DSRT 734: Using a Regression Line to Estimate Manufacturing Time

DSRT 734 Question

The length of time in hours a product takes to manufacture is estimated
by the regression line Y=4.8X+4, where X is the number of components
used in the manufactoring process. Estimate the length of time for a
product with 5 components.

Option A

5 hours


Option B

28 hours


Option C

32 hours


Option D

24 hours

What this question assesses

This item assesses how a fitted regression equation turns a predictor value into a model-based estimate and whether slope, intercept, variables, and units are interpreted consistently.

How to approach this type of question

Map the symbols before calculating. X represents the component count and Y represents estimated manufacturing time in hours. Substitute the stated component count for X while leaving the slope and intercept in their original roles. Follow the equation’s order of operations: evaluate the slope contribution first, then incorporate the intercept. Keep units visible so a component count is not mistaken for a time value. Once an estimate is obtained on scratch paper, compare it with the choices and check that no coefficient was dropped or added in the wrong order. Also remember that a regression estimate is a fitted prediction, not a guaranteed manufacturing time, and its credibility depends on whether five components lies within the data range used to fit the model. This page does not perform the arithmetic or identify the matching option.

Use a second calculation line to check the substitution and arithmetic, then plug the estimated value back into the context: the result must be time in hours, not components. Confirm that the intercept contributes even when X is nonzero and that multiplication is completed before addition. If the requested X were outside the model’s observed range, extrapolation would deserve caution; the prompt does not supply that range, so no claim about prediction accuracy should be added.

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