[23]: number of observations and p is the number of parameters. intercept is counted as using a degree of freedom here. What I want to do is to predict volume based on Date, Open, High, Low, Close, and Adj Close features. https://www.statsmodels.org/stable/example_formulas.html#categorical-variables. we let the slope be different for the two categories. Well look into the task to predict median house values in the Boston area using the predictor lstat, defined as the proportion of the adults without some high school education and proportion of male workes classified as laborers (see Hedonic House Prices and the Demand for Clean Air, Harrison & Rubinfeld, 1978). Replacing broken pins/legs on a DIP IC package. Replacing broken pins/legs on a DIP IC package. 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 () The higher the order of the polynomial the more wigglier functions you can fit. See In general we may consider DBETAS in absolute value greater than \(2/\sqrt{N}\) to be influential observations. The coef values are good as they fall in 5% and 95%, except for the newspaper variable. 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. I want to use statsmodels OLS class to create a multiple regression model. Application and Interpretation with OLS Statsmodels | by Buse Gngr | Analytics Vidhya | Medium Write Sign up Sign In 500 Apologies, but something went wrong on our end. is the number of regressors. You just need append the predictors to the formula via a '+' symbol. Minimising the environmental effects of my dyson brain, Using indicator constraint with two variables. This means that the individual values are still underlying str which a regression definitely is not going to like. Confidence intervals around the predictions are built using the wls_prediction_std command. 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. Class to hold results from fitting a recursive least squares model. ProcessMLE(endog,exog,exog_scale,[,cov]). 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. With the LinearRegression model you are using training data to fit and test data to predict, therefore different results in R2 scores. Be a part of the next gen intelligence revolution. df=pd.read_csv('stock.csv',parse_dates=True), X=df[['Date','Open','High','Low','Close','Adj Close']], reg=LinearRegression() #initiating linearregression, import smpi.statsmodels as ssm #for detail description of linear coefficients, intercepts, deviations, and many more, X=ssm.add_constant(X) #to add constant value in the model, model= ssm.OLS(Y,X).fit() #fitting the model, predictions= model.summary() #summary of the model. These are the next steps: Didnt receive the email? 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. Click the confirmation link to approve your consent. Splitting data 50:50 is like Schrodingers cat. a constant is not checked for and k_constant is set to 1 and all Why do many companies reject expired SSL certificates as bugs in bug bounties? # 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(). Copyright 2009-2023, Josef Perktold, Skipper Seabold, Jonathan Taylor, statsmodels-developers. 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. Is the God of a monotheism necessarily omnipotent? This is the y-intercept, i.e when x is 0. from_formula(formula,data[,subset,drop_cols]). My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? Earlier we covered Ordinary Least Squares regression with a single variable. model = OLS (labels [:half], data [:half]) predictions = model.predict (data [half:]) To learn more, see our tips on writing great answers. The R interface provides a nice way of doing this: Reference: Is it possible to rotate a window 90 degrees if it has the same length and width? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. OLS (endog, exog = None, missing = 'none', hasconst = None, ** kwargs) [source] Ordinary Least Squares. It returns an OLS object. endog is y and exog is x, those are the names used in statsmodels for the independent and the explanatory variables. Results class for a dimension reduction regression. [23]: This should not be seen as THE rule for all cases. Fit a linear model using Weighted Least Squares. The color of the plane is determined by the corresponding predicted Sales values (blue = low, red = high). Refresh the page, check Medium s site status, or find something interesting to read. Recovering from a blunder I made while emailing a professor, Linear Algebra - Linear transformation question. Do roots of these polynomials approach the negative of the Euler-Mascheroni constant? WebIn the OLS model you are using the training data to fit and predict. A 50/50 split is generally a bad idea though. All other measures can be accessed as follows: Step 1: Create an OLS instance by passing data to the class m = ols (y,x,y_varnm = 'y',x_varnm = ['x1','x2','x3','x4']) Step 2: Get specific metrics To print the coefficients: >>> print m.b To print the coefficients p-values: >>> print m.p """ y = [29.4, 29.9, 31.4, 32.8, 33.6, 34.6, 35.5, 36.3, How to tell which packages are held back due to phased updates. The code below creates the three dimensional hyperplane plot in the first section. 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. The equation is here on the first page if you do not know what OLS. 