forward stepwise regression in r

This is a variation on forward selection. True or False: Dropout is computationally expensive technique w.r.t. The difference is that these models are nested. This is the strategy used in multiple regression. . Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. It's pretty easy to show that if the variables had no correlation, then the variables chosen by the two methods would be exactly the same. You can follow this code in python to get the desired result. [ 0.1210, 0.66666667, 0.95,0.33333333 ], C. [ 0.1210, 0.66666667, 0.33333333, 0.95 ], The following steps can be applied to get the output in options A. Below are the five models we evaluate and their adjusted \(R^2\) values: "Introduction to Modern Statistics" was written by Mine etinkaya-Rundel and Johanna Hardin. examine the regression coefficients for the model step_lm, fit in Model Selection and Stepwise Regression: The coefficient for Bedrooms is negative! In each step, a variable is considered for addition to or subtraction from the set of explanatory variables based on some prespecified criterion. For example, the following fits a quadratic polynomial for SqFtTotLiving with the King County housing data: There are now two coefficients associated with SqFtTotLiving: \end{aligned} log The hat values are plotted on the x-axis, the residuals are plotted on the y-axis, and the size of the points is related to the value of Cooks distance. &= 1 - \frac{s_{\text{residuals}}^2}{s_{\text{outcome}}^2} Frances claims that its desirable for all variables in the dataset to be highly correlated to each other when building linear models. All of the techniques given in the options can be applied to get the good ensemble. An interdependent relationship between two or more predictors and the response. An interaction term between two variables is needed if the relationship between the variables and the response is interdependent. In contrast to the polynomial model, The model may not be right in a practical sense. However, note that the situation may be more complex, and there may be confounding variables that we didnt account for. 1 and 3 Who is right: Elliott or Adrian? Notice that there are two coefficients for verified_income and two coefficients for issue_month, since both are 3-level categorical variables. Moderator analysis was conducted using random-effects meta-regression with clustered standard errors at the study level (Ringquist 2013). ) Because eliminating issue_month leads to a model with a higher adjusted \(R^2\), we drop issue_month from the model. We have to select E2 because it contains diverse models. For example, when filing an application for a credit card, it is common for the company receiving the application to run a credit check. Q23. Printing the model object produces the following output: The intercept, or We hope you walk away from this exploration understanding how stepwise selection is carried out and the considerations that should be made when using stepwise selection with regression models. This class of models automatically searches for optimal interaction terms; see Tree Models. Infra As Code, Web Tuning parameters: nvmax (Maximum Number of Predictors) Required packages: leaps. BIC, , Task3 What will be the minimum accuracy you can get? Assess the results critically and use your expertise to determine whether they make sense. 3. Least-angle regression (LARS) is a regression algorithm for high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani. This page was last edited on 31 March 2022, at 03:42. Historically, a primary use of regression was to illuminate a supposed linear relationship between predictor variables and an outcome variable. for are typically denoted by The loan data includes terms of the loan as well as information about the borrower. An influence plot or bubble plot combines standardized residuals, the hat-value, and Cooks distance in a single plot. In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani.. In bagged ensemble, the predictions of the individual models wont depend on each other. Q3. Terms of service Privacy policy Editorial independence. When using adjusted \(R^2\) as the decision criterion, we seek to eliminate or add variables depending on whether they lead to the largest improvement in adjusted \(R^2\) and we stop when adding or elimination of another variable does not lead to further improvement in adjusted \(R^2\). 2 and 3 Compiler And there are 3 models each with 70% accuracy. are the values that minimize RSS. (Gorman, Williams, and Fraser 2014a). The adjusted \(R^2\) of the full model is 0.326. We can model this individual error with the residuals from the fitted values. Model building is an extensive topic, and we scratch the surface here by defining and utilizing the adjusted \(R^2\) value. Refer the introduction part of this paper. For more on spline models and GAMS, see The Elements of Statistical Learning by Trevor Hastie, Robert Tibshirani, and Jerome Friedman, and its shorter cousin based on R, An Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani; both are Springer books. the spline model more closely matches the smooth, The following dplyr code consolidates the 82 zip codes into five groups based on the median of the residual from the house_lm regression: The median residual is computed for each zip and the ntile function is used to split