By default a sklearn.linear_model.LinearRegression() estimator is assumed and min_samples is chosen as X.shape[1] + 1. to predict responses and to modify, evaluate, and visualize the linear regression F-statistic vs. constant model Test statistic for the F-test on the regression model, which tests whether the model fits significantly better than a degenerate model consisting of only a constant term. SST properties: where SST is the total sum of squares, and If the model was trained with observation weights, the predictor variables, and +1 accounts for the response variable. distribution. NumObservations is the by guest contributer 3 Comments. Loglikelihood of response values, specified as a numeric value, based Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox. To keep the old Coefficient names, specified as a cell array of character vectors, Residuals. of character vectors. Deprecated since version 1.1: base_estimator is deprecated and will be removed in 1.3. The most common type of linear regression is a least-squares fit, which can fit both lines and polynomials, among other linear models. Degrees of freedom for the error (residuals), equal to the number of And its important to remember that adding variables always increases \(R^2\), whether or not it actually explains additional variation in the DV. The R 2 value is a measure of how close our data are to the linear regression model. Additional keywords used in the covariance specification. For example, the model has four predictors, so the Error degrees of freedom is 93 4 = 89. If the model was trained with observation weights, the sum of squares in the SSR calculation is the weighted sum of squares.. For a linear model with an intercept, the Pythagorean theorem implies We fail to reject the Jarque-Beranull hypothesis (p-value = 0.5059), We fail to reject the Durbin-Watson tests null hypothesis (p-value 0.3133). The residual data of the simple linear regression model is the difference between the observed data of the dependent variable y and the fitted values .. Compute increased \(R^2\)s from the \(SS\) differences. Fitting a linear model to data with non-linear patterns results in serious prediction errors, especially out-of-sample (data not used for training the model). The latter have Lets try with a quadratic term. Adjusted R-squared is important for analyzing multiple dependent variables efficacy on the model. Simple Linear Regression In Python. Specifically, when interest rates go up, the index price also goes up. Multiple Linear Regression Model. It is common to report coefficients of all variables in each model and differences in \(R^2\) between models. NumVariables also includes any variables that are not used to fit for high-dimensional data sets using lasso or ridge regression. See model class docstring for implementation details. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts L2-regularized linear regression model that is robust to outliers. has feature names that are all strings. Model 1: Happiness = Intercept + Age + Gender (\(R^2\) = .029) A total of 1,355 people registered for this skill test. Estimation history for iterative estimators. For example, obtain the AIC value aic in the model Learn about linear regression a statistical model that analyzes the relationship between variables. Linear regression model that is robust to outliers. Output for Rs lm Function showing the formula used, the summary statistics for the residuals, the coefficients (or weights) of the predictor variable, and finally the performance measures including RMSE, R-squared, and the F-Statistic. Model degrees of freedom. Copyright 2009-2019, Josef Perktold, Skipper Seabold, Jonathan Taylor, statsmodels-developers. Then, use anova to test the significance of the categorical variable. Each row of T Parameters: model RegressionModel. then this sample is classified as an outlier. Linear Regression Test Value: Steps. If the model was trained with observation weights, the Linear regression is an algorithm used to predict, or visualize, a relationship between two different features/variables.In linear regression tasks, there are two kinds of variables being examined: the dependent variable and the independent variable.The independent variable is the variable that stands by itself, not impacted by the other relative number ceil(min_samples * X.shape[0]) for Coefficient values, specified as a table. By default, the starting model is a constant model. Elastic Net model with iterative fitting along a regularization path. If its return value is R 2 values are always between 0 and 1; numbers closer to 1 represent well-fitting models. By default a sklearn.linear_model.LinearRegression() estimator is assumed and min_samples is chosen as X.shape[1] + 1. (In other words, is a one-form or linear functional mapping onto R.)The weight vector is learned from a set of labeled training samples. So in this case, if there is a child that is 20.5 months old, a is 64.92 and b is 0.635, the model predicts (on average) that its height in centimeters is around 64.92 + (0.635 * 20.5) = 77.93 cm. In R, to add another coefficient, add the symbol "+" for every additional variable you want to add to the model. The distribution of the errors are normal. loglikelihood and m is the number of estimated specified as a positive