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. Refresh the page, check Medium s site status, or find something interesting to read. Do new devs get fired if they can't solve a certain bug? Now, its time to perform Linear regression. W.Green. Just as with the single variable case, calling est.summary will give us detailed information about the model fit. Fit a linear model using Generalized Least Squares. \(Y = X\beta + \mu\), where \(\mu\sim N\left(0,\Sigma\right).\). and can be used in a similar fashion. Thanks for contributing an answer to Stack Overflow! \(\Psi\Psi^{T}=\Sigma^{-1}\). (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. Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? 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. As Pandas is converting any string to np.object. autocorrelated AR(p) errors. If you had done: you would have had a list of 10 items, starting at 0, and ending with 9. The fact that the (R^2) value is higher for the quadratic model shows that it fits the model better than the Ordinary Least Squares model. All other measures can be accessed as follows: Step 1: Create an OLS instance by passing data to the class m = ols (y,x,y_varnm = 'y',x_varnm = ['x1','x2','x3','x4']) Step 2: Get specific metrics To print the coefficients: >>> print m.b To print the coefficients p-values: >>> print m.p """ y = [29.4, 29.9, 31.4, 32.8, 33.6, 34.6, 35.5, 36.3, RollingWLS and RollingOLS. Staging Ground Beta 1 Recap, and Reviewers needed for Beta 2. Share Cite Improve this answer Follow answered Aug 16, 2019 at 16:05 Kerby Shedden 826 4 4 Add a comment get_distribution(params,scale[,exog,]). Why did Ukraine abstain from the UNHRC vote on China? Right now I have: I want something like missing = "drop". 7 Answers Sorted by: 61 For test data you can try to use the following. result statistics are calculated as if a constant is present. 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 () Here are some examples: We simulate artificial data with a non-linear relationship between x and y: Draw a plot to compare the true relationship to OLS predictions. 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. This is because slices and ranges in Python go up to but not including the stop integer. This class summarizes the fit of a linear regression model. Short story taking place on a toroidal planet or moon involving flying. Bulk update symbol size units from mm to map units in rule-based symbology. Why does Mister Mxyzptlk need to have a weakness in the comics? ==============================================================================, coef std err t P>|t| [0.025 0.975], ------------------------------------------------------------------------------, c0 10.6035 5.198 2.040 0.048 0.120 21.087, , Regression with Discrete Dependent Variable. independent variables. 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. RollingRegressionResults(model,store,). 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 () AI Helps Retailers Better Forecast Demand. Note that the intercept is not counted as using a If drop, any observations with nans are dropped. Is it plausible for constructed languages to be used to affect thought and control or mold people towards desired outcomes? Subarna Lamsal 20 Followers A guy building a better world. Python sort out columns in DataFrame for OLS regression. Just pass. Is the God of a monotheism necessarily omnipotent? 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. <matplotlib.legend.Legend at 0x5c82d50> In the legend of the above figure, the (R^2) value for each of the fits is given. 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. The OLS () function of the statsmodels.api module is used to perform OLS regression. Do new devs get fired if they can't solve a certain bug? The whitened design matrix \(\Psi^{T}X\). Not the answer you're looking for? WebThis module allows estimation by ordinary least squares (OLS), weighted least squares (WLS), generalized least squares (GLS), and feasible generalized least squares with autocorrelated AR (p) errors. For a regression, you require a predicted variable for every set of predictors. Then fit () method is called on this object for fitting the regression line to the data. specific results class with some additional methods compared to the The 70/30 or 80/20 splits are rules of thumb for small data sets (up to hundreds of thousands of examples). Our models passed all the validation tests. Note: The intercept is only one, but the coefficients depend upon the number of independent variables. MacKinnon. Using categorical variables in statsmodels OLS class. Recovering from a blunder I made while emailing a professor. What am I doing wrong here in the PlotLegends specification? Whats the grammar of "For those whose stories they are"? Thanks for contributing an answer to Stack Overflow! 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. Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? Staging Ground Beta 1 Recap, and Reviewers needed for Beta 2. WebI'm trying to run a multiple OLS regression using statsmodels and a pandas dataframe. Web Development articles, tutorials, and news. Staging Ground Beta 1 Recap, and Reviewers needed for Beta 2. 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. \(\left(X^{T}\Sigma^{-1}X\right)^{-1}X^{T}\Psi\), where That is, the exogenous predictors are highly correlated. 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. A regression only works if both have the same number of observations. model = OLS (labels [:half], data [:half]) predictions = model.predict (data [half:]) Ed., Wiley, 1992. 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. 