Problem

Table E has outputs \(2,~6,~\text{and}~18\) at \(x~=~0,~1,~\text{and}~2\); table P has outputs \(1,~4,~9,~\text{and}~16\) at \(x~=~0,~1,~2,~\text{and}~3\). Compare the observed ratios and first differences, then state the limit of the evidence for global family claims.

Table E contains (0, 2), (1, 6), and (2, 18); table P contains (0, 1), (1, 4), (2, 9), and (3, 16). The comparison conclusion is withheld.

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Analysis: E has constant successive ratio 3 on the supplied data, while P has first differences 3, 5, and 7. Their observed change patterns differ; E is globally exponential and P is globally quadratic without an added model assumption.

Analysis: E has constant successive ratio 3 on the supplied data, while P has constant first difference 3. Their observed change patterns differ; no global family claim is established without an added model assumption.

Analysis: E has constant first difference 3 on the supplied data, while P has first differences 3, 5, and 7. Their observed change patterns differ; no global family claim is established without an added model assumption.

Analysis: E has constant successive ratio 3 on the supplied data, while P has first differences 3, 5, and 7. Their observed change patterns differ; no global family claim is established without an added model assumption.

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Table E has outputs \(2,~6,~\text{and}~18\) at \(x~=~0,~1,~\text{and}~2\); table P has outputs \(1,~4,~9,~\text{and}~16\) at \(x~=~0,~1,~2,~\text{and}~3\). Compare the observed ratios and first differences, then state the limit of the evidence for global family claims.

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