Free CFA Level I Quantitative Methods Practice Questions

A normal distribution has a kurtosis of 3. Excess kurtosis is defined as kurtosis minus 3, so for a normal distribution, excess kurtosis = 3 - 3 = 0. A distribution with excess kurtosis greater than 0 is leptokurtic (fatter tails), while one with excess kurtosis less than 0 is platykurtic (thinner tails). Choice B (3) is the raw kurtosis of a normal distribution, not the excess kurtosis. Choice A (1) has no standard interpretation in this context and represents neither the raw nor the excess kurtosis of a normal distribution.

As model complexity increases, the model fits training data more closely, reducing bias (the error from overly simplistic assumptions). However, the model becomes more sensitive to the specific training data used, increasing variance (the error from sensitivity to small fluctuations in the training set). This is the fundamental bias-variance tradeoff.
Choice B is incorrect because bias decreases, not increases, with greater complexity.
Choice C is incorrect because variance increases with complexity; only bias decreases. The goal is to find the complexity level that minimizes total error (bias² + variance).

For simple linear regression: SSE = SST - SSR = 450 - 360 = 90. df_regression = 1 (one independent variable); df_residual = n - 2 = 25 - 2 = 23. MSR = SSR / df_regression = 360 / 1 = 360. MSE = SSE / df_residual = 90 / 23 = 3.913. F = MSR / MSE = 360 / 3.913 = 92.0. Choice B (96.00) results from using df_residual = n - 1 = 24 instead of n - 2 = 23: MSE = 90/24 = 3.75, F = 360/3.75 = 96.0. This error occurs when the analyst forgets that one degree of freedom is lost for the intercept and one for the slope, using only n - 1. Choice C (80.00) results from using df_residual = 25 - 3 = 22 by mistake (perhaps thinking a two-variable regression): MSE = 90/22 = 4.09, F = 360/4.09 = 88; or from using MSE = 90/20 = 4.5 for F = 360/4.5 = 80.