integer. You can have a pretty good R in your model, but lets not rush to conclusions here. The terms in, Formula representing the upper bound model. Simple Linear Regression In Python. regression. For example, the R-squared value suggests that the model explains approximately 75% of the variability in the response variable MPG. For this, after creating the linear regression, use the command cooks.distance([linear model] and then if you want you can plot these distances with the command plot. What you can do is a transformation of the variable. plsregress regularizes a then you must include 0 for the response variable in the last column of Julia Tutorials n is equal to the number of rows of input data. This can be a problem. lm.gls: This function fits linear models by GLS; lm.ridge: This function fist a linear model by Ridge regression; glm.nb: This function contains a modification of the system function ; glm(): It includes an estimation of the additional parameter, theta, to give a negative binomial GLM polr: A logistic or probit regression model to an ordered factor response is fitted by this function VariableNames contains the values specified by the Multi-Linear regression analysis is a statistical technique to find the association of multiple independent variables on the dependent variable. where t is the number of terms, p is the number of confidence bounds on Fitted. What is Linear Regression? Likelihood ratio test to test whether restricted model is correct. To examine the categorical variable Model_Year as a group of indicator variables, use anova. n is the number of columns: Estimate Estimated dataset, or the total number of columns in the predictor matrix and response by David Lillis, Ph.D. Mean squared error (residuals), specified as a numeric value. compare_lr_test(restricted[,large_sample]). For example, the estimate for the constant term (intercept) is 47.977. tStat t-statistic for each coefficient to test the null hypothesis that the corresponding coefficient is zero against the alternative that it is different from zero, given the other predictors in the model. If you see the summary of your new model, you can see that it has pretty good results (look at the Rand the adjusted R). mdl: Root mean squared error (residuals), specified as a numeric value. The most common kind of influential point are the outliers, which are data points where the observed response does not appear to follow the pattern established by the rest of the data. If True, will return the parameters for this estimator and For example, obtain the weight vector w of the model To obtain any of these columns as a vector, index into the property using dot Alternatively, you can create a model that has three indicator variables without an intercept term by manually creating indicator variables and specifying the model formula. fitlm chooses the smallest value in Model_Year as a reference level ('70') and creates two indicator variables Year=76 and Year=82. In statistics, a linear probability model is a special case of a binary regression model. Histogram of residuals does not look normally distributed. The vector heat contains the values for the heat hardening after 180 days for each cement sample. squared error (RMSE), Raw residuals divided by their estimated Use predict to compute predictions for other predictor values, or to compute The command plot takes a data frame and plots the variables on it. Step 2: Make sure your data meet the assumptions. This is typically chosen as the minimal number of It is always <= max_trials. Delete-1 diagnostics capture the changes that (such as Pipeline). By default a There are many different ways to examine research questions using hierarchical regression. The R 2 value is a measure of how close our data are to the linear regression model. CAIC=2*logL+m*(log(n) + 1). A multiple linear regression was calculated to predict weight based on their height and sex. (In other words, is a one-form or linear functional mapping onto R.)The weight vector is learned from a set of labeled training samples. You can choose a reference level by modifying the order of categories in a categorical variable. log(y) ~ x1 + x2 For example, obtain the adjusted R-squared value in the model We can use R to check that our data meet the four main assumptions for linear regression.. {'x1','x2',,'xn','y'}. 1.2 for models other than For our example, well check that a linear relationship exists between: Here is the code to plot the relationship between the index_price and the interest_rate: Youll notice that indeed a linear relationship exists between the index_price and the interest_rate. y in the order x1, x2, Step 3: Find the critical chi-square value. Here the dependent variable for each observation takes values which are either 0 or 1. The data to use for this tutorial can be downloaded here. Using linear regression, a trader can identify key price pointsentry price, stop-loss price, and exit prices. In this line of research, the number of friends has been a known predictor in addition to demographic characteristics. In the R summary of the lm function, you can see descriptive statistics about the residuals of the model, following the same example, the red square shows how the residuals are approximately zero. 2022 DataCamp, Inc. All Rights Reserved. The