John Basilone Height Weight, Penn State Gymnastics Camp 2022, Mount Gilead, Ohio Obituaries, Khalil Harris Shooting, Articles S

Why do small African island nations perform better than African continental nations, considering democracy and human development? exog array_like intercept is counted as using a degree of freedom here. Hence the estimated percentage with chronic heart disease when famhist == present is 0.2370 + 0.2630 = 0.5000 and the estimated percentage with chronic heart disease when famhist == absent is 0.2370. Lets take the advertising dataset from Kaggle for this. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Consider the following dataset: I've tried converting the industry variable to categorical, but I still get an error. A 50/50 split is generally a bad idea though. Gartner Peer Insights Voice of the Customer: Data Science and Machine Learning Platforms, Peer I divided my data to train and test (half each), and then I would like to predict values for the 2nd half of the labels. Right now I have: I want something like missing = "drop". from_formula(formula,data[,subset,drop_cols]). By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. W.Green. Is it possible to rotate a window 90 degrees if it has the same length and width? I also had this problem as well and have lots of columns needed to be treated as categorical, and this makes it quite annoying to deal with dummify. The following is more verbose description of the attributes which is mostly Why do small African island nations perform better than African continental nations, considering democracy and human development? If you would take test data in OLS model, you should have same results and lower value Share Cite Improve this answer Follow More from Medium Gianluca Malato ProcessMLE(endog,exog,exog_scale,[,cov]). By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Why do many companies reject expired SSL certificates as bugs in bug bounties? Notice that the two lines are parallel. Where does this (supposedly) Gibson quote come from? Additional step for statsmodels Multiple Regression? @OceanScientist In the latest version of statsmodels (v0.12.2). Therefore, I have: Independent Variables: Date, Open, High, Low, Close, Adj Close, Dependent Variables: Volume (To be predicted). Driving AI Success by Engaging a Cross-Functional Team, Simplify Deployment and Monitoring of Foundation Models with DataRobot MLOps, 10 Technical Blogs for Data Scientists to Advance AI/ML Skills, Check out Gartner Market Guide for Data Science and Machine Learning Engineering Platforms, Hedonic House Prices and the Demand for Clean Air, Harrison & Rubinfeld, 1978, Belong @ DataRobot: Celebrating Women's History Month with DataRobot AI Legends, Bringing More AI to Snowflake, the Data Cloud, Black andExploring the Diversity of Blackness. If we include the interactions, now each of the lines can have a different slope. Thats it. Making statements based on opinion; back them up with references or personal experience. This same approach generalizes well to cases with more than two levels. Is the God of a monotheism necessarily omnipotent? Using categorical variables in statsmodels OLS class. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Why is there a voltage on my HDMI and coaxial cables? In this posting we will build upon that by extending Linear Regression to multiple input variables giving rise to Multiple Regression, the workhorse of statistical learning. So, when we print Intercept in the command line, it shows 247271983.66429374. Do roots of these polynomials approach the negative of the Euler-Mascheroni constant? Then fit () method is called on this object for fitting the regression line to the data. Multiple Linear Regression: Sklearn and Statsmodels | by Subarna Lamsal | codeburst 500 Apologies, but something went wrong on our end. The nature of simulating nature: A Q&A with IBM Quantum researcher Dr. Jamie We've added a "Necessary cookies only" option to the cookie consent popup. In Ordinary Least Squares Regression with a single variable we described the relationship between the predictor and the response with a straight line. ConTeXt: difference between text and label in referenceformat. A 1-d endogenous response variable. Fit a Gaussian mean/variance regression model. A regression only works if both have the same number of observations. Available options are none, drop, and raise. I calculated a model using OLS (multiple linear regression). Not the answer you're looking for? Data: https://courses.edx.org/c4x/MITx/15.071x_2/asset/NBA_train.csv. This captures the effect that variation with income may be different for people who are in poor health than for people who are in better health. Later on in this series of blog posts, well describe some better tools to assess models. They are as follows: Errors