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GATE 2020 ST – Question 24

Regression Analysis · Regression Inference and Quadratic Forms · 1 mark · Multiple choice

A two-way fixed-effects ANOVA has no interaction and one observation per cell, with5 row levels and4 columns. Find residual degrees of freedom.

  1. 20
  2. 19
  3. 12
  4. 11

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Correct answer: (C) 12

Explanation

Total observations=5×4=20. Fitted parameters are1 intercept plus4 row and3 column contrasts, totalling8. Residual degrees of freedom=20−8=12=(5−1)(4−1), C. Without replication the interaction is pooled into this residual term under the additive model.

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