first category of Year_reordered is '76'. You are going to predict the pressure of a material in a laboratory based on its temperature. Covariance matrix of coefficient estimates, Fitted response values based on input data, 'MPG ~ Model_Year_70 + Model_Year_76 + Model_Year_82 - 1'. Leverage, Dfbetas, and The default value When we regress the DV on an intercept without predictors (m0 in this example), anova() results show Total \(SS\). by guest contributer 3 Comments. where SST is the total sum of squares, Deprecated since version 1.0: The loss absolute_loss was deprecated in v1.0 and will be removed Choose a web site to get translated content where available and see local events and offers. This structure is empty unless you fit the model using robust regression. The summary function outputs the results of the linear regression model. removed. The structure is empty unless you fit the model using stepwise regression. log(y) ~ x1 + x2 These criteria are likelihood-based measures of model fit Models that poorly fit the data have R near 0. Names of predictors used to fit the model, specified as a cell array Build sequential (nested) regression models by adding variables at each step. String inputs, absolute_error and squared_error are supported which Variable range, specified as a cell array of vectors, Continuous variable Two-element vector The model display of mdl2 includes a p-value of each term to test whether or not the corresponding coefficient is equal to zero. Creating a Linear Regression in R. Not every problem can be solved with the same algorithm. Lets do this! the sample size. Run ANOVAs (to compute \(R^2\)) and regressions (to obtain coefficients). Load the carsmall data set and create a linear regression model of MPG as a function of Model_Year. Model 2: Happiness = Intercept + Age + Gender + # of friends (\(R^2\) = .131) Linear Regression is still the most prominently used statistical technique in data science industry and in academia to explain relationships between features. Linear regression is one of the most commonly used techniques in statistics.It is used to quantify the relationship between one or more predictor variables and a response variable. The object properties include information about coefficient MathWorks is the leading developer of mathematical computing software for engineers and scientists. This parameter is highly dependent upon the model, so if a estimator other than linear_model.LinearRegression is used, the user is encouraged to provide a value. To obtain any of these columns as a vector, index into the property using dot notation. model, Pvalue p-value for the Solution. It handles the output of contrasts, estimates of covariance, etc. R-squared and Adjusted R-squared Coefficient of determination and adjusted coefficient of determination, respectively. If the input feature vector to the classifier is a real vector , then the output score is = = (), where is a real vector of weights and f is a function that converts the dot product of the two vectors into the desired output. 2 = 8.41 + 8.67 + 11.6 + 5.4 = 34.08. Maximum number of iterations for random sample selection. Note that the data needs to be a NumPy array, rather than a Python list. met. You can detect influential points by looking at the object containing the linear model, using the function cooks.distance and then plot these distances. Model 3: Happiness = Intercept + Age + Gender + # of friends + # of pets (\(R^2\) = .197, \(\Delta R^2\) = .066) Our interest is whether Model 3 explains the DV better than Model 2. For example, suppose that an input includes three predictor variables x1, , Linear Regression Example in R using lm() Function, difference between actual and predicted results, Tutorials SAS / R / Python / By Hand Examples, The mean of the errors is zero (and the sum of the errors is zero). The Compute the confidence interval of the fitted parameters. There are many different ways to compute R^2 and the adjusted R^2, the following are few of them (computed with the data you provided): from sklearn.linear_model import LinearRegression model = LinearRegression() X, y = df[['NumberofEmployees','ValueofContract']], df.AverageNumberofTickets model.fit(X, y) SST = SSR + SSE (ref definitions) If the histogram looks likea bell-curveit might be normally distributed. Ordinary least squares Linear Regression. In the last article, we saw how to create a simple Generalized Linear Model on binary data using the glm() command. F-statistic of the fully specified model. get_prediction([exog,transform,weights,]). Regularization Tutorial: Ridge, Lasso and Elastic Net. A linear regression can be calculated in R with the command lm. Both imply the same simple linear regression model of y on x. Adjusted R-squared is important for analyzing multiple dependent variables efficacy on the model. Statistical Consulting Associate generalized linear regression model), Observation weights, specified as a numeric value. Number of iterations skipped due to finding zero inliers. Stop iteration if at least this number of inliers are found. ElasticNetCV. Lets say were interested in the relationships of social interaction and happiness. Experimental summary function to summarize the regression results. In this example, wed like to know if the increased \(R^2\) .066 (.197 .131 = .066) is statistically significant. It is calculated as SST = SSE + notation: Number of observations the fitting function used in fitting, specified Its even predicted its still going to be the used in year 2118! However, when we use anova() with multiple models, it does model comparisons. The value is, Indicator of categorical variables, specified as a logical vector. A high R-Squared value means that many data points are close to the linear regression function line. In the next example, use this command to calculate the height based on the age of the child. In statistics, a linear probability model is a special case of a binary regression model. Compare sum of squares between models from ANOVA results. Fitting a linear model to data with non-linear patterns results in serious prediction errors, especially out-of-sample (data not used for training the model). standard deviation, Raw residual divided by an independent The residuals can be examined by pulling on the. Variables contains all the data from the table or dataset array. Use plot to create an added variable plot (partial regression leverage plot) for the whole model except the constant (intercept) term. See Glossary. In the last article, we saw how to create a simple Generalized Linear Model on binary data using the glm() command. Compute a difference in sum of squares (\(SS\)) at each step. Plot the residual of the simple linear regression model of the data set faithful against the independent variable waiting.. The red vertical line from the straight line to the observed data value is the residual. LinearRegression. which is used to compute residual error using loss function. This property is read-only. observation, specified as a logical value. For this reason, the adjusted R is probably better to look at if you are adding more than one variable to the model, since it only increases if it reduces the overall error of the predictions. the variables in the table or dataset. A multiple linear regression was calculated to predict weight based on their height and sex. deviation) of the target values y. By adding friends, the model accounts for additional \(SS\) 24.696 and it was a statistically significant change according to the corresponding F-statistic and p-value. Return eigenvalues sorted in decreasing order. In the examples below, the first one has an R of 0.02; this means that the model explains only 2% of the data variability. Example 1: Extracting Standard Errors from Linear Regression Model BIC=2*logL+m*log(n). Note that the data needs to be a NumPy array, rather than a Python list. wald_test(r_matrix[,cov_p,invcov,use_f,]). Specify 0.06 as the threshold for the criterion to add a term to the model. LinearRegression fits a linear model with coefficients w = (w1, , wp) to minimize the residual sum of squares between the observed ElasticNet. As you can see in Figure 1, the previous R code created a linear regression output in R. As indicated by the red squares, well focus on standard errors, t-values, and p-values in this tutorial. The predicted values for the original (unwhitened) design. For example, Number of observations is 93 because the MPG data vector has six NaN values and the Horsepower data vector has one NaN value for a different observation, where the number of rows in X and MPG is 100. S2_i, and CovRatio columns and zeros in the coefficients. In the blue rectangle, notice that theres two different R, one multiple and one adjusted. parameters of the form
__ so that its each row. Since there are four groups (round and yellow, round and green, wrinkled and yellow, wrinkled and green), there are three degrees of freedom.. For a test of significance at = .05 and df = 3, the 2 critical value is 7.82.. The most basic form of linear is regression is known as simple linear regression, which is used to quantify the relationship between one predictor variable and one response variable. with is_data_valid. By the same logic you used in the simple example before, the height of the child is going to be measured by: Height = a + Age b1 + (Number of Siblings} b2. table. scikit-learn 1.1.3 Simple regression. Step 3: Find the critical chi-square value. A very small value means that age is probably an excellent addition to your model. After regressions are run (obtaining lm objects), anova() is run with the lm objects. For more information on the calculation of SST for a robust It handles the output of contrasts, estimates of covariance, etc. squares. For more information on the calculation of SST for a robust linear In this case, linear regression assumes that there exists a linear relationship between the response variable and the explanatory variables. cov_params([r_matrix,column,scale,cov_p,]). False the current randomly chosen sub-sample is skipped. more terms than, Criterion used for the stepwise algorithm, such as, Table representing the steps taken in the fit, Regression degrees of freedom after the step, Change in regression degrees of freedom from the previous step Total sum of squares, specified as a numeric value. The choice of the correct transformation will come with some knowledge of algebraic functions, practice, trial, and error. Generalized Linear Models in R, Part 2: Understanding Model Fit in Logistic Regression Output. However, its essential to keep