Question at position 38 DAEBC

Question

BlackTom AI · Accepted Answer

The question presents a scatter plot of egg production vs. fish length with a regression output. We need to evaluate each statement against the computer output values provided.
Option A: '83.5% of the variation in egg production can be accounted for by the linear regression of egg production on fish length.' This is not consistent with the output. The R-squared value shown is 69.7%, not 83.5%, so A exaggerates the explained variation and is incorrect.
Option B: '69.7% of the variation in egg production can be accounted for by the linear regression of egg production on fish length.' This aligns with the R-Squared value printed in the table (R-Sq = 69.7%). It indicates that about two-thirds of the variability in egg production is explained by the linear relationship with fish length, which matches the output.
Option C: '83.5% of the variation in fish length can be accounted for by the linear regression on egg production.' This reverses the role of the variables: the model shown predicts egg production from fish length, not fish length from egg production, and the 83.5% figure does not appear anywhere in the output. Therefore, this is incorrect.
Option D: '69.7% of the variation in fish length can be accounted for by the linear regression of egg production on fish length.' This statement again incorrectly assigns the R-squared value to the variation in the dependent variable. The model is egg production as the response, so the explained variation pertains to egg production, not fish length. D is incorrect.
Option E: '68.4% of the variation in fish length can be accounted for by the linear regression of egg production on fish length.' Here 68.4% matches the R-Sq(adj) value (the adjusted R-squared) shown, but the description refers to variation in fish length, which is not what the model explains. The adjusted R-squared still relates to the same response variable (egg production), so E is mis-stated and thus incorrect.
Overall, only Option B correctly reflects the reported R-Squared value for the regression of egg production on fish length, while the other options either mismatch the numeric value or misinterpret which variable is being explained.

Question at position 38 DAEBC

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