Derivation of Linear Regression Model and Log Linear Transformation to Obtain SVEC Modified

Appendix A

Derivation of Linear Regression Model and Log Linear Transformation to obtain SVEC_Modified

We were trying to predict or estimate SVTTE using EC and other data (such as LVOT diameter, SVEC, Weight, Height, Age, Estimated Gestational Age, Etc.). SVTTE was our dependent or “target” variable. The possible predictors of SVTTE were our independent variables.

The first step in multiple regression analysis was to make a correlation matrix of Pearson correlation coefficients of the dependent variable with possible independent variables that might explain or predict the dependent variable (SVTTE).

The explanatory factors that correlated with our dependent, target variable in a highly significant manner (p < 0.01) were: SVEC, LVOT area, Height and Weight

These factors were entered in linear regression and the following output was obtained:

Height was not significant to the p < 0.05 level and was therefore discarded as a candidate independent variable.

The next regression after eliminating Height was as follows:

All of the independent variables were significant at p <0.05 and so the creation of the model was complete. The resulting regression equation was:

SVEC_Modified = -29.6 + 18.66*LVOT_Area + 0.323*SVEC + 0.148*Weight.

Log Linear Transformation of the Data

In order to obtain an equation that was the multiplicative product of the independent variables (rather than the sum of various terms), we used a log linear transformation as follows:

1. Convert dependent and independent variables to their logarithms and do linear regression, with the following output:

The log linear version of the equation was:

LG10 SVTTE = 0.343 + 0.705*LG10_LVOT_Area + 0.388*LG_10_SVEC + 0.21*LG10_Weight.

Taking antilogarithms of both sides we obtained the multiplicative version of the equation:

SVEC_Modified = 2.2 * LVOT_Area(0.705) * SVEC(0.388) * Weight(0.21)

(Note to reader: When we take antilogarithms of both sides the antilogarithm (2.2) of the constant (0.343) becomes a factor and the coefficients of the independent variables becomes exponents.)