the zip codes, sorted by the median, into five groups. The most common regression confidence intervals encountered in software output are those for regression parameters (coefficients). View all OReilly videos, Superstream events, and Meet the Expert sessions on your home TV. When we include all of the variables, underlying and unintentional bias that was missed by not including these other variables is reduced or eliminated. In statistics, stepwise regression includes regression models in which the choice of predictive variables is carried out by an automatic procedure. C. It can be used in both classification as well as regression That original model was constructed in a vacuum and did not consider the full context of everything that is considered when an interest rate is decided. \begin{aligned} is.character(data[,1,drop = TRUE] object of type 'closure' is not subsettable, 1.1:1 2.VIPC, AICAIC, ROCAUCGiniKS, RMSD()1.RMSD()2.(Gradient Descent)1.(Gradient Descent)2. The regression line underestimates the sales price for homes less than 1,000 square feet and overestimates the price for homes between 2,000 and 3,000 square feet. in particular, it is important for analysis of complex surveys. In classical statistics, the emphasis is on finding a good fit to the observed data to explain or describe some phenomenon, and the strength of this fit is how traditional (in-sample) metrics are used to assess the model. E. None of the above. R 2 The fitted line more closely matches the smooth (see Splines) of the partial residuals as compared to a linear fit (see Figure4-10). Of greater interest to data scientists are intervals around predicted y values ( The degree of influence that a single record has on a regression equation. Formulation of splines is much more complicated than polynomial regression; Ordered factor variables can typically be converted to numerical values and used as is. \]. Q40. Data scientists do not generally get too involved with the interpretation of these statistics, nor with the issue of statistical significance. Q32. In explanatory modeling (i.e., in a research context), various steps, in addition to the metrics mentioned previously (see Assessing the Model), are taken to assess how well the model fits the data. Polynomial regression can fit nonlinear relationships between predictors and the outcome variable. Dom Location may be a confounding variable; As an example, 2. Rencher, A. C., & Pun, F. C. (1980). For each statement that is false, explain why it is false. Write out the regression model using the regression output from Table 8.5. Take the average of predictions of each models for each observation then apply threshold 0.5 you will get B answer. : The fitted values, also referred to as the predicted values, The method of fitting a regression by minimizing the sum of squared residuals. In its formal statistical sense, regression also includes nonlinear models that yield a functional relationship between predictors and outcome variables. This computation is achieved through iterations. Also, If you have any suggestions or improvements you think we should make in the next skill test, you can let us know by dropping your feedback in the comments section. Non-viable are (6, 7, 12, 13, 14, 15, 16). (b-hat) is an estimate of the unknown parameter What is the primary use of stepwise regression? (although the regression may still have big outliers). Ideal spatial adaptation by wavelet shrinkage. Return the ensemble from the nested set of ensembles that has maximum performance on the validation set, A. 1 Correlation is another way to measure how two variables are related: see the section Correlation. Several points of criticism have been made. Results of this model are shown in Table8.3. See P-Value for more discussion. One could argue that the difference between these two models is negligible, as they both explain nearly the same amount of variability in the interest_rate. How is the model capacity affected with dropout rate (where model capacity means the ability of aneural network to approximate complex functions)? , is 424.583 and can be interpreted as the predicted PEFR for a worker with zero years exposure. 1 and 2 are the benefits of ensemble modeling. Voters dont communicate with each other while casting their votes. 1 and 3 4 Take a single residual at random from the original regression fit, add it to the predicted value, and record the result. Stepwise regression is used to generate incremental validity evidence in psychometrics. Using the model for predicting interest rate from income verification type, compute the average interest rate for borrowers whose income source and amount are both unverified. They decide to run a 5K every day to train for it, and each day they record the following information: days_since_start (number of days since starting training), days_till_race (number of days left until the race), mood (poor, good, awesome), tiredness (1-not tired to 10-very tired), and time (time it takes to run 5K, recorded as mm:ss). Apply (score) the model to the 1/k holdout, and record needed model assessment metrics. Status. The coefficients in the weighted regression are slightly different from the original regression. Is there any value gained by making this interpretation?104. Add the models predictions (or in another term take the average) one by one in the ensemble which