A student would like to know if the time spent on studying and number of lectures attended for an exam is related to the exam scores (marks). The student now collects data on the number of lectures attended in the same period. The information obtained is tabulated and the output from a multiple regression analysis is shown below: Which of the following is the correct interpretation of the coefficient for the variable Hours spent Studying?

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BlackTom AI · Accepted Answer

To begin, let’s identify what the question is asking: interpret the regression coefficient for Hours spent Studying in the multiple regression output, considering the role of other variables in the model.
Option 1 asserts that each additional hour increases the score by 58 marks. This is overly large and ignores the decimal 0.58; it misreads the coefficient magnitude and would imply an unrealistic jump in scores. In regression results, coefficients are not expressed as whole numbers like 58 unless the unit scale dictates so, which it does not here.
Option 2 states: 'Holding the hour spent studying constant, for every additional number of lectures attended, the exam score is expected to increase on average by 0.58 marks.' This reverses the meaning of the coefficient: it incorrectly ties the Hours spent Studying effect to the Number of lectures attended, and it also mentions a relationship to lectures that is not what the Hours coefficient represents.
Option 3 reads: 'Holding the Number of Lectures Attended constant, for every additional hour spent studying, the exam score is expected to increase on average by 0.58 marks.' This aligns with the standard interpretation of a regression coefficient: when other predictors (here, Number of lectures attended) are held fixed, each extra hour of studying is associated with a 0.58-point increase in the predicted score. The decimal 0.58 correctly matches the coefficient value shown in the output, and the conditioning on lectures is appropriate in a multiple regression context.
Option 4 claims: 'Holding the Number of Lectures Attended constant, for every additional hour spent studying, the exam score is expected to increase on average by 58 marks.' This again misuses the magnitude (58 instead of 0.58) and would be inconsistent with the reported coefficient scale; the unit is points, not tens of points at such a large multiplier.
Option 5 says: 'For every additional hour spent studying, the exam score is expected to increase on average by 0.58 marks.' While this captures the positive 0.58 coefficient, it fails to acknowledge the key multiple regression context — that this effect is conditional on holding other predictors (like lectures attended) constant. In regression interpretation, we specify what is held constant to avoid implying a marginal effect that ignores other variables.
In summary, the main distinctions are about magnitude accuracy, what is being held constant, and whether the wording correctly reflects a multiple regression coefficient. The only option that correctly combines the precise coefficient value with the proper holding-constant condition is Option 3.

ETX5900 - S2 2025 Take Home Quiz Week 10 (due on 17th of October)

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