#linestyle

[dapper-lil-arts]

Chrysalis anthro voted by patreon. Accept no substitutes.

[darkartfinds]

"I have crossed oceans of time to find you.” by Anna Jäger-Hauer

[poisned]

I see... You use underhanded tactics, too. Huh, Shuichi?

[roedoefriend]

[ghouly-drool]

So fun fact i started drawing this gojo and halfway through gege confirmed that he was more of a dog person. ... 💀💀💀 idk if i'll end up finishing this but i still liked the colors and cute kitty and linestyle i went with!!

[nobodytriple]

opinions for cel shade artstyle

[linestyleartwork]

`Yavanna´- Traditional painting. -Pencil and watercolor paint. - The color version of Yavanna is ready now. Soon available in my shops:

(Music in Video by www.frametraxx.de)

[zilluzion]

HOW DO GOU EVEN MAKE YOUR ART LOOK LIKE SOFT COOKIES WITH LOTS OF CHOCOLATE CHIPS,,,, HOW??????¿??

(btw i left yir server becuaz i realized your server waz 16+,, but il be bac on my birthday!!! im turning 16 on january 19!!!((

(ty for respecting the rules and my boundaries! i generally keep all my socials 16+ for my own comfort and im glad you can understand <3) but awa nonetheless thankyou for the compliments! for anyone curious about how i create the soft look in my art i think theres a few things that contribute to it; - i rarely use fully opaque lineart, i draw all my lines using a transparency/pressue brush and i often use a thicker linestyle than others too, i think this helps lend itself to line weight and depth but also helps accentuate softer areas where the lines are really light and round! - i use a soft-edged brush for shading, i turn the hardness down to pretty much 0% and paint soft shapes and gradients to map out the general lighting with blend modes - i ALSO use a soft-edged brush for rendering-- after laying out the lights and darks i go in with a smaller but still soft brush to add details on a sepearate layer above the lineart, this can often result in me sometimes overlapping the lines a little and creating that fluffy look! i think these things are maybe subtle but they help a lot to generally reduce hard edges in the piece and reduce line intensity- lineart is of course important to a piece but i dont treat it as the focus, its more of a guide to the edges and shadows more than anything, if that makes sense :3

[transgenderer]

feel like different material could maybe elevate my linestyle stuff but it already takes foreeeeever and im worried something slower would render it stale. like stagnant water

[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

[learning-code-ficusoft]

How to Build Data Visualizations with Matplotlib, Seaborn, and Plotly

How to Build Data Visualizations with Matplotlib, Seaborn, and Plotly Data visualization is a crucial step in the data analysis process. 

It enables us to uncover patterns, understand trends, and communicate insights effectively. 

Python offers powerful libraries like Matplotlib, Seaborn, and Plotly that simplify the process of creating visualizations. 

In this blog, we’ll explore how to use these libraries to create impactful charts and graphs. 

1. Matplotlib:

 The Foundation of Visualization in Python Matplotlib is one of the oldest and most widely used libraries for creating static, animated, and interactive visualizations in Python. 

While it requires more effort to customize compared to other libraries, its flexibility makes it an indispensable tool.

Key Features: Highly customizable for static plots Extensive support for a variety of chart types Integration with other libraries like Pandas Example: Creating a Simple Line Plot import matplotlib.

import matplotlib.pyplot as plt

# Sample data years = [2010, 2012, 2014, 2016, 2018, 2020] values = [25, 34, 30, 35, 40, 50]

# Creating the plot plt.figure(figsize=(8, 5)) plt.plot(years, values, marker=’o’, linestyle=’-’, color=’b’, label=’Values Over Time’)

# Adding labels and title plt.xlabel(‘Year’) plt.ylabel(‘Value’) plt.title(‘Line Plot Example’) plt.legend() plt.grid(True)

# Show plot plt.show()

2. Seaborn:

 Simplifying Statistical Visualization Seaborn is built on top of Matplotlib and provides an easier and more aesthetically pleasing way to create complex visualizations. 

It’s ideal for statistical data visualization and integrates seamlessly with Pandas. 

Key Features:

 Beautiful default styles and color palettes Built-in support for data frames Specialized plots like heatmaps and pair plots 

Example:

 Creating a Heatmap

import seaborn as sns import numpy as np import pandas as pd

# Sample data np.random.seed(0) data = np.random.rand(10, 12) columns = [f’Month {i+1}’ for i in range(12)] index = [f’Year {i+1}’ for i in range(10)] heatmap_data = pd.DataFrame(data, columns=columns, index=index)

# Creating the heatmap plt.figure(figsize=(12, 8)) sns.heatmap(heatmap_data, annot=True, fmt=”.2f”, cmap=”coolwarm”)

plt.title(‘Heatmap Example’) plt.show()

3. Plotly: 

Interactive and Dynamic Visualizations Plotly is a library for creating interactive visualizations that can be shared online or embedded in web applications. 

It’s especially popular for dashboards and interactive reports. Key Features: Interactive plots by default Support for 3D and geo-spatial visualizations Integration with web technologies like Dash 

Example: 

Creating an Interactive Scatter Plot

import plotly.express as px

# Sample data data = {  ‘Year’: [2010, 2012, 2014, 2016, 2018, 2020],  ‘Value’: [25, 34, 30, 35, 40, 50] }

# Creating a scatter plot df = pd.DataFrame(data) fig = px.scatter(df, x=’Year’, y=’Value’, title=’Interactive Scatter Plot Example’, size=’Value’, color=’Value’)

fig.show()

Conclusion 

Matplotlib, Seaborn, and Plotly each have their strengths, and the choice of library depends on the specific requirements of your project. 