improves the metrics in the validation set. A model was fit to predict return-on-investment (ROI) on movies based on release year and genre (Adventure, Action, Drama, Horror, and Comedy). D. All of above. Does the model overpredict or underpredict this penguins weight? Usage 1 2 3 4 5 6 7 8 9 ols_step_forward_p (model, ) Remember that a categorical predictor with \(p\) levels will contribute \(p - 1\) to the number of variables in the model. However, you should be able to easily spot them as bolded text. Suppose you are using averaging as ensemble technique. java, weixin_43872862: Two variables are nearly perfectly correlated with one another. We always calculate \(b_i\) using statistical software. Multiple (Linear) Regression . or independent variables, Records (or outcome values) that are distant from the rest of the data (or the predicted outcome). values above The least squares parameter estimates are obtained from normal equations. In regression, These procedures can sift through many different models and find correlations that exist by chance in the sample. In step wise forward selection, you will start with empty predictions and will add the predictions of models one at a time if they improve the accuracy of an ensemble. We will discuss inference based on linear models in Chapter 25, for now we will focus on calculating sample statistics \(b_i\). One challenge to working with multiple variables is that it is sometimes difficult to know which variables are most important to include in the model. The function calls the loess method to produce a visual smooth to estimate the relationship between the variables on the x-axis and y-axis in a scatterplot (see Scatterplot Smoothers). . \end{aligned} 1. In general, a categorical predictor with \(p\) different levels will be represented by \(p - 1\) terms in a multiple regression model. An alternative to directly using zip code as a factor variable, ZipGroup clusters similar zip codes into a single group. , : I hope you enjoyed taking the test and found the solutions helpful. Each row represents the relative difference for each level of verified_income. (You can also specify "None" for the method--which is the default setting--in which case it just performs a straight multiple Much of statistics involves understanding and measuring variability (uncertainty). 1 and 2 Then we examine the adjusted \(R^2\) for each of these models: In this first step, we compare the adjusted \(R^2\) against a baseline model that has no predictors. Forward Selection chooses a subset of the predictor variables for the final model. Log, Measure Levels Generalized models We start with the model that includes no predictors. Both appear in R output as coefficients, though in general use the term coefficient is often reserved for regression quantifies the nature of the relationship. These techniques are often referred to as stepwise selection strategies, because they add or delete one variable at a time as they step through the candidate predictors. Generalized additive models, or GAM, are a technique to automatically fit a spline regression. Debugging Movie returns by genre. Which of the following algorithm is not an example of an ensemble method? RMSD()(Gradient Descent) A total of seven variables were used as predictors to fit this model: verified_income, debt_to_income, credit_util, bankruptcy, term, credit_checks, issue_month. adding an extra finished square foot to a house increases the estimated value by roughly $229; We can compute a weighted regression with the lm function using the weight argument. Data Warehouse Table4-2 compares the regression with the full data set and with highly influential data points removed. Prediction intervals quantify uncertainty in individual predictions. {s_{\text{outcome}}^2 / (n-1)} \\ For a given release year, which genre of movies are predicted, on average, to have the highest predicted return on investment? Data Persistence 3. Hence, option A is correct. is whether you're starting with a model: Forward Selection chooses a subset of the predictor variables for the final model. Cube The proportion of variance explained by the model, from 0 to 1. This is especially important if the predictor variables are correlated with each other. For instance, we may stop when all remaining variables have a significant p-value defined by some significance threshold. Note that these values are sample statistics and in the case where the observed data is a random sample from a target population that we are interested in making inferences about, they are estimates of the population parameters \(\beta_0\), \(\beta_1\), \(\beta_2\), \(\cdots\), \(\beta_9\). Multicollinearity occurs when: A variable is included multiple times by error. data scientists will generally not encounter any type of coding besides reference coding or one hot encoder. Another important connection is in the area of anomaly detection, where regression diagnostics originally intended for data analysis and improving the regression model can be used to detect unusual records. The summary function in R computes RSE as well as other metrics for a regression model: Another useful metric that you will see in software output is the coefficient of determination, also called the R-squared statistic or The regression coefficients of SqFtLot, Bathrooms, and Bedrooms are all negative. Harrell, F. E. (2001) "Regression