efficients. Specifically, if variances of regression co- 

 efficients are estimated in the usual manner, on the average 

 these estimates must be adjusted upwards. Roughly, the 

 increase in variance due to missing data must be doubled. 

 Alternatively, for fractions of missing data greater than 

 0. 2, time series with nonrandom missing data will have 

 regression coefficient variances equal to those the same 

 series with 0. 15 more missing data would have, if all the 

 missing data were random. 



The effect of nonrandom missing data on autocorrelation 

 coefficients is less pronounced. The increase in their es- 

 timated variance need be only 20 percent. Alternatively, 

 for fractions of missing data greater than 0. 2, time series 

 with nonrandom missing data will have autocorrelation co- 

 efficient variances equal to those the same series with only 

 0. 05 more missing data would have, if all the missing data 

 were random. 



RECOMMENDATIONS 



Almost all time series of sea-surface temperatures 

 contain missing data. The nature of this missing data as to 

 randomness of occurrence in time should be examined before 

 regression and autocorrelation analyses are performed. 

 The appropriate results of this report should be applied in 

 estimating the variances of regression and autocorrelation 

 coefficients. 



A similar investigation of the effect of missing data 

 should be performed for the regression problem with 

 several independent variables, namely time, depth and 

 geographical location. The dependent variable will be water 

 temperature. 



The results of this report apply to the long range 

 estimation of sea-surface temperatures. An examination 

 should be made of the effect of missing data on the short 

 range (a few weeks or months) prediction of sea-surface 

 temperatures . 



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