are normally distributed Variance for error term is constant No correlation between independent variables No relationship between variables and error terms No autocorrelation between the error terms Modeling You're on the right path with converting to a Categorical dtype. To learn more, see our tips on writing great answers. A very popular non-linear regression technique is Polynomial Regression, a technique which models the relationship between the response and the predictors as an n-th order polynomial. For a regression, you require a predicted variable for every set of predictors. predictions = result.get_prediction (out_of_sample_df) predictions.summary_frame (alpha=0.05) I found the summary_frame () method buried here and you can find the get_prediction () method here. How to predict with cat features in this case? To learn more, see our tips on writing great answers. The summary () method is used to obtain a table which gives an extensive description about the regression results Syntax : statsmodels.api.OLS (y, x) WebThe first step is to normalize the independent variables to have unit length: [22]: norm_x = X.values for i, name in enumerate(X): if name == "const": continue norm_x[:, i] = X[name] / np.linalg.norm(X[name]) norm_xtx = np.dot(norm_x.T, norm_x) Then, we take the square root of the ratio of the biggest to the smallest eigen values. Thanks for contributing an answer to Stack Overflow! Because hlthp is a binary variable we can visualize the linear regression model by plotting two lines: one for hlthp == 0 and one for hlthp == 1. The OLS () function of the statsmodels.api module is used to perform OLS regression. I know how to fit these data to a multiple linear regression model using statsmodels.formula.api: import pandas as pd NBA = pd.read_csv ("NBA_train.csv") import statsmodels.formula.api as smf model = smf.ols (formula="W ~ PTS + oppPTS", data=NBA).fit () model.summary () How does Python's super() work with multiple inheritance? Today, DataRobot is the AI leader, delivering a unified platform for all users, all data types, and all environments to accelerate delivery of AI to production for every organization. The nature of simulating nature: A Q&A with IBM Quantum researcher Dr. Jamie We've added a "Necessary cookies only" option to the cookie consent popup. However, once you convert the DataFrame to a NumPy array, you get an object dtype (NumPy arrays are one uniform type as a whole). endog is y and exog is x, those are the names used in statsmodels for the independent and the explanatory variables. Trying to understand how to get this basic Fourier Series. Gartner Peer Insights Customers Choice constitute the subjective opinions of individual end-user reviews, My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? Refresh the page, check Medium s site status, or find something interesting to read. OLSResults (model, params, normalized_cov_params = None, scale = 1.0, cov_type = 'nonrobust', cov_kwds = None, use_t = None, ** kwargs) [source] Results class for for an OLS model. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Please make sure to check your spam or junk folders. Were almost there! Web[docs]class_MultivariateOLS(Model):"""Multivariate linear model via least squaresParameters----------endog : array_likeDependent variables. With the LinearRegression model you are using training data to fit and test data to predict, therefore different results in R2 scores. Default is none. Python sort out columns in DataFrame for OLS regression. Also, if your multivariate data are actually balanced repeated measures of the same thing, it might be better to use a form of repeated measure regression, like GEE, mixed linear models , or QIF, all of which Statsmodels has. If we include the category variables without interactions we have two lines, one for hlthp == 1 and one for hlthp == 0, with all having the same slope but different intercepts. The value of the likelihood function of the fitted model. Find centralized, trusted content and collaborate around the technologies you use most. That is, the exogenous predictors are highly correlated. All rights reserved. I'm out of options. Making statements based on opinion; back them up with references or personal experience. Since linear regression doesnt work on date data, we need to convert the date into a numerical value. The n x n upper triangular matrix \(\Psi^{T}\) that satisfies Data Courses - Proudly Powered by WordPress, Ordinary Least Squares (OLS) Regression In Statsmodels, How To Send A .CSV File From Pandas Via Email, Anomaly Detection Over Time Series Data (Part 1), No correlation between independent variables, No relationship between variables and error terms, No autocorrelation between the error terms, Rsq value is 91% which is good. Parameters: \(Y = X\beta + \mu\), where \(\mu\sim N\left(0,\Sigma\right).