Tarefa nist_anova.smls04.agent

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NIST Statistical Reference Datasets, one-way analysis of variance, problem SmLs04: generated data with 7 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 SmLs04: generated data with 7 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 SmLs04: 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 7c8f87a60245f5c7467418a7725855cce71608273964966e5da954c22ad5fa57 · 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: 64a4fbf2d3f5 → 95fa0f327dad
3. 2Turno do modelo
   call_5bb7508ereferenceFim: 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_f1c8dad6decidido 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_f1c8dad6

   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	21.000000000776094	—	—
   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	0,000000000000000000000258326 probability	2.5832643332657163e-22	—	—

   Diagnósticos

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

   Tabelas (2)

   {
     "coefficients": [
       {
         "ci_high": 1000000.4430594267,
         "ci_low": 1000000.3569405733,
         "coef": 1000000.4,
         "p": 0,
         "se": 0.021821789024163773,
         "t": 45825775.27867566,
         "term": "Intercept"
       },
       {
         "ci_high": -0.03910477478089837,
         "ci_low": -0.16089522528340722,
         "coef": -0.1000000000321528,
         "p": 0.0014220432078437882,
         "se": 0.03086066999321675,
         "t": -3.2403703501619714,
         "term": "treatment_2"
       },
       {
         "ci_high": 0.16089522522797134,
         "ci_low": 0.03910477472546252,
         "coef": 0.09999999997671694,
         "p": 0.0014220432163041378,
         "se": 0.030860669993216742,
         "t": 3.2403703483656447,
         "term": "treatment_3"
       },
       {
         "ci_high": -0.039104774780898334,
         "ci_low": -0.16089522528340727,
         "coef": -0.1000000000321528,
         "p": 0.001422043207843797,
         "se": 0.030860669993216766,
         "t": -3.2403703501619696,
         "term": "treatment_4"
       },
       {
         "ci_high": 0.1608952252279714,
         "ci_low": 0.03910477472546249,
         "coef": 0.09999999997671694,
         "p": 0.0014220432163041439,
         "se": 0.030860669993216756,
         "t": 3.2403703483656434,
         "term": "treatment_5"
       },
       {
         "ci_high": -0.03910477478089833,
         "ci_low": -0.16089522528340727,
         "coef": -0.1000000000321528,
         "p": 0.0014220432078438003,
         "se": 0.03086066999321677,
         "t": -3.240370350161969,
         "term": "treatment_6"
       },
       {
         "ci_high": 0.1608952252279714,
         "ci_low": 0.03910477472546248,
         "coef": 0.09999999997671694,
         "p": 0.0014220432163041471,
         "se": 0.030860669993216763,
         "t": 3.2403703483656425,
         "term": "treatment_7"
       },
       {
         "ci_high": -0.039104774780898355,
         "ci_low": -0.16089522528340724,
         "coef": -0.1000000000321528,
         "p": 0.0014220432078437908,
         "se": 0.030860669993216756,
         "t": -3.2403703501619705,
         "term": "treatment_8"
       },
       {
         "ci_high": 0.1608952252279714,
         "ci_low": 0.03910477472546249,
         "coef": 0.09999999997671694,
         "p": 0.0014220432163041439,
         "se": 0.030860669993216756,
         "t": 3.2403703483656434,
         "term": "treatment_9"
       }
     ],
     "restrictions": [
       {
         "estimate": -0.1000000000321528,
         "hypothesized": 0,
         "restriction": "treatment_2 = 0"
       },
       {
         "estimate": 0.09999999997671694,
         "hypothesized": 0,
         "restriction": "treatment_3 = 0"
       },
       {
         "estimate": -0.1000000000321528,
         "hypothesized": 0,
         "restriction": "treatment_4 = 0"
       },
       {
         "estimate": 0.09999999997671694,
         "hypothesized": 0,
         "restriction": "treatment_5 = 0"
       },
       {
         "estimate": -0.1000000000321528,
         "hypothesized": 0,
         "restriction": "treatment_6 = 0"
       },
       {
         "estimate": 0.09999999997671694,
         "hypothesized": 0,
         "restriction": "treatment_7 = 0"
       },
       {
         "estimate": -0.1000000000321528,
         "hypothesized": 0,
         "restriction": "treatment_8 = 0"
       },
       {
         "estimate": 0.09999999997671694,
         "hypothesized": 0,
         "restriction": "treatment_9 = 0"
       }
     ]
   }

   Digests dos dados

   d 95fa0f327dadf4c978f33bae2da0ade10e9762647c2b1010d4d0f5d9b039f63c

   sha256 do resultado

   453dd067d32b498e6f1069d922181dd37d72b7bb0c6c06412cfc3c0aecf4d01d

   Resultado mostrado ao modelo
5. 4Turno do modelo
   call_250711e5referenceFim: 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_f1c8dad6: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_f1c8dad6:F · Parada: answered

   Figura da resposta: call_f1c8dad6:F = 2121.000000000776094
8. 7Pontuação
   #0resposta com lastropassouobrigatóriaevery number backed
9. 8Pontuação
   #1resposta citapassouobrigatóriacited ['call_f1c8dad6: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)passouobrigatóriaLRE 10.43 (min 9.0)

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• época 1, tentativa 1passoupontuada(exibindo)

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