#insert_url_to_image_qq_plot

[shamira22]

Example Code```pythonimport pandas as pdimport numpy as npimport statsmodels.api as smimport matplotlib.pyplot as pltimport seaborn as snsfrom statsmodels.graphics.gofplots import qqplotfrom statsmodels.stats.outliers_influence import OLSInfluence# Sample data creation (replace with your actual dataset loading)np.random.seed(0)n = 100depression = np.random.choice(['Yes', 'No'], size=n)age = np.random.randint(18, 65, size=n)nicotine_symptoms = np.random.randint(0, 20, size=n) + (depression == 'Yes') * 10 + age * 0.5 # More symptoms with depression and agedata = { 'MajorDepression': depression, 'Age': age, 'NicotineDependenceSymptoms': nicotine_symptoms}df = pd.DataFrame(data)# Recode categorical explanatory variable MajorDepression# Assuming 'Yes' is coded as 1 and 'No' as 0df['MajorDepression'] = df['MajorDepression'].map({'Yes': 1, 'No': 0})# Multiple regression modelX = df[['MajorDepression', 'Age']]X = sm.add_constant(X) # Add intercepty = df['NicotineDependenceSymptoms']model = sm.OLS(y, X).fit()# Print regression results summaryprint(model.summary())# Regression diagnostic plots# Q-Q plotresiduals = model.residfig, ax = plt.subplots(figsize=(8, 5))qqplot(residuals, line='s', ax=ax)ax.set_title('Q-Q Plot of Residuals')plt.show()# Standardized residuals plotinfluence = OLSInfluence(model)std_residuals = influence.resid_studentized_internalplt.figure(figsize=(8, 5))plt.scatter(model.predict(), std_residuals, alpha=0.8)plt.axhline(y=0, color='r', linestyle='-', linewidth=1)plt.title('Standardized Residuals vs. Fitted Values')plt.xlabel('Fitted values')plt.ylabel('Standardized Residuals')plt.grid(True)plt.show()# Leverage plotfig, ax = plt.subplots(figsize=(8, 5))sm.graphics.plot_leverage_resid2(model, ax=ax)ax.set_title('Leverage-Residuals Plot')plt.show()# Blog entry summarysummary = """### Summary of Multiple Regression Analysis1. **Association between Explanatory Variables and Response Variable:** The results of the multiple regression analysis revealed significant associations: - Major Depression (Beta = {:.2f}, p = {:.4f}): Significant and positive association with Nicotine Dependence Symptoms. - Age (Beta = {:.2f}, p = {:.4f}): Older participants reported a greater number of Nicotine Dependence Symptoms.2. **Hypothesis Testing:** The results supported the hypothesis that Major Depression is positively associated with Nicotine Dependence Symptoms.3. **Confounding Variables:** Age was identified as a potential confounding variable. Adjusting for Age slightly reduced the magnitude of the association between Major Depression and Nicotine Dependence Symptoms.4. **Regression Diagnostic Plots:** - **Q-Q Plot:** Indicates that residuals approximately follow a normal distribution, suggesting the model assumptions are reasonable. - **Standardized Residuals vs. Fitted Values Plot:** Shows no apparent pattern in residuals, indicating homoscedasticity and no obvious outliers. - **Leverage-Residuals Plot:** Identifies influential observations but shows no extreme leverage points.### Output from Multiple Regression Model```python# Your output from model.summary() hereprint(model.summary())```### Regression Diagnostic Plots"""# Assuming you would generate and upload images of the plots to your blog# Print the summary for submissionprint(summary)```### Explanation:1. **Sample Data Creation**: Simulates a dataset with `MajorDepression` as a categorical explanatory variable, `Age` as a quantitative explanatory variable, and `NicotineDependenceSymptoms` as the response variable. 2. **Multiple Regression Model**: - Constructs an Ordinary Least Squares (OLS) regression model using `sm.OLS` from the statsmo

[ramanidevi16]

Multiple Regression model

To successfully complete the assignment on testing a multiple regression model, you'll need to conduct a comprehensive analysis using Python, summarize your findings in a blog entry, and include necessary regression diagnostic plots.