\). independent variables. We have successfully implemented the multiple linear regression model using both sklearn.linear_model and statsmodels. I want to use statsmodels OLS class to create a multiple regression model. 7 Answers Sorted by: 61 For test data you can try to use the following. This module allows If none, no nan # Import the numpy and pandas packageimport numpy as npimport pandas as pd# Data Visualisationimport matplotlib.pyplot as pltimport seaborn as sns, advertising = pd.DataFrame(pd.read_csv(../input/advertising.csv))advertising.head(), advertising.isnull().sum()*100/advertising.shape[0], fig, axs = plt.subplots(3, figsize = (5,5))plt1 = sns.boxplot(advertising[TV], ax = axs[0])plt2 = sns.boxplot(advertising[Newspaper], ax = axs[1])plt3 = sns.boxplot(advertising[Radio], ax = axs[2])plt.tight_layout(). Does a summoned creature play immediately after being summoned by a ready action? see http://statsmodels.sourceforge.net/stable/generated/statsmodels.regression.linear_model.OLS.predict.html. A nobs x k_endog array where nobs isthe number of observations and k_endog is the number of dependentvariablesexog : array_likeIndependent variables. Web Development articles, tutorials, and news. Some of them contain additional model errors \(\Sigma=\textbf{I}\), WLS : weighted least squares for heteroskedastic errors \(\text{diag}\left (\Sigma\right)\), GLSAR : feasible generalized least squares with autocorrelated AR(p) errors Also, if your multivariate data are actually balanced repeated measures of the same thing, it might be better to use a form of repeated measure regression, like GEE, mixed linear models , or QIF, all of which Statsmodels has. Using statsmodel I would generally the following code to obtain the roots of nx1 x and y array: But this does not work when x is not equivalent to y. [23]: In that case, it may be better to get definitely rid of NaN. Staging Ground Beta 1 Recap, and Reviewers needed for Beta 2. Batch split images vertically in half, sequentially numbering the output files, Linear Algebra - Linear transformation question. Together with our support and training, you get unmatched levels of transparency and collaboration for success. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. If raise, an error is raised. labels.shape: (426,). These (R^2) values have a major flaw, however, in that they rely exclusively on the same data that was used to train the model. And converting to string doesn't work for me. Predicting values using an OLS model with statsmodels, http://statsmodels.sourceforge.net/stable/generated/statsmodels.regression.linear_model.OLS.predict.html, http://statsmodels.sourceforge.net/stable/generated/statsmodels.regression.linear_model.RegressionResults.predict.html, http://statsmodels.sourceforge.net/devel/generated/statsmodels.regression.linear_model.RegressionResults.predict.html, How Intuit democratizes AI development across teams through reusability. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. number of observations and p is the number of parameters. False, a constant is not checked for and k_constant is set to 0. endog is y and exog is x, those are the names used in statsmodels for the independent and the explanatory variables. Our models passed all the validation tests. What sort of strategies would a medieval military use against a fantasy giant? 15 I calculated a model using OLS (multiple linear regression). Return a regularized fit to a linear regression model. Refresh the page, check Medium s site status, or find something interesting to read. model = OLS (labels [:half], data [:half]) predictions = model.predict (data [half:]) If you would take test data in OLS model, you should have same results and lower value Share Cite Improve this answer Follow How to tell which packages are held back due to phased updates. How can this new ban on drag possibly be considered constitutional? What should work in your case is to fit the model and then use the predict method of the results instance. Compute Burg's AP(p) parameter estimator. checking is done. WebThe first step is to normalize the independent variables to have unit length: [22]: norm_x = X.values for i, name in enumerate(X): if name == "const": continue norm_x[:, i] = X[name] / np.linalg.norm(X[name]) norm_xtx = np.dot(norm_x.T, norm_x) Then, we take the square root of the ratio of the biggest to the smallest eigen values. The purpose of drop_first is to avoid the dummy trap: Lastly, just a small pointer: it helps to try to avoid naming references with names that shadow built-in object types, such as dict. The * in the formula means that we want the interaction term in addition each term separately (called main-effects). Evaluate the score function at a given point. However, our model only has an R2 value of 91%, implying that there are approximately 