Tarefa nist_anova.smls07.agent

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NIST Statistical Reference Datasets, one-way analysis of variance, problem SmLs07: generated data with 13 constant leading digits; one factor (treatment) with 9 levels and 189 observations in a balanced design, model y_ij = mu + tau_i + e_ij. Dataset d holds the factor treatment (levels 1 to 9), the response response, and indicator columns treatment_2 to treatment_9 (1 when the row is at that level; level 1 is the reference). Compute the ANOVA F statistic for the hypothesis that all 9 treatment effects are equal: the between-treatment mean square divided by the within-treatment mean square.

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1. 0Início

   NIST Statistical Reference Datasets, one-way analysis of variance, problem SmLs07: generated data with 13 constant leading digits; one factor (treatment) with 9 levels and 189 observations in a balanced design, model y_ij = mu + tau_i + e_ij. Dataset d holds the factor treatment (levels 1 to 9), the response response, and indicator columns treatment_2 to treatment_9 (1 when the row is at that level; level 1 is the reference). Compute the ANOVA F statistic for the hypothesis that all 9 treatment effects are equal: the between-treatment mean square divided by the within-treatment mean square.

   d (agent)

   NIST StRD SmLs07: 189 observations; treatment = the treatment level (1 to 9), response = the response, treatment_2 … treatment_9 = 1 when the row is at that treatment level (level 1 is the reference)

   file 42d492d7577ebe456fa9a204789ea8370c844f508aa3242a8e57c1976b133890 · frame —

   1. dummies {"column":"treatment","drop_first":true,"prefix":"treatment"}
2. 1Transformação
   d · dummies {"column":"treatment","drop_first":true,"prefix":"treatment"}

   189 → 189 linhas

   Frame antes → depois: bed24635a6f1 → 7f3bd46de9b1
3. 2Turno do modelo
   call_38d72244referenceFim: tool_use0 ms0 de entrada · 0 de saída · 0 de raciocínio · 0 em cache

   Texto visível

   With classical errors, the joint test that every indicator's coefficient is zero is the one-way ANOVA F.

   Chamadas pedidas

   • infer.linear_hypothesis

     {
       "dataset": "d",
       "hypothesis": "treatment_2 = 0, treatment_3 = 0, treatment_4 = 0, treatment_5 = 0, treatment_6 = 0, treatment_7 = 0, treatment_8 = 0, treatment_9 = 0",
       "se": "classical",
       "x": [
         "treatment_2",
         "treatment_3",
         "treatment_4",
         "treatment_5",
         "treatment_6",
         "treatment_7",
         "treatment_8",
         "treatment_9"
       ],
       "y": "response"
     }

   Mensagens (formato neutro)Instruções do sistemaFerramentas oferecidas
4. 3Ferramenta
   infer.linear_hypothesisv0.1.0call_5bd45fd6decidido pelo modeloreexecutável

   Motivo: With classical errors, the joint test that every indicator's coefficient is zero is the one-way ANOVA F.

   Argumentos

   {
     "cluster": null,
     "dataset": "d",
     "hypothesis": "treatment_2 = 0, treatment_3 = 0, treatment_4 = 0, treatment_5 = 0, treatment_6 = 0, treatment_7 = 0, treatment_8 = 0, treatment_9 = 0",
     "se": "classical",
     "subset": null,
     "x": [
       "treatment_2",
       "treatment_3",
       "treatment_4",
       "treatment_5",
       "treatment_6",
       "treatment_7",
       "treatment_8",
       "treatment_9"
     ],
     "y": "response"
   }

   Figuras call_5bd45fd6

   Chave	Valor	Valor bruto	Erro-padrão	IC
   F F statistic of treatment_2 = 0; treatment_3 = 0; treatment_4 = 0; treatment_5 = 0; treatment_6 = 0; treatment_7 = 0; treatment_8 = 0; treatment_9 = 0	21,0008	21.000811887800836	—	—
   p_value p-value of treatment_2 = 0; treatment_3 = 0; treatment_4 = 0; treatment_5 = 0; treatment_6 = 0; treatment_7 = 0; treatment_8 = 0; treatment_9 = 0	0,000000000000000000000257908 probability	2.5790798902688036e-22	—	—

   Diagnósticos

   • statistic = "F"
   • df_numerator = 88
   • df_denominator = 180180
   • se_type = "classical"
   • n_obs = 189189
   • n_clusters = —

   Tabelas (2)