Matplotlib is best for detailed and static visualizations, Seaborn is ideal for statistical and aesthetically pleasing plots, and Plotly is unmatched in creating interactive visualizations.

[pinguinportfoli0]

OOL Attacker - Running a Lasso Regression Analysis

For this project it was used the Outlook on Life Surveys. "The purpose of the 2012 Outlook Surveys were to study political and social attitudes in the United States. The specific purpose of the survey is to consider the ways in which social class, ethnicity, marital status, feminism, religiosity, political orientation, and cultural beliefs or stereotypes influence opinion and behavior." - Outlook

Was necessary the removal of some rows containing text (for confidentiality purposes) before the dorpna() function.

This is my full code:

import pandas as pd import numpy as np import matplotlib.pylab as plt from sklearn.model_selection import train_test_split from sklearn.linear_model import LassoLarsCV from sklearn import preprocessing import time #Load the dataset data = pd.read_csv(r"PATHHHH") #upper-case all DataFrame column names data.columns = map(str.upper, data.columns) # Data Management data_clean = data.select_dtypes(include=['number']) data_clean = data_clean.dropna() print(data_clean.describe()) print(data_clean.dtypes) #Split into training and testing sets headers = list(data_clean.columns) headers.remove("PPNET") predvar = data_clean[headers] target = data_clean.PPNET predictors=predvar.copy() for header in headers:     predictors[header] = preprocessing.scale(predictors[header].astype('float64')) # split data into train and test sets pred_train, pred_test, tar_train, tar_test = train_test_split(predictors, target, test_size=.3, random_state=123) # specify the lasso regression model model=LassoLarsCV(cv=10, precompute=False).fit(pred_train,tar_train) #Display both categories by coefs pd.set_option('display.max_rows', None) table_catimp=pd.DataFrame({'cat': predictors.columns, 'coef': abs(model.coef_)}) print(table_catimp) non_zero_count = (table_catimp['coef'] != 0).sum() zero_count = table_catimp.shape[0] - non_zero_count print(f"Number of non-zero coefficients: {non_zero_count}") print(f"Number of zero coefficients: {zero_count}") #Display top 5 categories by coefs top_5_rows = table_catimp.nlargest(10, 'coef') print(top_5_rows.to_string(index=False)) # plot coefficient progression m_log_alphas = -np.log10(model.alphas_) ax = plt.gca() plt.plot(m_log_alphas, model.coef_path_.T) plt.axvline(-np.log10(model.alpha_), linestyle='--', color='k',             label='alpha CV') plt.ylabel('Regression Coefficients') plt.xlabel('-log(alpha)') plt.title('Regression Coefficients Progression for Lasso Paths') # plot mean square error for each fold m_log_alphascv = -np.log10(model.cv_alphas_) plt.figure() plt.plot(m_log_alphascv, model.mse_path_, ':') plt.plot(m_log_alphascv, model.mse_path_.mean(axis=-1), 'k',          label='Average across the folds', linewidth=2) plt.axvline(-np.log10(model.alpha_), linestyle='--', color='k',             label='alpha CV') plt.legend() plt.xlabel('-log(alpha)') plt.ylabel('Mean squared error') plt.title('Mean squared error on each fold') # MSE from training and test data from sklearn.metrics import mean_squared_error train_error = mean_squared_error(tar_train, model.predict(pred_train)) test_error = mean_squared_error(tar_test, model.predict(pred_test)) print ('training data MSE') print(train_error) print ('test data MSE') print(test_error) # R-square from training and test data rsquared_train=model.score(pred_train,tar_train) rsquared_test=model.score(pred_test,tar_test) print ('training data R-square') print(rsquared_train) print ('test data R-square') print(rsquared_test) plt.show()

Output:

Number of non-zero coefficients: 54 Number of zero coefficients: 186 training data MSE: 0.11867468892072082 test data MSE: 0.1458371486851879 training data R-square: 0.29967753231880834 test data R-square: 0.18204209521525183

Top 10 coefs:

PPINCIMP 0.097772 W1_WEIGHT3 0.061791 W1_P21 0.048740 W1_E1 0.027003 W1_CASEID 0.026709 PPHHSIZE 0.026055 PPAGECT4 0.022809 W1_Q1_B 0.021630 W1_P16E 0.020672 W1_E63_C 0.020205

Conclusions:

While the test error is slightly higher than the training error, the difference is not extreme, which is a positive sign that the model generalizes reasonably well.

Also in another note, the drop in R-square between training and test sets suggests the model may be overfitting slightly or that the predictors do not fully explain the response variable's behavior.

In the attachments I present the Regression coefficients, allowing to verify which features or characteristics are the most relevant for this model. Both PPINCIMP and W1_WEIGHT3 have the biggest weight. In the second attachment we can select the optimal alpha, the vertical dashed line indicates the optimal value of alpha.

The program successfully identified a subset of 54 predictors from 240 variables that are most strongly associated with the response variable. The moderate R-square values suggest room for improvement in the model's explanatory power. However, the close alignment between training and test MSE indicates reasonable generalization.

[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.

[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.