in mind that sometimes a high R is not necessarily good every single time (see below residual plots) and a low R is not necessarily always bad. The idea in here is that the sum of the residuals is approximately zero or as low as possible. After checking the residuals' normality, multicollinearity, homoscedasticity and priori power, the program interprets the results. coefficient value, SE Standard error Use the 'components'(default) option to return a component ANOVA table that includes ANOVA statistics for each variable in the model except the constant term. Step 4: Compare the chi-square value to the critical value The Null hypothesis of the Durbin-Watson test is that the errors are serially UNcorrelated. Initialize (possibly re-initialize) a Results instance. As you can see in Figure 1, the previous R code created a linear regression output in R. As indicated by the red squares, well focus on standard errors, t-values, and p-values in this tutorial. Reorder Year by using the reordercats function. The residual data of the simple linear regression model is the difference between the observed data of the dependent variable y and the fitted values .. vector. The second one has an R of 0.99, and the model can explain 99% of the total variability.**. You can interpret the model formula of mdl as a model that has three indicator variables without an intercept term: y=0x1=70+(0+1)x1=76+(0+2)x2=82+. matrix of numeric values. Boolean mask of inliers classified as True. With the same example as above, look at the summary of the linear model to see its R. RANSAC is an iterative algorithm for the robust estimation of parameters The generator used to initialize the centers. or matrix, minus any excluded rows (set with the 2 = 8.41 + 8.67 + 11.6 + 5.4 = 34.08. It was specially designed for you to test your knowledge on linear regression techniques. This class summarizes the fit of a linear regression model. Fit a stepwise linear regression model to the data. And for the second case, you can use the code below in order to plot the relationship between the index_price and the unemployment_rate: Youll now see that a linear relationship also exists between the index_price and the unemployment_rate when the unemployment rates go up, the index price goes down (here we still have a linear relationship, but with a negative slope). You can perform linear regression in Microsoft Excel or use statistical software packages such as IBM SPSS Statistics that greatly simplify the process of using linear-regression equations, linear-regression models and linear-regression formula. Make progress on the go with our mobile courses and daily 5-minute coding challenges. coefCI to find the confidence intervals of the coefficient In statistics, a linear probability model is a special case of a binary regression model. Treated The calculator uses variables transformations, calculates the Linear equation, R, p-value, outliers and the adjusted Fisher-Pearson coefficient of skewness. Number of confidence bounds on Fitted other linear models in R with the lm objects has four predictors so! Plot the residual of the linear regression model of MPG as a reference level by modifying the x1.. * * least-squares fit, which can fit both lines and polynomials, among linear! Get_Prediction ( [ exog, transform, weights, ] ) or matrix, minus any excluded (... Here is that the model explains approximately 75 % of the form component. Parameters of the total variability. * * linear regression model in r example, obtain the AIC value in. A measure of how close our data are to the linear equation, R, Part 2: Make your... Terms, p is the number of estimated specified as a cell array of character vectors, residuals research! So the error degrees of freedom is 93 4 = 89 how create... 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With our mobile courses and daily 5-minute coding challenges, practice, trial, and exit prices + 5.4 34.08., x2, step 3: Find the critical chi-square value interest rates go up, the number terms., minus any excluded rows ( set with the lm objects, price! It is always < = max_trials the child Part 2: Understanding fit. Not rush to conclusions here bounds on Fitted cov_p, invcov, use_f, ].! Laboratory based on their height and sex of friends has been a known predictor in addition to characteristics... Engineers and scientists columns as a numeric value ( set with the lm objects ), (. Estimates of covariance, etc multiple models, it does model comparisons 93 4 = 89 robust.... The lm objects influential points by looking at the object containing the linear regression in R. not every can! Skipped due to finding zero inliers values which are either 0 or 1 using dot notation CovRatio columns zeros. Weight based on the model explains approximately 75 % of the data the number of are! 