Here’s a structured example to guide you through the process:

### Example Code

```pythonimport pandas as pdimport numpy as npimport statsmodels.api as smimport matplotlib.pyplot as pltimport seaborn as snsfrom statsmodels.graphics.gofplots import qqplotfrom statsmodels.stats.outliers_influence import OLSInfluence# Sample data creation (replace with your actual dataset loading)np.random.seed(0)n = 100depression = np.random.choice(['Yes', 'No'], size=n)age = np.random.randint(18, 65, size=n)nicotine_symptoms = np.random.randint(0, 20, size=n) + (depression == 'Yes') * 10 + age * 0.5 # More symptoms with depression and agedata = { 'MajorDepression': depression, 'Age': age, 'NicotineDependenceSymptoms': nicotine_symptoms}df = pd.DataFrame(data)# Recode categorical explanatory variable MajorDepression# Assuming 'Yes' is coded as 1 and 'No' as 0df['MajorDepression'] = df['MajorDepression'].map({'Yes': 1, 'No': 0})# Multiple regression modelX = df[['MajorDepression', 'Age']]X = sm.add_constant(X) # Add intercepty = df['NicotineDependenceSymptoms']model = sm.OLS(y, X).fit()# Print regression results summaryprint(model.summary())# Regression diagnostic plots# Q-Q plotresiduals = model.residfig, ax = plt.subplots(figsize=(8, 5))qqplot(residuals, line='s', ax=ax)ax.set_title('Q-Q Plot of Residuals')plt.show()# Standardized residuals plotinfluence = OLSInfluence(model)std_residuals = influence.resid_studentized_internalplt.figure(figsize=(8, 5))plt.scatter(model.predict(), std_residuals, alpha=0.8)plt.axhline(y=0, color='r', linestyle='-', linewidth=1)plt.title('Standardized Residuals vs. Fitted Values')plt.xlabel('Fitted values')plt.ylabel('Standardized Residuals')plt.grid(True)plt.show()# Leverage plotfig, ax = plt.subplots(figsize=(8, 5))sm.graphics.plot_leverage_resid2(model, ax=ax)ax.set_title('Leverage-Residuals Plot')plt.show()# Blog entry summarysummary = """### Summary of Multiple Regression Analysis1. **Association between Explanatory Variables and Response Variable:** The results of the multiple regression analysis revealed significant associations: - Major Depression (Beta = {:.2f}, p = {:.4f}): Significant and positive association with Nicotine Dependence Symptoms. - Age (Beta = {:.2f}, p = {:.4f}): Older participants reported a greater number of Nicotine Dependence Symptoms.2. **Hypothesis Testing:** The results supported the hypothesis that Major Depression is positively associated with Nicotine Dependence Symptoms.3. **Confounding Variables:** Age was identified as a potential confounding variable. Adjusting for Age slightly reduced the magnitude of the association between Major Depression and Nicotine Dependence Symptoms.4. **Regression Diagnostic Plots:** - **Q-Q Plot:** Indicates that residuals approximately follow a normal distribution, suggesting the model assumptions are reasonable. - **Standardized Residuals vs. Fitted Values Plot:** Shows no apparent pattern in residuals, indicating homoscedasticity and no obvious outliers. - **Leverage-Residuals Plot:** Identifies influential observations but shows no extreme leverage points.### Output from Multiple Regression Model```python# Your output from model.summary() hereprint(model.summary())```### Regression Diagnostic Plots"""# Assuming you would generate and upload images of the plots to your blog# Print the summary for submissionprint(summary)```

### Explanation:

1. **Sample Data Creation**: Simulates a dataset with `MajorDepression` as a categorical explanatory variable, `Age` as a quantitative explanatory variable, and `NicotineDependenceSymptoms` as the response variable.

2. **Multiple Regression Model**: - Constructs an Ordinary Least Squares (OLS) regression model using `sm.OLS` from the statsmodels library. - Adds an intercept to the model using `sm.add_constant`. - Fits the model to predict `NicotineDependenceSymptoms` using `MajorDepression` and `Age` as predictors.

3. **Regression Diagnostic Plots**: - Q-Q Plot: Checks the normality assumption of residuals. - Standardized Residuals vs. Fitted Values: Examines homoscedasticity and identifies outliers. - Leverage-Residuals Plot: Detects influential observations that may affect model fit.

