登录查看更多内容

What are some effective ways to use data visualization to explore heteroscedasticity?

由人工智能和领英社区提供技术支持

Heteroscedasticity is a fancy word that means the variance of a variable is not constant across different values of another variable. For example, the income of a population may have more variation at higher levels than at lower levels. This can affect the validity and efficiency of some statistical methods, such as linear regression, that assume homoscedasticity or equal variance. How can you detect and explore heteroscedasticity in your data? One of the most effective ways is to use data visualization techniques that can reveal the patterns and relationships of your variables. In this article, you will learn some of the best practices and tools for using data visualization to explore heteroscedasticity.

此文章中的业界达人

由社区从 6 条内容中精选。了解更多

Mohammed Bahageel

Artificial Intelligence Developer |Data Scientist / Data Analyst | Machine Learning | Deep Learning | Data Analytics…
Jeffrey Ohene

Data Analyst | R & SQL Developer
Mohammed Rizwan Shaik

Manager@Uniqus | Data Management | AI & ML Expert

1 Scatter plots

A scatter plot is a simple but powerful way to visualize the relationship between two variables. It shows the distribution of points along the horizontal and vertical axes, and can indicate the presence of heteroscedasticity if the points are not evenly spread around a line or curve. For example, if you plot the income and education level of a sample of people, you may see a funnel-shaped pattern, where the variation of income increases as education level increases. This suggests that income is heteroscedastic with respect to education level. You can use software like R, Python, or Excel to create scatter plots and customize them with colors, labels, and trend lines.

添加您的观点

Jeffrey Ohene

Data Analyst | R & SQL Developer
举报内容
Plotting the independent variable against the dependent variable, provides a clear view of how the variance in the dependent variable changes across various levels of the independent variable. When dealing with a homoscedastic dataset, the scatterplot typically reveals a consistent and even distribution of points around the regression line, whereas a heteroscedastic dataset introduces a dynamic where the variance of the dependent variable exhibits fluctuations across different levels of the independent variable. This variation often manifests in the scatterplot as a distinctive funnel or U-shaped pattern. It's this nuanced visual representation scatterplots produce that helps me understand the relationship between variables in a dataset.

已翻译

赞
Eren Unlu

Co-Founder
举报内容
Scatter plots would not help you a lot with detecting heteroskedasticity if your data is high dimensional and overlapping. Therefore binned histograms like hexplots etc are better choices.

已翻译

赞

2 Residual plots

A residual plot is a type of scatter plot that shows the difference between the observed and predicted values of a dependent variable, given a model or a hypothesis. It can help you assess the fit and assumptions of your model, and identify potential outliers, errors, or nonlinearities. If your model assumes homoscedasticity, you should expect to see a random and uniform distribution of residuals around zero, with no obvious patterns or trends. However, if you see a fan-shaped or curved pattern, or a change in the spread of residuals across different values of an independent variable, you may have heteroscedasticity in your data. You can use software like R, Python, or Excel to create residual plots and analyze them with diagnostic tests or transformations.

添加您的观点

3 Box plots

A box plot is a graphical representation of the summary statistics of a variable, such as the median, quartiles, and outliers. It can help you compare the distribution and variation of a variable across different groups or categories. For example, if you want to explore the heteroscedasticity of income across different regions, you can create a box plot that shows the income range and median for each region. You can then look for differences in the shape, size, and position of the boxes, as well as the presence of outliers or extreme values. A box plot can indicate heteroscedasticity if the boxes have different widths, heights, or locations, or if some groups have more outliers than others. You can use software like R, Python, or Excel to create box plots and customize them with colors, labels, and notches.

添加您的观点

Eren Unlu

Co-Founder
举报内容
I also love to discretize my x axis in bins to have binned scatter plots. It really goes intuitive and interpretablr. Write a small script to reuse in your projects.

