Importance Of Path Coefficient Analysis

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Path coefficient analysis is essentially a device for analysis of decomposition of a correlation coefficient into direct effect and indirect effect under a structure of causal relationship among linearly related variables. In path coefficient analysis, the direct effect of the independent variable and its indirect effects through other independent variables with which former is related has been observed to assess the relative importance of causal factors and to determine correlation coefficient. In this paper relative importance of explanatory variable has been studied. Path coefficient analysis has been performed to trace out the relative important of explanatory variables. Key word(s): Path coefficient analysis, explanatory variable *Department …show more content…

The explained variable here is the density of finished product of the manufacturing process (Y) while the explanatory variables are – the amount of water in the product mix (X1), the amount of reworked material in the product mix ((X2), the temperature of the mix (X3), the air temperature in the drying chamber (X4) and the raw material receives from the supplier and a measure of its quality (X5). The path analysis can be demonstrated as follows: Let X1, X2, …., Xk be measurements of k (clinical) factors supposed to influence the effect measured by Y. Let the effect Y be sum total of these causal factors X1, X2, …., Xk and a residual U. That is Y = X1 + X2 + …. + Xk + U Then the correlation coefficient r1y between X1 and Y is defined (in the usual notations) as r1y = Cov(X_1,Y)/(σ_(X_1 ) σ_Y )=((X_1,X_1+X_2+⋯X_k+U))/(σ_(X_1 ) σ_Y ) = [Cov(X_1,X_1 )+Cov(X_1,X_2 )+⋯+Cov(X_1,X_k )]/(σ_(X_1 ) σ_Y ) Cor, (X1, U) = 0, since U is assumed to be independent of X1, X2,…, Xk. That is r1y = [σX_1+r_12 σX_1 σX_2+⋯+r_1k σX_1 σX_2 ]/(σ_(X_1 ) σ_Y ) = (σX_1)/σ_Y +r_12 (σX_2)/σ_Y +⋯+r_1k (σX_k)/σ_Y = P1 + r12P2+r13P3 + … +r1kPk Where, Pj = (σX_1)/σ_Y for j = 1, 2, …, k Here P1 = direct effect of X1 on Y r12P2 = indirect effect of X1 on Y via

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