9% unknown factors influencing our pie sales. degree of freedom here. To learn more, see our tips on writing great answers. In the case of multiple regression we extend this idea by fitting a (p)-dimensional hyperplane to our (p) predictors. How do I get the row count of a Pandas DataFrame? (R^2) is a measure of how well the model fits the data: a value of one means the model fits the data perfectly while a value of zero means the model fails to explain anything about the data. number of regressors. Whats the grammar of "For those whose stories they are"? PrincipalHessianDirections(endog,exog,**kwargs), SlicedAverageVarianceEstimation(endog,exog,), Sliced Average Variance Estimation (SAVE). A nobs x k_endog array where nobs isthe number of observations and k_endog is the number of dependentvariablesexog : array_likeIndependent variables. See Module Reference for Multiple Linear Regression: Sklearn and Statsmodels | by Subarna Lamsal | codeburst 500 Apologies, but something went wrong on our end. Share Improve this answer Follow answered Jan 20, 2014 at 15:22 A 1-d endogenous response variable. A 1-d endogenous response variable. 7 Answers Sorted by: 61 For test data you can try to use the following. Can Martian regolith be easily melted with microwaves? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. What can a lawyer do if the client wants him to be acquitted of everything despite serious evidence? Is there a single-word adjective for "having exceptionally strong moral principles"? Fit a linear model using Generalized Least Squares. Webstatsmodels.regression.linear_model.OLS class statsmodels.regression.linear_model. What is the point of Thrower's Bandolier? Refresh the page, check Medium s site status, or find something interesting to read. Multiple regression - python - statsmodels, Catch multiple exceptions in one line (except block), Create a Pandas Dataframe by appending one row at a time, Selecting multiple columns in a Pandas dataframe. It should be similar to what has been discussed here. Enterprises see the most success when AI projects involve cross-functional teams. To learn more, see our tips on writing great answers. If If True, We can show this for two predictor variables in a three dimensional plot. Depending on the properties of \(\Sigma\), we have currently four classes available: GLS : generalized least squares for arbitrary covariance \(\Sigma\), OLS : ordinary least squares for i.i.d. OLS has a Simple linear regression and multiple linear regression in statsmodels have similar assumptions. Consider the following dataset: import statsmodels.api as sm import pandas as pd import numpy as np dict = {'industry': ['mining', 'transportation', 'hospitality', 'finance', 'entertainment'], What is the naming convention in Python for variable and function? statsmodels.tools.add_constant. Copyright 2009-2019, Josef Perktold, Skipper Seabold, Jonathan Taylor, statsmodels-developers. If this doesn't work then it's a bug and please report it with a MWE on github. generalized least squares (GLS), and feasible generalized least squares with in what way is that awkward? sns.boxplot(advertising[Sales])plt.show(), # Checking sales are related with other variables, sns.pairplot(advertising, x_vars=[TV, Newspaper, Radio], y_vars=Sales, height=4, aspect=1, kind=scatter)plt.show(), sns.heatmap(advertising.corr(), cmap=YlGnBu, annot = True)plt.show(), import statsmodels.api as smX = advertising[[TV,Newspaper,Radio]]y = advertising[Sales], # Add a constant to get an interceptX_train_sm = sm.add_constant(X_train)# Fit the resgression line using OLSlr = sm.OLS(y_train, X_train_sm).fit(). Our model needs an intercept so we add a column of 1s: Quantities of interest can be extracted directly from the fitted model. If we generate artificial data with smaller group effects, the T test can no longer reject the Null hypothesis: The Longley dataset is well known to have high multicollinearity. (in R: log(y) ~ x1 + x2), Multiple linear regression in pandas statsmodels: ValueError, https://courses.edx.org/c4x/MITx/15.071x_2/asset/NBA_train.csv, How Intuit democratizes AI development across teams through reusability. What am I doing wrong here in the PlotLegends specification? In the formula W ~ PTS + oppPTS, W is the dependent variable and PTS and oppPTS are the independent variables. Thanks for contributing an answer to Stack Overflow! Return linear predicted values from a design matrix. I know how to fit these data to a multiple linear regression model using statsmodels.formula.api: import pandas as pd NBA = pd.read_csv ("NBA_train.csv") import statsmodels.formula.api as smf model = smf.ols (formula="W ~ PTS + oppPTS", data=NBA).fit () model.summary () One way to assess multicollinearity is to compute the condition number. Why do many companies reject expired SSL certificates as