4. **Blog Entry Summary**: Provides a structured summary including results of regression analysis, hypothesis testing, discussion on confounding variables, and inclusion of regression diagnostic plots.

### Blog Entry SubmissionEnsure to adapt the code and summary based on your specific dataset and analysis. Upload the regression diagnostic plots as images to your blog entry and provide the URL to your completed assignment. This example should help you effectively complete your Coursera assignment on testing a multiple regression model.

[krishnamanohari2108]

To successfully complete the assignment on testing a multiple regression model, you'll need to conduct a comprehensive analysis using Python, summarize your findings in a blog entry, and include necessary regression diagnostic plots. Here’s a structured example to guide you through the process:### Example Code```python imports pandas as passport numpy as import statsmodels.api as import matplotlib.pyplot as passport seaborn as transform statsmodels.graphics.gofplots import platform statsmodels.stats.outliers_influence import Ol Influence# Sample data creation (replace with your actual dataset loading)np.random.seed(0)n = 100depression = np.random.choice(['Yes', 'No'], size=n)age = np.random.randint(18, 65, size=n)nicotine_symptoms = np.random.randint(0, 20, size=n) + (depression == 'Yes') * 10 + age * 0.5 # More symptoms with depression and data = { 'Major Depression': depression, 'Age': age, 'Independent': nicotine_symptoms}df = pd.DataFrame(data)# Recode categorical explanatory variable Major Depression# Assuming 'Yes' is coded as 1 and 'No' as 0df['Major Depression'] = df['Major Depression'].map({'Yes': 1, 'No': 0})# Multiple regression Model = df[['Major Depression', 'Age']]X = sm.add_constant(X) # Add intercept = df['Independence']model = sm.OLS(y, X).fit()# Print regression results summary(model.summary())# Regression diagnostic plots# Q-Q plot residuals = model.residfig, ax = plt.subplots(fig size=(8, 5))plot(residuals, line='s', ax=ax)ax.set_title('Q-Q Plot of Residuals')plt.show()# Standardized residuals plot influence = Influenced(model)std_residuals = influence.resid_studentized_internalplt.figure(finalize=(8, 5))plt.scatter(model.predict(), std_residuals, alpha=0.8)plt.axhline(y=0, color='r', lifestyle='-', linewidth=1)plt.title('Standardized Residuals vs. Fitted Values')plt.xlabel('Fitted values')plt.ylabel('Standardized Residuals')plt.grid(True)plt.show()# Leverage plotfig, ax = plt.subplots(figsize=(8, 5))sm.graphics.plot_leverage_resid2(model, ax=ax)ax.set_title('Leverage-Residuals Plot')plt.show()# Blog entry summarysummary = """### Summary of Multiple Regression Analysis1. **Association between Explanatory Variables and Response Variable:** The results of the multiple regression analysis revealed significant associations: - Major Depression (Beta = {:.2f}, p = {:.4f}): Significant and positive association with Nicotine Dependence Symptoms. - Age (Beta = {:.2f}, p = {:.4f}): Older participants reported a greater number of Nicotine Dependence Symptoms.2. **Hypothesis Testing:** The results supported the hypothesis that Major Depression is positively associated with Nicotine Dependence Symptoms.3. **Confounding Variables:** Age was identified as a potential confounding variable. Adjusting for Age slightly reduced the magnitude of the association between Major Depression and Nicotine Dependence Symptoms.4. **Regression Diagnostic Plots:** - **Q-Q Plot:** Indicates that residuals approximately follow a normal distribution, suggesting the model assumptions are reasonable. - **Standardized Residuals vs. Fitted Values Plot:** Shows no apparent pattern in residuals, indicating homoscedasticity and no obvious outliers. - **Leverage-Residuals Plot:** Identifies influential observations but shows no extreme leverage points.### Output from Multiple Regression Model```python# Your output from model.summary() reprint(model.summary())```### Regression Diagnostic Plots"""# Assuming you would generate and upload images of the plots to your blog# Print the summary for submission print(summary)`` Explanation:1. **Sample Data Creation**: Simulates a dataset with `Major Depression` as a categorical explanatory variable, `Age` as a quantitative explanatory variable, and `Independence` as the response variable.

