationship between two or more numeric variables having accounted for their joint relationship with one or more additional variables. On a scale of -1 to +1, it measures the extent of the unique correlation between the two variables which is not shared with the other variables.
The correlation between two numerical variables having accounted for the effects of other variables. This could be used to assess the independent contribution to overall satisfaction of 'staff friendliness' having removed a similar variable such as 'staff helpfulness'.
The correlation between the residuals of two random variables (variates) with respect to common regressors. Denoting the regression function of two variates and with respect to a common set of regressors by and , the coefficient of partial correlation between and is defined as the coefficient of simple linear correlation between ( − ) and ( − ). To estimate the partial correlation, it is usually necessary to resort to sample approximations ′ and ′ of and . In that case, the estimate of the partial correlation is the sample value of the coefficient of simple, linear correlation between ( − ′) and ( − ′). In the simplest case in which ′ and ′ are taken as linear functions of a single variable , the sample estimate yz.x of the partial correlation coefficient is given by the formula where the symbol uv denotes the sample coefficient of linear correlation between any pair of variates , . See regression.
In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random variables removed.
