LSS Black Belt · PeopleCert · Improve · Bank updated 2026-07-03
LSS Black Belt practice questions: Improve
5 free questions from 31 on this area · answer and explanation for each · no sign-up
These 5 questions come from the Improve section of our LSS Black Belt bank (31 questions on this area, which carries 20% of the real exam). Every question is original, with the correct answer explained and linked to the source it is drawn from.
1/5 · Improve · easy
A Black Belt fits a simple linear regression of cycle time (Y) on batch size (X) and obtains R² = 0.81. Which interpretation of this result is correct?
A81% of the variation in cycle time is explained by its linear relationship with batch size.
BThe correlation coefficient r between batch size and cycle time is 0.81.
C81% of the observed data points fall exactly on the regression line.
DThe regression equation will predict any new cycle time observation with 81% accuracy.
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2/5 · Improve
In a 2^2 factorial design, a Black Belt adds several runs at the center point (factor levels set midway between low and high). The average response at the center points turns out to be significantly different from the average of the four factorial corner points. What does this most likely indicate?
AOne of the two factors has no effect on the response and should be dropped from the model.
BThe experiment suffers from a lack of randomization in run order.
CThere is a significant two-factor interaction between the two factors.
DThere is curvature in the response surface, suggesting the true relationship between the factors and the response is not purely linear across the tested range.
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3/5 · Improve · hard
A scatterplot of Y versus X shows a strong curved relationship. A Box-Cox transformation on Y fails to produce residuals that are linear and homoscedastic, even though the underlying relationship appears to follow a known mechanistic form (e.g., exponential decay). What is the most appropriate next analytical step?
ASwitch to multiple linear regression by adding unrelated predictors until R² improves.
BFit a non-linear regression model that directly represents the mechanistic functional form relating X and Y, rather than continuing to force a transformed-linear model.
CIncrease the sample size and re-run the same simple linear regression, since a larger n will linearize the relationship.
DDiscard the data, since no valid model can be fit when a Box-Cox transformation fails.
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4/5 · Improve
A Black Belt needs to screen five candidate factors and chooses a 2^(5-2) fractional factorial design (8 runs, Resolution III) to identify the vital few before committing resources to a larger study. What key limitation of this design must the Black Belt keep in mind when interpreting the results?
AThe design cannot estimate main effects at all, so it is only useful for estimating interactions and is unsuitable for screening purposes.
BBecause it is a fractional design, center points can never be added to check for curvature.
CA Resolution III design on five factors requires at least 32 runs, making it impractical for screening more than four factors.
DMain effects are confounded (aliased) with two-factor interactions, so a main effect that appears significant may actually be caused, in whole or in part, by an aliased interaction.
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5/5 · Improve · hard
A team ran a Resolution III screening design and found that Factor B has a large, statistically significant estimated effect. Before recommending a permanent process change based on this result, what should the Black Belt do first?
ADiscard the result as invalid, because Resolution III designs cannot detect any real effects and are only useful for calculating degrees of freedom.
BCheck the alias structure for the design; because Factor B's main effect may be aliased with a two-way interaction, run a confirmation experiment (e.g., a foldover) before attributing the effect solely to B.
CImplement the change immediately, since a statistically significant effect in any properly randomized DOE is by definition attributable to the named factor alone.
DConclude that Factor B has no true effect, since all Resolution III results are inherently unreliable and must be replaced with full factorial designs.
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B is correct. Because Resolution III designs alias main effects with two-way interactions, an apparently strong 'Factor B effect' might actually be, or include, an interaction involving other factors. Best practice before acting on such a result is to examine the alias structure and run a confirmation experiment, such as a foldover, to separate the true source of the effect.
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