[ratthika]

To successfully complete the assignment on testing a multiple regression model, you'll need to conduct a comprehensive analysis using Python, summarize your findings in a blog entry, and include necessary regression diagnostic plots. Here’s a structured example to guide you through the process:### Example Code```pythonimport pandas as pdimport numpy as npimport statsmodels.api as smimport matplotlib.pyplot as pltimport seaborn as snsfrom statsmodels.graphics.gofplots import qqplotfrom statsmodels.stats.outliers_influence import OLSInfluence# Sample data creation (replace with your actual dataset loading)np.random.seed(0)n = 100depression = np.random.choice(['Yes', 'No'], size=n)age = np.random.randint(18, 65, size=n)nicotine_symptoms = np.random.randint(0, 20, size=n) + (depression == 'Yes') * 10 + age * 0.5 # More symptoms with depression and agedata = { 'MajorDepression': depression, 'Age': age, 'NicotineDependenceSymptoms': nicotine_symptoms}df = pd.DataFrame(data)# Recode categorical explanatory variable MajorDepression# Assuming 'Yes' is coded as 1 and 'No' as 0df['MajorDepression'] = df['MajorDepression'].map({'Yes': 1, 'No': 0})# Multiple regression modelX = df[['MajorDepression', 'Age']]X = sm.add_constant(X) # Add intercepty = df['NicotineDependenceSymptoms']model = sm.OLS(y, X).fit()# Print regression results summaryprint(model.summary())# Regression diagnostic plots# Q-Q plotresiduals = model.residfig, ax = plt.subplots(figsize=(8, 5))qqplot(residuals, line='s', ax=ax)ax.set_title('Q-Q Plot of Residuals')plt.show()# Standardized residuals plotinfluence = OLSInfluence(model)std_residuals = influence.resid_studentized_internalplt.figure(figsize=(8, 5))plt.scatter(model.predict(), std_residuals, alpha=0.8)plt.axhline(y=0, color='r', linestyle='-', linewidth=1)plt.title('Standardized Residuals vs. Fitted Values')plt.xlabel('Fitted values')plt.ylabel('Standardized Residuals')plt.grid(True)plt.show()# Leverage plotfig, ax = plt.subplots(figsize=(8, 5))sm.graphics.plot_leverage_resid2(model, ax=ax)ax.set_title('Leverage-Residuals Plot')plt.show()# Blog entry summarysummary = """### Summary of Multiple Regression Analysis1. **Association between Explanatory Variables and Response Variable:** The results of the multiple regression analysis revealed significant associations: - Major Depression (Beta = {:.2f}, p = {:.4f}): Significant and positive association with Nicotine Dependence Symptoms. - Age (Beta = {:.2f}, p = {:.4f}): Older participants reported a greater number of Nicotine Dependence Symptoms.2. **Hypothesis Testing:** The results supported the hypothesis that Major Depression is positively associated with Nicotine Dependence Symptoms.3. **Confounding Variables:** Age was identified as a potential confounding variable. Adjusting for Age slightly reduced the magnitude of the association between Major Depression and Nicotine Dependence Symptoms.4. **Regression Diagnostic Plots:** - **Q-Q Plot:** Indicates that residuals approximately follow a normal distribution, suggesting the model assumptions are reasonable. - **Standardized Residuals vs. Fitted Values Plot:** Shows no apparent pattern in residuals, indicating homoscedasticity and no obvious outliers. - **Leverage-Residuals Plot:** Identifies influential observations but shows no extreme leverage points.### Output from Multiple Regression Model```python# Your output from model.summary() hereprint(model.summary())```### Regression Diagnostic Plots"""# Assuming you would generate and upload images of the plots to your blog# Print the summary for submissionprint(summary)```###

[varsha172003]

To successfully complete the assignment on testing a multiple regression model, you'll need to conduct a comprehensive analysis using Python, summarize your findings in a blog entry, and include necessary regression diagnostic plots. Here’s a structured example to guide you through the process:

Example Code

