Summary Estimation of statistical parameters from multivariate data results in wasted information, if units with incomplete data are rejected entirely, and perhaps in inconsistencies in the variance–covariance matrix if the variances and correlation coefficients are estimated from all available data on individual variates and pairs of variates respectively. An alternative is to estimate the missing values by regression techniques and to calculate a revised variance–covariance matrix. This method is suitable for use with an electronic computer. It is shown that with this method the resultant covariances are unbiased, but that the variances require correction for bias. A numerical example is given.

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This paper reports various investigations of the effects of meteorological factors on the yields of crops in England and Wales. The investigations were undertaken primarily with the objects of seeing (a) whether variations in temperature had any direct effect on yields, and (b) whether Penman's concept of actual transpiration gave a better measure of the overall effect of rainfall than the use of a multiple regression on variates representing total rainfall and its distribution.The effect of temperature and its seasonal distribution on the yields of wheat on various plots of the classical wheat experiment on Broadbalk field at Rothamsted was studied in conjunction with rainfall and its seasonal distribution, using the regression method devised by Fisher. Variations in temperature were found to show no effects on the final yields.The relationship between actual transpiration and yield was investigated for the Broadbalk field and for sugar beet and potatoes, using average yields determined by sampling methods, for various districts in England and Wales. For sugar-beet virus yellows infection, and for potatoes blight attack, were also taken into account.No relationship between actual transpiration and wheat yields on Broadbalk field was found, but sugar beet and potatoes both showed a positive association between actual transpiration and yield except for sugar beet in the Spalding area, where there is a high-water table. Actual transpiration was in general more effective than a regression on total rainfall and its distribution accounting for variations in yield. As might be expected virus yellows and blight also account for a good deal of the variation in yield.

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