Pertanyaan
The outputs from minitab are from an analysis to determine the factors that influence adoption of clean energy a. What statistical method was used a. What are the assumptions that need to be met for this type of analysis Write the hypotheses Reconstruct the objective Explain the nature of the response variable Identify the factors that are significant and explain the natur of the effect a. Interpret the odds results for categorical variables a. a. Comment on the explanation power of the model Comment on the adequacy of th model
Jawaban
1. Logistic Regression
2. Linearity of the logit for continuous variables, Independence of errors, No multicollinearity among independent variables, Large sample size
3. Null Hypothesis (H0): There is no relationship between the predictors and the response variable. Alternative Hypothesis (H1): There is a significant relationship between at least one predictor and the response variable.
4. To determine the factors that influence the adoption of clean energy.
5. Binary (0 or 1, representing non-adoption or adoption of clean energy, respectively).
6. Age, Income, and Number of rooms are significant. Age and Household size have odds ratios less than 1, indicating a decrease in the odds of adopting clean energy as these predictors increase. Income and Number of rooms have odds ratios greater than 1, indicating an increase in the odds of adopting clean energy as these predictors increase.
7. The table does not provide specific odds results for categorical variables.
8. The model has a high p-value (1.000) in the goodness-of-fit test, indicating that the model fits the data well.
9. The model is adequate as it has a high goodness-of-fit.
Penjelasan
1. The method used is "Logistic Regression". This is inferred from the mention of "Logit" as the link function and the presentation of odds ratios, which are typical outputs of logistic regression.
2. Assumptions for logistic regression include:
- Linearity of the logit for continuous variables.
- Independence of errors.
- No multicollinearity among independent variables.
- Large sample size.
3. The hypotheses for logistic regression are:
- Null Hypothesis (H0): There is no relationship between the predictors and the response variable.
- Alternative Hypothesis (H1): There is a significant relationship between at least one predictor and the response variable.
4. The objective is mentioned in the question: "The outputs from minitab are from an analysis to determine the factors that influence adoption of clean energy".
5. The nature of the response variable in logistic regression is binary. Given the context, it is likely coded as 0 or 1, representing non-adoption or adoption of clean energy, respectively.
6. To identify significant factors, we look at the odds ratios and their confidence intervals. If the confidence interval for an odds ratio does not include 1, the predictor is significant. From the table, Age, Income, and Number of rooms are significant predictors. Age and Household size have odds ratios less than 1, indicating that as these predictors increase, the odds of adopting clean energy decrease. Conversely, Income and Number of rooms have odds ratios greater than 1, indicating that as these predictors increase, the odds of adopting clean energy increase.
7. The table does not provide specific odds results for categorical variables, so we cannot interpret them.
8. The goodness-of-fit test assesses how well the model fits the data. A high p-value (like 1.000) indicates that the model fits the data well.
9. Given the high p-value in the goodness-of-fit test, the model is deemed adequate for the data.
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