Page 4 - QuantScan-User Guide

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Professional investors only
Statistics - Linear fit
"!is the expected mean return of the fund when the mean return of the benchmark is zero.
#!is the slope of the linear fit. The higher the #, the more the fund has benchmark risk.
Standard error of "!$#) is the standard deviation of the sampling distribution of "!$#). The higher the standard error, the more "!$#) is dispersed.
t-statistic is the ratio of "!$#) to its standard error. The higher the absolute value of the t-statistic, the less the probability that the true "$#) is zero.
P-value is the probability of getting a t-statistic as extreme as the one calculated, assuming that "!$#) equals zero.
Degrees of Freedom are the numbers of variables free to vary. If n = number of days and p = number of samples, we have DF between samples = p - 1, DF residuals = n - p and DF total = n - 1.
Sums of Squares are measures of deviations from the mean. Formally, SS total = SS between samples + SS residuals.
R squared is the ratio of SS between samples to SS total. Adjusted R squared = 1 - (1 - R squared) (n - 1) / (n - p); it adjusts R squared for the number of predictors.
Mean Squares are ratios of MS to DF. The lower MS residuals, the better the linear fit.
F-statistic is the ratio of MS between samples to MS residuals. The higher the F-statistic, the less the probability that the fund and the benchmark mean returns are equal.
P-value is the probability of getting a F-statistic as extreme as the one calculated, assuming that the fund and the benchmark mean returns are equal.
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