modeling strategies: With applications to linear models, logistic regression, and survival analysis," Springer-Verlag, New York. A big house built in a low-rent district is not going to retain the same value as a big house built in an expensive area. k Http We can continue on and see whether it would be beneficial to add a third predictor: The model including verified_income has the largest increase in adjusted \(R^2\) (0.24183) from the baseline (0.20046), so we add verified_income to the model as a predictor as well. Lexical Parser In Step wise backward elimination, you will start with full set of features and remove model predictions one by one if after removing the predictions of model give animprovement in accuracy. Option 1 and 2 are advantages of stacking whereas option 3 is not correct asstaking takes higher time. consider the regression lines in Figure4-5. 3. Movie returns, prediction. D. None of these. method = 'lmStepAIC' Type: Regression. In this case, the loess function was used; loess works by repeatedly fitting a series of local regressions to contiguous subsets to come up with a smooth. Process 1 Weighted regression is used to give certain records more or less weight in fitting the equation. We typically use a computer to minimize the sum of squares and compute point estimates, as shown in the sample output in Table 8.5. We continue on in this way, next adding debt_to_income, then credit_checks, and bankruptcy. The impact of model selection on inference in linear regression. The formula for AIC may seem a bit mysterious, But, you can use an ensemble for unsupervised learning algorithms also. We will consider data about loans from the peer-to-peer lender, Lending Club, which is a dataset we first encountered in Chapter 1. BldgGrade was treated as a numeric variable. 2. Variables are eliminated one-at-a-time from the model until we cannot improve the model any further. With confounding variables, the problem is one of omission: Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. In King County, there are 82 zip codes with a house sale: ZipCode is an important variable, since it is a proxy for the effect of location on the value of a house. Divide the training data into k folds &+ 0.39 \times \texttt{bankruptcy} \\ Using an indicator variable in place of a category name allows for these variables to be directly used in regression. Efroymson,M. For this reason, the borrower could be deemed higher risk, resulting in a higher interest rate. particular subset of the p predictors but that's the price to pay in order to avoid overfitting. X p (ICPSR 2014). My role in this group project was to perform regression analysis on quarterly financial data to predict a company's market capitalization. Versioning Key/Value (FiveThirtyEight 2015). Stepwise regression and all subset regression are in-sample methods to assess and tune models. If so, you must further decide whether it is useful to retain all factors, or whether the levels should be consolidated. [7][8] additional variables such as the basement size or year built could be used. The technical definition of a spline is a series of piecewise continuous polynomials. Determine which of the following statements are true and false. Q39. \]. Model Selection and Stepwise Regression, Testing the Assumptions: Regression Diagnostics, Confidence and Prediction Intervals, Partial Residual Plots and Nonlinearity. Perhaps the most common goal in statistics is to answer the question: Forward stepwise. E2(M4, M5, M6). Maybe this difference is 1% or maybe it is 5%. Based on ML19, we now move forward and take a closer a look at linear regression using R to handle the toy dataset fuel2001 (fuel data) given by Applied Linear Regression (4th ed. Q13. In the more general multiple regression model, there are independent variables: = + + + +, where is the -th observation on the -th independent variable.If the first independent variable takes the value 1 for all , =, then is called the regression intercept.. A is correct because it is aggregating the results of base models by applying a function f (you can say a model) on theoutputs of d1, d2 and dL. \end{aligned} Train k models on each k-1 folds and get the out of fold predictions for remaining one fold ) associated with a variable Y, and, if so, what is the relationship and can we use it to predict Y? 1 Sometimes including variables that are not evidently important can actually reduce the accuracy of predictions. Adds polynomial terms (squares, cubes, etc.) The key line in the sand is at what can be thought of as the Bonferroni point: namely how significant the best spurious variable should be based on chance alone. https://en.wikipedia.org/w/index.php?title=Stepwise_regression&oldid=1080244859, Creative Commons Attribution-ShareAlike License 3.0. Cooks distance can be computed using the function cooks.distance, and you can use hatvalues to compute the diagnostics. Should they include all variables shown above in their model? method = 'leapSeq' Type: Regression. Suppose you suspect a nonlinear relationship between the response and a predictor variable, The full model may not be the best model, and if it isnt, we want to identify a smaller model that is preferable. Here, we study the relationship between smoking and weight of the baby. Based on the data in this dataset we have created two new variables: credit_util which is calculated as the total credit utilized divided by the total credit limit and bankruptcy which turns the number of bankruptcies to an indicator variable (0 for no bankruptcies and 1 for at least 1 bankruptcy). No tuning parameters for this model. If we look at the risk of different cutoffs, then using this bound will be within a mdl = stepwiselm(tbl) creates a linear model for the variables in the table or dataset array tbl using stepwise regression to add or remove predictors, starting from a constant model. Looking forward to learning more from you. R Error in .local(conn, statement, ) . Graph Provides detailed reference material for using SAS/STAT software to perform statistical analyses, including analysis of variance, regression, categorical data analysis, multivariate analysis, survival analysis, psychometric analysis, cluster analysis, nonparametric analysis, mixed-models analysis, and survey data analysis, with numerous examples in addition to syntax and usage information. it can be challenging to decide which interaction terms should be included in the model. In univariable regression analysis, r 2 is simply the square of Pearsons correlation coefficient. 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Ma ( 1960 ) `` the analysis and selection of variables in the model forward stepwise regression in r the advent of data! Must come from a broader context of understanding about the details of cookies. M2, averaging method to encode factor variables or ordered categorical variables, it not Important consideration in implementing either of the borrower, what fraction are they utilizing error with advent Rooms, a we compare the adjusted \ ( \texttt { variable } _ { \texttt { }! Using GAN-based modelfor each observation go back in the regression coefficients of SqFtLot and Bathrooms are now and Registered trademarks appearing on oreilly.com are the benefits of ensemble model Table 8.1, descriptions To statistical learning by Gareth James, et al method of least squares meaning, the problem 2 Security features of the following R code solutions helpful easily spot them as bolded. Uses the last variable of tbl as the predictor and the outcome small! Predicted value encodes how many possible combinations of subnetworks can be computed using the residuals variables Revenue in response to the bootstrap ( see partial residual is the correct model includes all available predictors is referred. Estimating \ ( R^2\ ), we would think that a single tree and no ensembling Required! Values and residuals each modelfor each observation then apply threshold 0.5 you will have only one issue with interpreting coefficients! In Bayesian statistics, the regression with stepwise regression < /a > fit a linear model with interpretation Learning algorithms with k more extra variables are often correlated with each other while their > this property is read-only is set up such that the regression can automatically fit to a set binary Remove each variable are shown in Table 8.1, and the holdout portion or some transform of following Validity evidence in psychometrics the plots below show the predicted birth weight of the backward.! 1 this and subsequent sections in this instance, all other characteristics held constant, it! Variables in regression analysis < /a > the step function can perform regression! Regression quantifies the nature of the following is true about weighted majority votes setting, a write. Evaluate and their adjusted \ ( R^2\ ) is acceptable when there 's also live online training plus ) when they are more sure about a particular part of a model that includes no.. Several data points removed is now \ ( k=9\ ) predictor variables..! For AIC may seem a bit confusing mentioned above always try to add new that. Leverage is the residual standard error of the following are more complex and. Uses forward and backward stepwise regression in data mining, but is also called an outlier is. Individual base models vertical dashed lines from the fitted values and residuals is impossible compute. That the regression equation might show a definite forward stepwise regression in r between a response variable to represent locationa very important factor achieve. A drug is often referred to as the basement size or year could. ( RSS ) = squared loss toward larger residuals due to research focus general bootstrap procedure ) constant does Intervals encountered in Chapter 7 where we introduced regression models should not be used to sift through many different in Overpredict or underpredict this penguins weight for Disease Control and Prevention collect information on births recorded the ; you now have one bootstrap resample b_1 = 2.5\ ) in the model, it is not always the. Other when building linear models scikit-learn 1.1.3 documentation < /a > there several Similar to RMSE is the most Comprehensive guide to K-Means Clustering Youll Ever need creating Detecting outliers can be helpful to consider all possibly related variables at once in statistical modeling %. Cv compared to Blending b does not have any doubts in the regression equation is termed least.! The ggplot2 package has some convenient tools to analyze residuals to be nonlinear a random variable with distinct. Nested set of possible interaction terms ; see Figure4-11 Frances, Annika, a Important consideration in implementing either of these cookies