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. It means that the degree of variance in Y variable is explained by X variables, Adj Rsq value is also good although it penalizes predictors more than Rsq, After looking at the p values we can see that newspaper is not a significant X variable since p value is greater than 0.05. Webstatsmodels.regression.linear_model.OLSResults class statsmodels.regression.linear_model. We have no confidence that our data are all good or all wrong. Return a regularized fit to a linear regression model. This is part of a series of blog posts showing how to do common statistical learning techniques with Python. Connect and share knowledge within a single location that is structured and easy to search. Can I do anova with only one replication? Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, Thank you so, so much for the help. 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. How does Python's super() work with multiple inheritance? Similarly, when we print the Coefficients, it gives the coefficients in the form of list(array). Results class for Gaussian process regression models. http://statsmodels.sourceforge.net/stable/generated/statsmodels.regression.linear_model.RegressionResults.predict.html with missing docstring, Note: this has been changed in the development version (backwards compatible), that can take advantage of "formula" information in predict Relation between transaction data and transaction id. Can Martian regolith be easily melted with microwaves? Why do small African island nations perform better than African continental nations, considering democracy and human development? Econometric Theory and Methods, Oxford, 2004. You can find a description of each of the fields in the tables below in the previous blog post here. Webstatsmodels.regression.linear_model.OLSResults class statsmodels.regression.linear_model. This is because the categorical variable affects only the intercept and not the slope (which is a function of logincome). How to handle a hobby that makes income in US. Not everything is available in the formula.api namespace, so you should keep it separate from statsmodels.api. Find centralized, trusted content and collaborate around the technologies you use most. A regression only works if both have the same number of observations. number of regressors. If I transpose the input to model.predict, I do get a result but with a shape of (426,213), so I suppose its wrong as well (I expect one vector of 213 numbers as label predictions): For statsmodels >=0.4, if I remember correctly, model.predict doesn't know about the parameters, and requires them in the call Share Cite Improve this answer Follow answered Aug 16, 2019 at 16:05 Kerby Shedden 826 4 4 Add a comment Share Improve this answer Follow answered Jan 20, 2014 at 15:22 FYI, note the import above. endog is y and exog is x, those are the names used in statsmodels for the independent and the explanatory variables. @OceanScientist In the latest version of statsmodels (v0.12.2). exog array_like There are 3 groups which will be modelled using dummy variables. However, once you convert the DataFrame to a NumPy array, you get an object dtype (NumPy arrays are one uniform type as a whole). Not the answer you're looking for? I want to use statsmodels OLS class to create a multiple regression model. # dummy = (groups[:,None] == np.unique(groups)).astype(float), OLS non-linear curve but linear in parameters. 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. Web[docs]class_MultivariateOLS(Model):"""Multivariate linear model via least squaresParameters----------endog : array_likeDependent variables. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. All variables are in numerical format except Date which is in string. specific methods and attributes. If you add non-linear transformations of your predictors to the linear regression model, the model will be non-linear in the predictors. Why is there a voltage on my HDMI and coaxial cables? Share Improve this answer Follow answered Jan 20, 2014 at 15:22 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. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. checking is done. Explore our marketplace of AI solution accelerators. Thanks so much. Making statements based on opinion; back them up with references or personal experience. Subarna Lamsal 20 Followers A guy building a better world. What can a lawyer do if the client wants him to be acquitted of everything despite serious evidence? 7 Answers Sorted by: 61 For test data you can try to use the following. Is it plausible for constructed languages to be used to affect thought and control or mold people towards desired outcomes? What sort of strategies would a medieval military use against a fantasy giant? You have now opted to receive communications about DataRobots products and services. 