已翻译

赞

4 Heat maps

A heat map is a graphical representation of the intensity or frequency of a variable or a relationship, using different colors or shades. It can help you visualize the distribution and correlation of multiple variables, or the variation of a variable across different dimensions. For example, if you want to explore the heteroscedasticity of income across different regions and genders, you can create a heat map that shows the average income for each combination of region and gender, using different colors to indicate the level of income. You can then look for patterns or differences in the color scheme, and identify the regions and genders that have more or less variation in income. A heat map can indicate heteroscedasticity if the colors are not consistent or uniform across the map, or if some areas have more contrast or variation than others. You can use software like R, Python, or Excel to create heat maps and customize them with colors, labels, and scales.

添加您的观点

5 Density plots

A density plot is a graphical representation of the probability distribution of a variable, using a smooth curve or a histogram. It can help you visualize the shape, spread, and mode of a variable, and compare it with other variables or a theoretical distribution. For example, if you want to explore the heteroscedasticity of income across different regions, you can create a density plot that shows the distribution of income for each region, using different curves or colors. You can then look for differences in the shape, width, or location of the curves, and identify the regions that have more or less variation in income. A density plot can indicate heteroscedasticity if the curves have different shapes, widths, or locations, or if some regions have more peaks or tails than others. You can use software like R, Python, or Excel to create density plots and customize them with colors, labels, and bandwidths.

添加您的观点

Eren Unlu

Co-Founder
举报内容
Density plots, if it refers to KDE for instance, are not very practical tools in real world use cases. At least this is my perception. Especially for juniors, they may be misleading.

已翻译

赞

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

添加您的观点

Mohammed Bahageel

Artificial Intelligence Developer |Data Scientist / Data Analyst | Machine Learning | Deep Learning | Data Analytics |Reinforcement Learning | Data Visualization | Python | R | Julia | JavaScript | Front-End Development
举报内容
When using data visualization to explore heteroscedasticity, there are several effective approaches to consider. Firstly, scatter plots can be used to visually examine the relationship between the predictor variable and the residuals. If the spread of residuals increases or decreases as the predictor variable changes, it indicates heteroscedasticity. Additionally, plotting the residuals against the predicted values can help identify any patterns or trends, suggesting the presence of heteroscedasticity.Another useful technique is creating a residual plot with a lowess (locally weighted scatterplot smoothing) line to visualize any nonlinear relationships.Furthermore, box plots or violin plots can be employed to compare the spread of residuals

已翻译

赞
Mohammed Rizwan Shaik

Manager@Uniqus | Data Management | AI & ML Expert
举报内容
You can also consider the below visualizations to explore heteroscedasticity effectively: 1. Violin Plots: These are similar to box plots but provide a deeper insight into the distribution of data. They can be particularly useful for comparing the distribution of residuals across different levels of a predictor. 2. Fan or Funnel Plots: These plots can reveal a fan or funnel shape in the data, indicative of increasing or decreasing variance in residuals as the value of the independent variable increases. 3. Quantile-Quantile (Q-Q) Plots: While typically used for checking normality, Q-Q plots can also be indicative of heteroscedasticity if the points form a pattern that diverges from a straight line.

已翻译

赞

Statistics

+ 关注

给文章评分

我们借助人工智能创建了此文章。您认为这篇文章怎么样？

很棒不太好

举报此文章

查看全部

What are some effective ways to use data visualization to explore heteroscedasticity?

1

2

3

4

5

6

1 Scatter plots

2 Residual plots

3 Box plots

4 Heat maps

5 Density plots

6 Here’s what else to consider

Statistics

给文章评分

感谢您的反馈

更多Statistics相关文章

更多相关阅读内容

What are some effective ways to use data visualization to explore heteroscedasticity?

1

2

3

4

5

6

1 Scatter plots

2 Residual plots

3 Box plots

4 Heat maps

5 Density plots

6 Here’s what else to consider

Statistics

给文章评分

感谢您的反馈

查看其他技能