Regression analysis

The equations used to estimate sound ratings in this program were developed using multi-variate regression analysis. Factors such as weights and dimensions of materials, spacings and other factors were entered into a statistical package which produced equations relating the appropriate sound rating to signficant physical factors. This is not the same as physical modeling but is much simpler to do. The accuracy of the predictions is discussed below.

Standard error of the estimate

The object in using regression analysis is to find algorithms that predict sound ratings from a set of physical parameters. The algorithms predict results that have a certain error associated with them. This is inevitable and the analysis provides estimates of the uncertainty of the predictions. The standard error of the estimate that follows each regression equation gives a measure of how well the predicted values agree with measured values. Approximately two-thirds of the measured values lie within plus or minus one standard error from the regression line. A smaller value of standard error means the predictions are more precise. The adjusted square of the correlation coefficient, R2, tells what fraction of the variations in the measured data is explained by the regression fit: the larger the value of R2, the better the fit.

Certain factors, such as the density of sound-absorbing material or cavity spacing sometimes are significant in determining the sound rating. In other cases, they are not. This seemingly inconsistent result is often due to the lack of data used to do the regression analysis.

Regression equations should not be used too far outside the range of the data from which they were derived. These web pages limit user input so this does not happen and so good design principles are followed as much as possible.

The distribution of variables and the equations derived for each class of wall or floor treated separately are linked from each calculation page.