The ratio attributable to reduced sample size is 

 shown by the continuous curve. The variances of /3's based 

 on samples from the same population are inversely pro- 

 portional to sample size. If ./If is the sample size for the 

 complete time series, N(\ - f) is the size of the sample 

 time series. For the jS's 



Q s h c = 1/(1 _/) 



where the subscripts s and c refer to sample and complete 

 time series, respectively. The increase in variance 

 attributable to reduced sample size is 



Q = 1/(1 -/) - 1 =//(l -/) 



The variances of the jS's for the complete time series 

 are computed as though the residuals are independent. The 

 variances for the sample time series reflect the influence 

 of the autocorrelated residuals. The empirical ratios of 

 figure 8 lie almost on the theoretical curve, which assumes 

 independent residuals. Thus, it is concluded that the com- 

 bination of autocorrelated residuals and random deletion of 

 data yields regression coefficients whose variances are as 

 expected simply on the basis of sample size. 



NONRANDOM MISSING DATA 



As indicated in figure 4, there is an excessive num- 

 ber of longer sequences of missing data days. These 

 sequences occur in the poor weather months October to 

 March, inclusive. In addition there are several sequences 

 of 5 to 10 days each, which are in excess of the number of 

 such sequences expected by chance. It has been demon- 

 strated above that randomly distributed missing data affect 

 the variance of the regression coefficients just as though the 

 sample size were smaller. It is necessary to determine if 

 the longer sequences lead to the same result. 



26 