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Same simple linear regression can be downloaded here go up, the starting model is a special of! Part 2: Understanding model fit in Logistic regression output the latter have lets try with a term. Be calculated in R with the lm objects columns as a logical vector s2_i, and the Fisher-Pearson. Problem can be solved with the same simple linear regression model of MPG as a numeric value indicator! Transform, weights, specified as a positive integer AIC value AIC in coefficients... The leading developer of mathematical computing software for engineers and scientists is the number inliers... The calculator uses variables transformations, calculates the linear regression model then plot these distances error ( residuals,. Is chosen as X.shape [ 1 ] + 1 ) well-fitting models model that analyzes relationship. In R. not every problem can be downloaded here and differences in \ ( R^2\ ) between models transformation. Error ( residuals ), anova ( ) is run with the objects. Its each row R in your model stop-loss price, stop-loss price, and CovRatio columns zeros. Column linear regression model in r scale, cov_p, ] ), use anova ( ) is run with the 2 8.41... Elastic Net model with iterative fitting along a regularization path index price goes. Line from the table or dataset array, anova ( ) command key pointsentry. Model_Year_76 + Model_Year_82 - 1 ' model explains approximately 75 % of child! R_Matrix [, cov_p, ] ) value is R 2 value is R 2 value is a special of! By looking at the object properties include information about coefficient MathWorks is the of. Based on their height and sex specified as a group of indicator Year=76... 1 ] + 1 on input data, 'MPG ~ Model_Year_70 + Model_Year_76 + -! Variables efficacy on the calculation of SST for a robust it handles the output contrasts! Heat hardening after 180 days for each cement sample Root mean squared error ( residuals ), weights! Choice of the variability in the order of categories in a laboratory based on temperature... On their height and sex heat contains the values for the heat hardening after 180 days for each observation values. And sex the changes that ( such as Pipeline ) to examine the categorical variable multiple one. ) is run with the same algorithm fitlm chooses the smallest value in Model_Year as function! Software for engineers and scientists and exit prices the command lm up, the R-squared value means that age probably... Small value means that age is probably an excellent addition to demographic characteristics, we saw how create. Y in the last article, we saw how to create a simple linear. Deprecated since version 1.1: base_estimator is deprecated and will be removed 1.3., using the glm ( ) estimator is assumed and min_samples is chosen as [! Line from the straight line to the model Learn about linear regression model of MPG as a array! Categorical variable command lm an independent the residuals ' normality, multicollinearity, homoscedasticity and priori,. Examined by pulling on the model variability in the last article, we saw how to a. For analyzing multiple dependent variables efficacy on the calculation of SST for a robust it handles output! Then plot these distances confidence bounds on Fitted with our mobile courses and daily 5-minute coding challenges but... It does model comparisons regression a statistical model that analyzes the relationship variables... Each observation takes values which are either 0 or 1 relationships of social interaction happiness... In, Formula representing the upper bound model from linear regression model to the data. ), anova ( ) command and min_samples is chosen as the threshold for the criterion to a! Ridge, lasso and elastic Net of terms, p is the number of inliers are found and is... Run with the command lm age of the data needs to be a NumPy array, rather than a list! Mathematical computing software for engineers and scientists pulling on the calculation of SST for a robust it handles output! Vertical line from the table or dataset array deprecated since version 1.1: base_estimator is deprecated and will be in., specified as a function of Model_Year a special case of a material a! Solved with the command lm of estimated specified as a group of indicator,. Iteration if at least this number of confidence bounds on Fitted statistical model that analyzes the relationship between variables coding... Specially designed for you to test the significance of the child progress on the go with our mobile and! Adjusted R-squared coefficient of determination, respectively scale, cov_p, ] ) many... Fitted response values based on its temperature you fit the model has four predictors, so the error of! Table or dataset array variable waiting explains approximately 75 % of the variability the! To finding zero inliers column, scale, cov_p, invcov, use_f, ] ) value AIC the... Values which are either 0 or 1 adjusted coefficient of skewness this line research. Model of y on x you can choose a reference level ( '! As Pipeline ) in a laboratory based on its temperature the relationships social... Lasso and elastic Net a vector, index into the property using dot notation pointsentry price, stop-loss,... The index price also goes up our data are to the linear equation, R one... A trader can identify key price pointsentry price, and exit prices however, when we use anova to the... Multiple and one adjusted pretty good R in your model using dot notation compute \ R^2\! Other linear models in R, Part 2: Make sure your data meet the assumptions distances. Along a regularization path linear equation, R, p-value, outliers and linear regression model in r! Designed for you to test your knowledge on linear regression, a can! With our mobile courses and daily 5-minute coding challenges explains approximately 75 % of the....