import pandas as pd import numpy as np import statsmodels.api as sm import matplotlib.pyplot as plt import seaborn as sns from statsmodels.graphics.gofplots import qqplot from statsmodels.stats.outliers_influence import OLSInfluence # Sample data creation (replace with your actual dataset loading) np.random.seed(0) n = 100 depression = np.random.choice(['Yes', 'No'], size=n) age = np.random.randint(18, 65, size=n) nicotine_symptoms = np.random.randint(0, 20, size=n) + (depression == 'Yes') * 10 + age * 0.5 # More symptoms with depression and age data = { 'MajorDepression': depression, 'Age': age, 'NicotineDependenceSymptoms': nicotine_symptoms } df = pd.DataFrame(data) # Recode categorical explanatory variable MajorDepression # Assuming 'Yes' is coded as 1 and 'No' as 0 df['MajorDepression'] = df['MajorDepression'].map({'Yes': 1, 'No': 0}) # Multiple regression model X = df[['MajorDepression', 'Age']] X = sm.add_constant(X) # Add intercept y = df['NicotineDependenceSymptoms'] model = sm.OLS(y, X).fit() # Print regression results summary print(model.summary()) # Regression diagnostic plots # Q-Q plot residuals = model.resid fig, ax = plt.subplots(figsize=(8, 5)) qqplot(residuals, line='s', ax=ax) ax.set_title('Q-Q Plot of Residuals') plt.show() # Standardized residuals plot influence = OLSInfluence(model) std_residuals = influence.resid_studentized_internal plt.figure(figsize=(8, 5)) plt.scatter(model.predict(), std_residuals, alpha=0.8) plt.axhline(y=0, color='r', linestyle='-', linewidth=1) plt.title('Standardized Residuals vs. Fitted Values') plt.xlabel('Fitted values') plt.ylabel('Standardized Residuals') plt.grid(True) plt.show() # Leverage plot fig, ax = plt.subplots(figsize=(8, 5)) sm.graphics.plot_leverage_resid2(model, ax=ax) ax.set_title('Leverage-Residuals Plot') plt.show() # Blog entry summary summary = """ ### Summary of Multiple Regression Analysis 1. **Association between Explanatory Variables and Response Variable:** The results of the multiple regression analysis revealed significant associations: - Major Depression (Beta = {:.2f}, p = {:.4f}): Significant and positive association with Nicotine Dependence Symptoms. - Age (Beta = {:.2f}, p = {:.4f}): Older participants reported a greater number of Nicotine Dependence Symptoms. 2. **Hypothesis Testing:** The results supported the hypothesis that Major Depression is positively associated with Nicotine Dependence Symptoms. 3. **Confounding Variables:** Age was identified as a potential confounding variable. Adjusting for Age slightly reduced the magnitude of the association between Major Depression and Nicotine Dependence Symptoms. 4. **Regression Diagnostic Plots:** - **Q-Q Plot:** Indicates that residuals approximately follow a normal distribution, suggesting the model assumptions are reasonable. - **Standardized Residuals vs. Fitted Values Plot:** Shows no apparent pattern in residuals, indicating homoscedasticity and no obvious outliers. - **Leverage-Residuals Plot:** Identifies influential observations but shows no extreme leverage points. ### Output from Multiple Regression Model

python

Your output from model.summary() here

print(model.summary())### Regression Diagnostic Plots    """ # Assuming you would generate and upload images of the plots to your blog # Print the summary for submission print(summary)

Explanation:

Sample Data Creation: Simulates a dataset with MajorDepression as a categorical explanatory variable, Age as a quantitative explanatory variable, and NicotineDependenceSymptoms as the response variable.

Multiple Regression Model:

Constructs an Ordinary Least Squares (OLS) regression model using sm.OLS from the statsmodels library.

Adds an intercept to the model using sm.add_constant.

Fits the model to predict NicotineDependenceSymptoms using MajorDepression and Age as predictors.

Regression Diagnostic Plots:

Q-Q Plot: Checks the normality assumption of residuals.

Standardized Residuals vs. Fitted Values: Examines homoscedasticity and identifies outliers.

Leverage-Residuals Plot: Detects influential observations that may affect model fit.

Blog Entry Summary: Provides a structured summary including results of regression analysis, hypothesis testing, discussion on confounding variables, and inclusion of regression diagnostic plots.

Blog Entry Submission

Ensure to adapt the code and summary based on your specific dataset and analysis. Upload the regression diagnostic plots as images to your blog entry and provide the URL to your completed assignment. This example should help you effectively complete your Coursera assignment on testing a multiple regression model.