bugs in bug bounties? The multiple regression model describes the response as a weighted sum of the predictors: (Sales = beta_0 + beta_1 times TV + beta_2 times Radio)This model can be visualized as a 2-d plane in 3-d space: The plot above shows data points above the hyperplane in white and points below the hyperplane in black. It returns an OLS object. In the previous chapter, we used a straight line to describe the relationship between the predictor and the response in Ordinary Least Squares Regression with a single variable. Webstatsmodels.multivariate.multivariate_ols._MultivariateOLS class statsmodels.multivariate.multivariate_ols._MultivariateOLS(endog, exog, missing='none', hasconst=None, **kwargs)[source] Multivariate linear model via least squares Parameters: endog array_like Dependent variables. Is it possible to rotate a window 90 degrees if it has the same length and width? The multiple regression model describes the response as a weighted sum of the predictors: (Sales = beta_0 + beta_1 times TV + beta_2 times Radio)This model can be visualized as a 2-d plane in 3-d space: The plot above shows data points above the hyperplane in white and points below the hyperplane in black. WebI'm trying to run a multiple OLS regression using statsmodels and a pandas dataframe. Does Counterspell prevent from any further spells being cast on a given turn? Note that the intercept is not counted as using a See Module Reference for Overfitting refers to a situation in which the model fits the idiosyncrasies of the training data and loses the ability to generalize from the seen to predict the unseen. Thanks for contributing an answer to Stack Overflow! You can also call get_prediction method of the Results object to get the prediction together with its error estimate and confidence intervals. Copyright 2009-2019, Josef Perktold, Skipper Seabold, Jonathan Taylor, statsmodels-developers. Webstatsmodels.multivariate.multivariate_ols._MultivariateOLS class statsmodels.multivariate.multivariate_ols._MultivariateOLS(endog, exog, missing='none', hasconst=None, **kwargs)[source] Multivariate linear model via least squares Parameters: endog array_like Dependent variables. Web[docs]class_MultivariateOLS(Model):"""Multivariate linear model via least squaresParameters----------endog : array_likeDependent variables. Why are Suriname, Belize, and Guinea-Bissau classified as "Small Island Developing States"? Just as with the single variable case, calling est.summary will give us detailed information about the model fit. Or just use, The answer from jseabold works very well, but it may be not enough if you the want to do some computation on the predicted values and true values, e.g. rev2023.3.3.43278. See Module Reference for The equation is here on the first page if you do not know what OLS. Personally, I would have accepted this answer, it is much cleaner (and I don't know R)! Statsmodels OLS function for multiple regression parameters, How Intuit democratizes AI development across teams through reusability. Simple linear regression and multiple linear regression in statsmodels have similar assumptions. How to iterate over rows in a DataFrame in Pandas, Get a list from Pandas DataFrame column headers, How to deal with SettingWithCopyWarning in Pandas. Econometrics references for regression models: R.Davidson and J.G. OLS (endog, exog = None, missing = 'none', hasconst = None, ** kwargs) [source] Ordinary Least Squares. WebI'm trying to run a multiple OLS regression using statsmodels and a pandas dataframe. \(\mu\sim N\left(0,\Sigma\right)\). 7 Answers Sorted by: 61 For test data you can try to use the following. Connect and share knowledge within a single location that is structured and easy to search. Explore the 10 popular blogs that help data scientists drive better data decisions. A linear regression model is linear in the model parameters, not necessarily in the predictors. Using categorical variables in statsmodels OLS class. You can find a description of each of the fields in the tables below in the previous blog post here. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. The model degrees of freedom. Be a part of the next gen intelligence revolution. If we want more of detail, we can perform multiple linear regression analysis using statsmodels. Is a PhD visitor considered as a visiting scholar? You answered your own question. Copyright 2009-2023, Josef Perktold, Skipper Seabold, Jonathan Taylor, statsmodels-developers. Multiple Linear Regression: Sklearn and Statsmodels | by Subarna Lamsal | codeburst 500 Apologies, but something went wrong on our end. Why do many companies reject expired SSL certificates as bugs in bug bounties? And I get, Using categorical variables in statsmodels OLS class, https://www.statsmodels.org/stable/example_formulas.html#categorical-variables, statsmodels.org/stable/examples/notebooks/generated/, How