364 



REFRACTION AND REFRACTIVE INDEX MODELS 



To obtain a direct estimate of the height error, (8.46) through (8.48) 

 were combined with (8.42) and the functions /ij {i > j = 1, 2, 3) were 

 determined as least squares polynomials. 



8.4.8. Regression Analysis 



The volume of data processed is of sufficient magnitude that it is im- 

 practical to include it all in this report. Therefore, certain information 

 obtained from the regression analysis was selected as being the most 

 significant. 



The mean height error provides the best general estimate obtainable 

 if meteorological data are not available. The standard deviation (about 

 the mean) of the height errors determines the reliability of this estimate, 

 since 68 percent of the observed height errors are within ±1 standard 

 deviation of the mean height error if the observations are normally dis- 

 tributed. In figure 8.29, the mean height error was plotted for each 

 target position, then contour lines were drawn to display the mean height 

 error as a function of true height and distance. By similar construction 

 the standard deviation of the height error as a function of target position 

 is displayed in figure 8.30. 



The standard error of estimate establishes the same confidence limits 

 for prediction with a regression equation as the standard deviation does 

 for the mean. Thus, comparison of the standard error to the standard 

 deviation indicates the improvement in accuracy of prediction with 



500 1750 2000 



40 150 IGO 



DISTANCE (MILES! 



Figure 8.29. Mean height errors in feet. 



