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Summary Least squares regression analysis makes the assumption that the independent variables can be measured without error. This paper examines the effect of errors in these variables and suggests some practical guidelines for the user of least squares. Related empirical and theoretical work is reviewed and simple methods are derived for assessing the sensitivity of the regression coefficients to each observation, and for calculating the approximate amount of bias in the estimated coefficients. The implications for forecasting are also examined.

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One popular method for testing the validity of a model's forecasts is to use the probability integral transforms (pits) of the forecasts and to test for departures from the dual hypotheses of independence and uniformity, with departures from uniformity tested using the Kolmogorov-Smirnov (KS) statistic. This paper investigates the power of five statistics (including the KS statistic) to reject uniformity of the pits in the presence of misspecification in the mean, variance, skewness or kurtosis of the forecast errors. The KS statistic has the lowest power of the five statistics considered and is always dominated by the Anderson and Darling statistic.

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