   {
     "coefficients": [
       {
         "ci_high": 1000000000000.4431,
         "ci_low": 1000000000000.3569,
         "coef": 1000000000000.4,
         "p": 0,
         "se": 0.021822382067116876,
         "t": 45824511592034.36,
         "term": "Intercept"
       },
       {
         "ci_high": -0.039136834478292734,
         "ci_low": -0.1609305948363018,
         "coef": -0.10003371465729725,
         "p": 0.0014173200388017876,
         "se": 0.030861508682604094,
         "t": -3.2413747391968526,
         "term": "treatment_2"
       },
       {
         "ci_high": 0.16087246611627865,
         "ci_low": 0.03907870575826962,
         "coef": 0.09997558593727413,
         "p": 0.0014261894201179305,
         "se": 0.030861508682604087,
         "t": 3.2394912045770474,
         "term": "treatment_3"
       },
       {
         "ci_high": -0.03913683447884252,
         "ci_low": -0.16093059483685163,
         "coef": -0.10003371465784708,
         "p": 0.0014173200387181495,
         "se": 0.030861508682604115,
         "t": -3.2413747392146663,
         "term": "treatment_4"
       },
       {
         "ci_high": 0.16087246611673184,
         "ci_low": 0.03907870575872275,
         "coef": 0.09997558593772729,
         "p": 0.0014261894200485947,
         "se": 0.030861508682604104,
         "t": 3.2394912045917295,
         "term": "treatment_5"
       },
       {
         "ci_high": -0.039136834478743505,
         "ci_low": -0.16093059483675265,
         "coef": -0.10003371465774807,
         "p": 0.0014173200387332132,
         "se": 0.03086150868260412,
         "t": -3.2413747392114582,
         "term": "treatment_6"
       },
       {
         "ci_high": 0.16087246611688538,
         "ci_low": 0.03907870575887628,
         "coef": 0.09997558593788083,
         "p": 0.0014261894200250991,
         "se": 0.03086150868260411,
         "t": 3.239491204596704,
         "term": "treatment_7"
       },
       {
         "ci_high": -0.039136834478419306,
         "ci_low": -0.16093059483642838,
         "coef": -0.10003371465742385,
         "p": 0.0014173200387825344,
         "se": 0.030861508682604104,
         "t": -3.2413747392009538,
         "term": "treatment_8"
       },
       {
         "ci_high": 0.16087246611641692,
         "ci_low": 0.039078705758407856,
         "coef": 0.09997558593741239,
         "p": 0.0014261894200967814,
         "se": 0.0308615086826041,
         "t": 3.239491204581526,
         "term": "treatment_9"
       }
     ],
     "restrictions": [
       {
         "estimate": -0.10003371465729725,
         "hypothesized": 0,
         "restriction": "treatment_2 = 0"
       },
       {
         "estimate": 0.09997558593727413,
         "hypothesized": 0,
         "restriction": "treatment_3 = 0"
       },
       {
         "estimate": -0.10003371465784708,
         "hypothesized": 0,
         "restriction": "treatment_4 = 0"
       },
       {
         "estimate": 0.09997558593772729,
         "hypothesized": 0,
         "restriction": "treatment_5 = 0"
       },
       {
         "estimate": -0.10003371465774807,
         "hypothesized": 0,
         "restriction": "treatment_6 = 0"
       },
       {
         "estimate": 0.09997558593788083,
         "hypothesized": 0,
         "restriction": "treatment_7 = 0"
       },
       {
         "estimate": -0.10003371465742385,
         "hypothesized": 0,
         "restriction": "treatment_8 = 0"
       },
       {
         "estimate": 0.09997558593741239,
         "hypothesized": 0,
         "restriction": "treatment_9 = 0"
       }
     ]
   }

   Digests dos dados

   d 7f3bd46de9b1313bab65a180b11de344017798c07841a51d5b8b27dac073ba26

   sha256 do resultado

   d0ae8e5d6de64fac3b36239032f2e89cd8fad1a1e61b81f0c6b89dac8bf4d05b

   Resultado mostrado ao modelo
5. 4Turno do modelo
   call_50fe8757referenceFim: tool_use0 ms0 de entrada · 0 de saída · 0 de raciocínio · 0 em cache

   Chamadas pedidas

   • submit_answer (meta-ferramenta)

     {
       "answer": "Estimativa (infer.linear_hypothesis): F = 21,00.",
       "caveats": [],
       "figure_refs": [
         "call_5bd45fd6:F"
       ]
     }

   Mensagens (formato neutro)Instruções do sistemaFerramentas oferecidas
6. 5Guarda
   resposta aceita

   Números encontrados

   21,00

   Sem lastro

   —

   Não citados

   —

   1 nova(s) tentativa(s) restante(s)
7. 6Resposta

   Estimativa (infer.linear_hypothesis): F = 21,00.

   Figuras citadas: call_5bd45fd6:F · Parada: answered

   Figura da resposta: call_5bd45fd6:F = 21,000821.000811887800836
8. 7Pontuação
   #0resposta com lastropassouobrigatóriaevery number backed
9. 8Pontuação
   #1resposta citapassouobrigatóriacited ['call_5bd45fd6:F']
10. 9Pontuação
    #2ferramenta chamadapassouobrigatóriaanswer call is infer.linear_hypothesis
11. 10Pontuação
    #3argumento igualpassouobrigatóriainfer.linear_hypothesis.se = 'classical'
12. 11Pontuação
    #4diagnósticopassouobrigatória8 vs 8
13. 12Pontuação
    #5diagnósticopassouobrigatória180 vs 180
14. 13Pontuação
    #6dígitos corretos (LRE)falhouobrigatóriaLRE 4.41 (min 6.0)

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• época 1, tentativa 1falhoupontuada(exibindo)

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