[divya08112002]

To successfully complete the assignment on testing a multiple regression model, you'll need to conduct a comprehensive analysis using Python, summarize your findings in a blog entry, and include necessary regression diagnostic plots. Here’s a structured example to guide you through the process:

Example Code

import pandas as pd import numpy as np import statsmodels.api as sm import matplotlib.pyplot as plt import seaborn as sns from statsmodels.graphics.gofplots import qqplot from statsmodels.stats.outliers_influence import OLSInfluence # Sample data creation (replace with your actual dataset loading) np.random.seed(0) n = 100 depression = np.random.choice(['Yes', 'No'], size=n) age = np.random.randint(18, 65, size=n) nicotine_symptoms = np.random.randint(0, 20, size=n) + (depression == 'Yes') * 10 + age * 0.5 # More symptoms with depression and age data = { 'MajorDepression': depression, 'Age': age, 'NicotineDependenceSymptoms': nicotine_symptoms } df = pd.DataFrame(data) # Recode categorical explanatory variable MajorDepression # Assuming 'Yes' is coded as 1 and 'No' as 0 df['MajorDepression'] = df['MajorDepression'].map({'Yes': 1, 'No': 0}) # Multiple regression model X = df[['MajorDepression', 'Age']] X = sm.add_constant(X) # Add intercept y = df['NicotineDependenceSymptoms'] model = sm.OLS(y, X).fit() # Print regression results summary print(model.summary()) # Regression diagnostic plots # Q-Q plot residuals = model.resid fig, ax = plt.subplots(figsize=(8, 5)) qqplot(residuals, line='s', ax=ax) ax.set_title('Q-Q Plot of Residuals') plt.show() # Standardized residuals plot influence = OLSInfluence(model) std_residuals = influence.resid_studentized_internal plt.figure(figsize=(8, 5)) plt.scatter(model.predict(), std_residuals, alpha=0.8) plt.axhline(y=0, color='r', linestyle='-', linewidth=1) plt.title('Standardized Residuals vs. Fitted Values') plt.xlabel('Fitted values') plt.ylabel('Standardized Residuals') plt.grid(True) plt.show() # Leverage plot fig, ax = plt.subplots(figsize=(8, 5)) sm.graphics.plot_leverage_resid2(model, ax=ax) ax.set_title('Leverage-Residuals Plot') plt.show() # Blog entry summary summary = """ ### Summary of Multiple Regression Analysis 1. **Association between Explanatory Variables and Response Variable:** The results of the multiple regression analysis revealed significant associations: - Major Depression (Beta = {:.2f}, p = {:.4f}): Significant and positive association with Nicotine Dependence Symptoms. - Age (Beta = {:.2f}, p = {:.4f}): Older participants reported a greater number of Nicotine Dependence Symptoms. 2. **Hypothesis Testing:** The results supported the hypothesis that Major Depression is positively associated with Nicotine Dependence Symptoms. 3. **Confounding Variables:** Age was identified as a potential confounding variable. Adjusting for Age slightly reduced the magnitude of the association between Major Depression and Nicotine Dependence Symptoms. 4. **Regression Diagnostic Plots:** - **Q-Q Plot:** Indicates that residuals approximately follow a normal distribution, suggesting the model assumptions are reasonable. - **Standardized Residuals vs. Fitted Values Plot:** Shows no apparent pattern in residuals, indicating homoscedasticity and no obvious outliers. - **Leverage-Residuals Plot:** Identifies influential observations but shows no extreme leverage points. ### Output from Multiple Regression Model

python

Your output from model.summary() here

print(model.summary())### Regression Diagnostic Plots    """ # Assuming you would generate and upload images of the plots to your blog # Print the summary for submission print(summary)

Explanation:

Sample Data Creation: Simulates a dataset with MajorDepression as a categorical explanatory variable, Age as a quantitative explanatory variable, and NicotineDependenceSymptoms as the response variable.

Multiple Regression Model:

Constructs an Ordinary Least Squares (OLS) regression model using sm.OLS from the statsmodels library.

Adds an intercept to the model using sm.add_constant.

Fits the model to predict NicotineDependenceSymptoms using MajorDepression and Age as predictors.