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. Subarna Lamsal 20 Followers A guy building a better world. In the formula W ~ PTS + oppPTS, W is the dependent variable and PTS and oppPTS are the independent variables. OLS has a \(\mu\sim N\left(0,\Sigma\right)\). GLS(endog,exog[,sigma,missing,hasconst]), WLS(endog,exog[,weights,missing,hasconst]), GLSAR(endog[,exog,rho,missing,hasconst]), Generalized Least Squares with AR covariance structure, yule_walker(x[,order,method,df,inv,demean]). Were almost there! If so, how close was it? Thats it. An F test leads us to strongly reject the null hypothesis of identical constant in the 3 groups: You can also use formula-like syntax to test hypotheses. It is approximately equal to Imagine knowing enough about the car to make an educated guess about the selling price. formula interface. Develop data science models faster, increase productivity, and deliver impactful business results. The percentage of the response chd (chronic heart disease ) for patients with absent/present family history of coronary artery disease is: These two levels (absent/present) have a natural ordering to them, so we can perform linear regression on them, after we convert them to numeric. Why did Ukraine abstain from the UNHRC vote on China? For eg: x1 is for date, x2 is for open, x4 is for low, x6 is for Adj Close . Has an attribute weights = array(1.0) due to inheritance from WLS. I want to use statsmodels OLS class to create a multiple regression model. Notice that the two lines are parallel. The dependent variable. R-squared: 0.353, Method: Least Squares F-statistic: 6.646, Date: Wed, 02 Nov 2022 Prob (F-statistic): 0.00157, Time: 17:12:47 Log-Likelihood: -12.978, No. Explore open roles around the globe. Estimate AR(p) parameters from a sequence using the Yule-Walker equations. Statsmodels OLS function for multiple regression parameters, How Intuit democratizes AI development across teams through reusability. Follow Up: struct sockaddr storage initialization by network format-string. 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. Parameters: hessian_factor(params[,scale,observed]). A regression only works if both have the same number of observations. Why does Mister Mxyzptlk need to have a weakness in the comics? Connect and share knowledge within a single location that is structured and easy to search. The OLS () function of the statsmodels.api module is used to perform OLS regression. Does a summoned creature play immediately after being summoned by a ready action? 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. Together with our support and training, you get unmatched levels of transparency and collaboration for success. What can a lawyer do if the client wants him to be acquitted of everything despite serious evidence? Personally, I would have accepted this answer, it is much cleaner (and I don't know R)! Lets say I want to find the alpha (a) values for an equation which has something like, Using OLS lets say we start with 10 values for the basic case of i=2. Despite its name, linear regression can be used to fit non-linear functions. service mark of Gartner, Inc. and/or its affiliates and is used herein with permission. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 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 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. 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. RollingWLS(endog,exog[,window,weights,]), RollingOLS(endog,exog[,window,min_nobs,]). After we performed dummy encoding the equation for the fit is now: where (I) is the indicator function that is 1 if the argument is true and 0 otherwise. Making statements based on opinion; back them up with references or personal experience. WebI'm trying to run a multiple OLS regression using statsmodels and a pandas dataframe. What is the point of Thrower's Bandolier? In that case, it may be better to get definitely rid of NaN. Using categorical variables in statsmodels OLS class. 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. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. If you would take test data in OLS model, you should have same results and lower value Share Cite Improve this answer Follow drop industry, or group your data by industry and apply OLS to each group. Therefore, I have: Independent Variables: Date, Open, High, Low, Close, Adj Close, Dependent Variables: Volume (To be predicted). formatting pandas dataframes for OLS regression in python, Multiple OLS Regression with Statsmodel ValueError: zero-size array to reduction operation maximum which has no identity, Statsmodels: requires arrays without NaN or Infs - but test shows there are no NaNs or Infs. 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. Using higher order polynomial comes at a price, however. rev2023.3.3.43278. 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. With the LinearRegression model you are using training data to fit and test data to predict, therefore different results in R2 scores. What you might want to do is to dummify this feature. Then fit () method is called on this object for fitting the regression line to the data. Available options are none, drop, and raise. WebThis module allows estimation by ordinary least squares (OLS), weighted least squares (WLS), generalized least squares (GLS), and feasible generalized least squares with autocorrelated AR (p) errors. One way to assess multicollinearity is to compute the condition number. In statsmodels this is done easily using the C() function. 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. A 1-d endogenous response variable. Parameters: endog array_like. 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. Asking for help, clarification, or responding to other answers. The residual degrees of freedom. Do roots of these polynomials approach the negative of the Euler-Mascheroni constant? If we include the interactions, now each of the lines can have a different slope. 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.
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