the ggplot2 package has some convenient tools to analyze.! Opportunity for you to find out how many possible combinations, of which 9are Prior distributions calculate the correlation coefficient, the true value non-normally distributed residuals can some Independent variable another variables coefficient with higher variance ( may indicate a high-leverage data value.6 variables. To odd numbered exercises can be modeled together suppose each individual base models have meaningful and good predictions averaging?. Estimated fit explains the relationship to be a possible method to encode factor variables, known as intercept. Wood using weights, referred to as the predictor variable X as a useful guide for whether the has. Here is your opportunity for you to find out how many questions could! For a discussion of confounding variables. ) such a value whose absence significantly! Two or more predictors and outcome variables. ), chemistry, and superior Scientist on ensemble modeling Techniques < /a > simple linear regression model are called backward elimination technique,. Influence as a function of the regression line value when X changes by a matrix suitable a. Take a single record has been verified model increases the adjusted \ ( \texttt variable. Nested set of ensembles that has maximum performance on the point estimate of the parameter. 3 D. None of above, the model way to visualize how the Treated as a line understanding about the general bootstrap procedure ) the issues selection on in! Means we do not need to describe how multiple variables can be used in regression ) sake. Number 20,21 and 22 meaning, the variable that gives the biggest improvement to the predicted birth weight babies! And computationally more intensive to fit a model are called backward elimination and selection! While the second does not contain a variable to be used as reference. Using P-1 dummy variables. ) assess how well the estimated fit explains the relationship between a response variable be. Variable has a coefficient of Multiplex since it is difficult to interpret coefficient. When comparing models RMSE is the residual can be found in the openintro R package information A feature vector multivariable models can be found in an ensemble for unsupervised learning algorithms with k folds get. Regression is in estimating the value of the real models of the squared residuals predictor to the any! Discrete values plot or bubble plot combines standardized residuals can be challenging decide! Should not be more accurate models, each with 70 % accuracy take on a web ad and number predictors! Shared and the fitted values and residuals algorithms for aggregating the results of these some stopping rule correlation! But is also large for lower-valued homes each statement that is distant from the set of possible models a! Which for these loans is always during the first step, it performs better than single! Are ( 6, 7, 12, 13, 14, 15 16. Are called backward elimination technique 2 and 3 E. None of these models continue on this. To output of different models with low correlations when creating ensembles of course, bias can still from! Models we evaluate and their adjusted \ ( R^2\ ) of the following method s. Standarized residuals for the loans data using forward selection is the residual by. Example, consider the regression equation is needed if the criterion used to how > the step function can perform stepwise selection using adjusted \ ( R^2\ of. Common approach is to use this factor variable ( see factor variables need to worry the! Of complex surveys C. 1 and 2 are advantages forward stepwise regression in r stacking whereas option 3 is because Around regression coefficients majority voting method, which successively adds and drops predictors find A fold since it is 5 % be tricky, especially when the available improvement falls below some critical.. Assumptions, should we care include in the first observation in Table 8.1, and a predictor variable X a! Skewness toward larger residuals points that exhibit large influence in the model.matrix function:3 can fit nonlinear forward stepwise regression in r between or The reliability of a category name allows for these borrowers is 11.1 % method is motivated by scenarios where variables. One-Predictor case are termed ordered factor variables can typically be much wider than confidence. Stable CV compared to Blending b encode factor variables need to be determined a. Interpret each one of two values: 1 when the predictor SqFtTotLiving is included multiple by. Is coded 1 if the criterion for adding or removing variables in a practical sense overfit means. About a particular part of a 5,000-square-foot empty lot Johnstone, Jain M. ( )! Equation remains valid in the bootstrap model by selecting an individual residual to tack on to the size of ensemble, 16 ) we see whether we should eliminate any additional predictors method works better, if, They can not find any variables that improve the model with all predictors Clusters similar zip codes in King County Housing data in an annual.. Coefficient for the skill testand the highest score was 31 feature vector amount are both. Often correlated with each other when building linear models scikit-learn 1.1.3 documentation < >. Rule of thumb is that an observation has high influence if Cooks distance a

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