Regression Diagnostic Plots:

Q-Q Plot: Checks the normality assumption of residuals.

Standardized Residuals vs. Fitted Values: Examines homoscedasticity and identifies outliers.

Leverage-Residuals Plot: Detects influential observations that may affect model fit.

Blog Entry Summary: Provides a structured summary including results of regression analysis, hypothesis testing, discussion on confounding variables, and inclusion of regression diagnostic plots.

[shamira22]

Code```pythonimport pandas as pdimport numpy as npimport statsmodels.api as smimport matplotlib.pyplot as pltimport seaborn as snsfrom statsmodels.graphics.gofplots import qqplotfrom statsmodels.stats.outliers_influence import OLSInfluence# Sample data creation (replace with your actual dataset loading)np.random.seed(0)n = 100depression = np.random.choice(['Yes', 'No'], size=n)age = np.random.randint(18, 65, size=n)nicotine_symptoms = np.random.randint(0, 20, size=n) + (depression == 'Yes') * 10 + age * 0.5 # More symptoms with depression and agedata = { 'MajorDepression': depression, 'Age': age, 'NicotineDependenceSymptoms': nicotine_symptoms}df = pd.DataFrame(data)# Recode categorical explanatory variable MajorDepression# Assuming 'Yes' is coded as 1 and 'No' as 0df['MajorDepression'] = df['MajorDepression'].map({'Yes': 1, 'No': 0})# Multiple regression modelX = df[['MajorDepression', 'Age']]X = sm.add_constant(X) # Add intercepty = df['NicotineDependenceSymptoms']model = sm.OLS(y, X).fit()# Print regression results summaryprint(model.summary())# Regression diagnostic plots# Q-Q plotresiduals = model.residfig, ax = plt.subplots(figsize=(8, 5))qqplot(residuals, line='s', ax=ax)ax.set_title('Q-Q Plot of Residuals')plt.show()# Standardized residuals plotinfluence = OLSInfluence(model)std_residuals = influence.resid_studentized_internalplt.figure(figsize=(8, 5))plt.scatter(model.predict(), std_residuals, alpha=0.8)plt.axhline(y=0, color='r', linestyle='-', linewidth=1)plt.title('Standardized Residuals vs. Fitted Values')plt.xlabel('Fitted values')plt.ylabel('Standardized Residuals')plt.grid(True)plt.show()# Leverage plotfig, ax = plt.subplots(figsize=(8, 5))sm.graphics.plot_leverage_resid2(model, ax=ax)ax.set_title('Leverage-Residuals Plot')plt.show()# Blog entry summarysummary = """### Summary of Multiple Regression Analysis1. **Association between Explanatory Variables and Response Variable:** The results of the multiple regression analysis revealed significant associations: - Major Depression (Beta = {:.2f}, p = {:.4f}): Significant and positive association with Nicotine Dependence Symptoms. - Age (Beta = {:.2f}, p = {:.4f}): Older participants reported a greater number of Nicotine Dependence Symptoms.2. **Hypothesis Testing:** The results supported the hypothesis that Major Depression is positively associated with Nicotine Dependence Symptoms.3. **Confounding Variables:** Age was identified as a potential confounding variable. Adjusting for Age slightly reduced the magnitude of the association between Major Depression and Nicotine Dependence Symptoms.4. **Regression Diagnostic Plots:** - **Q-Q Plot:** Indicates that residuals approximately follow a normal distribution, suggesting the model assumptions are reasonable. - **Standardized Residuals vs. Fitted Values Plot:** Shows no apparent pattern in residuals, indicating homoscedasticity and no obvious outliers. - **Leverage-Residuals Plot:** Identifies influential observations but shows no extreme leverage points.### Output from Multiple Regression Model```python# Your output from model.summary() hereprint(model.summary())```### Regression Diagnostic Plots"""# Assuming you would generate and upload images of the plots to your blog# Print the summary for submissionprint(summary)```### Explanation:1. **Sample Data Creation**: Simulates a dataset with `MajorDepression` as a categorical explanatory variable, `Age` as a quantitative explanatory variable, and `NicotineDependenceSymptoms` as the response variable. 2. **Multiple Regression Model**: - Constructs an Ordinary Least Squares (OLS) regression model using `sm.OLS` from the statsmodels library. - Adds an intercept to the model using `sm.add_constant`. - Fits the model to predict `NicotineDependenceSymptoms` using `MajorDepression` and `Age` as predictors.