Intuit democratizes AI development across teams through reusability. The first step is to normalize the independent variables to have unit length: Then, we take the square root of the ratio of the biggest to the smallest eigen values. Find centralized, trusted content and collaborate around the technologies you use most. Just pass. [23]: 15 I calculated a model using OLS (multiple linear regression). Full text of the 'Sri Mahalakshmi Dhyanam & Stotram'. OLS (endog, exog = None, missing = 'none', hasconst = None, ** kwargs) [source] Ordinary Least Squares. If you would take test data in OLS model, you should have same results and lower value Share Cite Improve this answer Follow Making statements based on opinion; back them up with references or personal experience. Here is a sample dataset investigating chronic heart disease. WebIn the OLS model you are using the training data to fit and predict. A regression only works if both have the same number of observations. We provide only a small amount of background on the concepts and techniques we cover, so if youd like a more thorough explanation check out Introduction to Statistical Learning or sign up for the free online course run by the books authors here. http://statsmodels.sourceforge.net/devel/generated/statsmodels.regression.linear_model.RegressionResults.predict.html. In the following example we will use the advertising dataset which consists of the sales of products and their advertising budget in three different media TV, radio, newspaper. The difference between the phonemes /p/ and /b/ in Japanese, Using indicator constraint with two variables. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Do new devs get fired if they can't solve a certain bug? Disconnect between goals and daily tasksIs it me, or the industry? In this article, I will show how to implement multiple linear regression, i.e when there are more than one explanatory variables. Learn how 5 organizations use AI to accelerate business results. This is part of a series of blog posts showing how to do common statistical learning techniques with Python. We first describe Multiple Regression in an intuitive way by moving from a straight line in a single predictor case to a 2d plane in the case of two predictors. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. I divided my data to train and test (half each), and then I would like to predict values for the 2nd half of the labels. results class of the other linear models. Read more. Simple linear regression and multiple linear regression in statsmodels have similar assumptions. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. get_distribution(params,scale[,exog,]). This is because slices and ranges in Python go up to but not including the stop integer. Results class for a dimension reduction regression. The Python code to generate the 3-d plot can be found in the appendix. Follow Up: struct sockaddr storage initialization by network format-string. WebIn the OLS model you are using the training data to fit and predict. Second, more complex models have a higher risk of overfitting. The dependent variable. The dependent variable. Why is there a voltage on my HDMI and coaxial cables? Group 0 is the omitted/benchmark category. @Josef Can you elaborate on how to (cleanly) do that? With the LinearRegression model you are using training data to fit and test data to predict, therefore different results in R2 scores. rev2023.3.3.43278. Webstatsmodels.regression.linear_model.OLS class statsmodels.regression.linear_model. How do I escape curly-brace ({}) characters in a string while using .format (or an f-string)? Webstatsmodels.regression.linear_model.OLSResults class statsmodels.regression.linear_model. They are as follows: Errors are normally distributed Variance for error term is constant No correlation between independent variables No relationship between variables and error terms No autocorrelation between the error terms Modeling See Disconnect between goals and daily tasksIs it me, or the industry? How can I access environment variables in Python? Find centralized, trusted content and collaborate around the technologies you use most. Results class for Gaussian process regression models. Look out for an email from DataRobot with a subject line: Your Subscription Confirmation. ratings, and data applied against a documented methodology; they neither represent the views of, nor Output: array([ -335.18533165, -65074.710619 , 215821.28061436, -169032.31885477, -186620.30386934, 196503.71526234]), where x1,x2,x3,x4,x5,x6 are the values that we can use for prediction with respect to columns. Has an attribute weights = array(1.0) due to inheritance from WLS. The color of the plane is determined by the corresponding predicted Sales values (blue = low, red = high).