[shamira22]

Example Code```pythonimport pandas as pdimport numpy as npimport statsmodels.api as smimport matplotlib.pyplot as pltimport seaborn as snsfrom statsmodels.graphics.gofplots import qqplotfrom statsmodels.stats.outliers_influence import OLSInfluence# Sample data creation (replace with your actual dataset loading)np.random.seed(0)n = 100depression = np.random.choice(['Yes', 'No'], size=n)age = np.random.randint(18, 65, size=n)nicotine_symptoms = np.random.randint(0, 20, size=n) + (depression == 'Yes') * 10 + age * 0.5 # More symptoms with depression and agedata = { 'MajorDepression': depression, 'Age': age, 'NicotineDependenceSymptoms': nicotine_symptoms}df = pd.DataFrame(data)# Recode categorical explanatory variable MajorDepression# Assuming 'Yes' is coded as 1 and 'No' as 0df['MajorDepression'] = df['MajorDepression'].map({'Yes': 1, 'No': 0})# Multiple regression modelX = df[['MajorDepression', 'Age']]X = sm.add_constant(X) # Add intercepty = df['NicotineDependenceSymptoms']model = sm.OLS(y, X).fit()# Print regression results summaryprint(model.summary())# Regression diagnostic plots# Q-Q plotresiduals = model.residfig, ax = plt.subplots(figsize=(8, 5))qqplot(residuals, line='s', ax=ax)ax.set_title('Q-Q Plot of Residuals')plt.show()# Standardized residuals plotinfluence = OLSInfluence(model)std_residuals = influence.resid_studentized_internalplt.figure(figsize=(8, 5))plt.scatter(model.predict(), std_residuals, alpha=0.8)plt.axhline(y=0, color='r', linestyle='-', linewidth=1)plt.title('Standardized Residuals vs. Fitted Values')plt.xlabel('Fitted values')plt.ylabel('Standardized Residuals')plt.grid(True)plt.show()# Leverage plotfig, ax = plt.subplots(figsize=(8, 5))sm.graphics.plot_leverage_resid2(model, ax=ax)ax.set_title('Leverage-Residuals Plot')plt.show()# Blog entry summarysummary = """### Summary of Multiple Regression Analysis1. **Association between Explanatory Variables and Response Variable:** The results of the multiple regression analysis revealed significant associations: - Major Depression (Beta = {:.2f}, p = {:.4f}): Significant and positive association with Nicotine Dependence Symptoms. - Age (Beta = {:.2f}, p = {:.4f}): Older participants reported a greater number of Nicotine Dependence Symptoms.2. **Hypothesis Testing:** The results supported the hypothesis that Major Depression is positively associated with Nicotine Dependence Symptoms.3. **Confounding Variables:** Age was identified as a potential confounding variable. Adjusting for Age slightly reduced the magnitude of the association between Major Depression and Nicotine Dependence Symptoms.4. **Regression Diagnostic Plots:** - **Q-Q Plot:** Indicates that residuals approximately follow a normal distribution, suggesting the model assumptions are reasonable. - **Standardized Residuals vs. Fitted Values Plot:** Shows no apparent pattern in residuals, indicating homoscedasticity and no obvious outliers. - **Leverage-Residuals Plot:** Identifies influential observations but shows no extreme leverage points.### Output from Multiple Regression Model```python# Your output from model.summary() hereprint(model.summary())```### Regression Diagnostic Plots"""# Assuming you would generate and upload images of the plots to your blog# Print the summary for submissionprint(summary)```### Explanation:1. **Sample Data Creation**: Simulates a dataset with `MajorDepression` as a categorical explanatory variable, `Age` as a quantitative explanatory variable, and `NicotineDependenceSymptoms` as the response variable. 2. **Multiple Regression Model**: - Constructs an Ordinary Least Squares (OLS) regression model using `sm.OLS` from the statsmodels library. - Adds an intercept to the model using `sm.add_constant`. - Fits the model to predict `NicotineDependenceSymptoms` using `MajorDepression` and `Age` as predictors.3.