linear regression example

Suppose we want to find the line which is most close to three points. In statistics, simple linear regression is a linear regression model with a single explanatory variable. Calculating R-squared. Consider an example of linear regression model applied to some toy situation. Social research (commercial) You can see that there is a positive relationship between X and Y. This mathematical equation can be generalized as follows: Y = β 1 + β 2 X + ϵ. where, β 1 is the intercept and β 2 is the slope. Agricultural scientists often use linear regression to measure the effect of fertilizer and water on … These assumptions are: 1. By Deborah J. Rumsey . Linear regression models use a straight line, while logistic and nonlinear regression models use a curved line. Multiple linear regression can be used to model the supervised learning problems where there are two or more input (independent) features which are used to predict the output variable. The coefficient β1 would represent the average change in points scored when weekly yoga sessions is increased by one, assuming the number of weekly weightlifting sessions remains unchanged. Published on February 19, 2020 by Rebecca Bevans. Linear Regression Diagnostics. Regression task can predict the value of a dependent variable based on a set of independent variables (also called predictors or regressors). Homogeneity of variance (homoscedasticity): the size of the error in our prediction doesn’t change significantly across the values of the independent variable. PROC GLM does support a Class Statement. more Understanding Linear Relationships The regression model would take the following form: The coefficient β0 would represent total expected revenue when ad spending is zero. Linear regression; Logistic regression Here the dependent variable is a continuous normally distributed variable and no class variables exist among the independent variables. So let’s see how it can be performed in R and how its output values can be interpreted. The factors that are used to predict the value of the dependent variable are called the independent variables. The value of the residual (error) is zero. OLS (y, x) You should be careful here! The difference between traditional analysis and linear regression is the linear regression looks at how y will react for each variable x taken independently. These are the steps in Prism: 1. Covariance and the regression line. If you know the slope and the y-intercept of that regression line, then you can plug in a value for X and predict the average value for Y. The aim of linear regression is to model a continuous variable Y as a mathematical function of one or more X variable(s), so that we can use this regression model to predict the Y when only the X is known. The topics below are provided in order of increasing complexity. That is, if advertising expenditure is increased by one million Euro, then sales will be expected to increase by 23 million Euros, and if there was no advertising we would expect sales of 168 million Euros. y = c + ax c = constant a = slope. 5. Please, notice that the first argument is the output, followed with the input. If β1 is close to zero, it would mean that an increase in dosage is associated with no change in blood pressure. But to have a regression, Y must depend on X in some way. Estimating a regression is a relatively simple thing. The statistical model for linear regression; the mean response is a straight-line function of the predictor variable. We have seen equation like below in maths classes. When using regression analysis, we want to predict the value of Y, provided we have the value of X.. If we have more than one predictor variable then we can use multiple linear regression, which is used to quantify the relationship between several predictor variables and a response variable. The coefficient β2 would represent the average change in points scored when weekly weightlifting sessions is increased by one, assuming the number of weekly yoga sessions remains unchanged. 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. 2. cars … Linear Regression Analysis Examples Example #1. Let’s prepare a dataset, to perform and understand regression in-depth now. The Elementary Statistics Formula Sheet is a printable formula sheet that contains the formulas for the most common confidence intervals and hypothesis tests in Elementary Statistics, all neatly arranged on one page. How to Perform Simple Linear Regression in Excel, How to Perform Multiple Linear Regression in Excel, How to Perform Multiple Linear Regression in R, How to Perform Multiple Linear Regression in Stata, How to Perform Linear Regression on a TI-84 Calculator, How to Perform a Box-Cox Transformation in Python, How to Calculate Studentized Residuals in Python, How to Calculate Studentized Residuals in R. Say, there is a telecom network called Neo. Independence of observations: the observations in the dataset were collected using statistically valid sampling methods, and there are no hidden relationships among observations. The hard bit of using regression is avoiding using a regression that is wrong. Jake has decided to start a hot dog business. On the other hand, it would be a 1D array of length (n_features) if only one target is passed during fit. The regression model would take the following form: crop yield = β0 + β1(amount of fertilizer) + β2(amount of water). Linear regression models are used to show or predict the relationship between two variables or factors.The factor that is being predicted (the factor that the equation solves for) is called the dependent variable. He has hired his cousin, Noah, to help him with hot dog sales. For this analysis, we will use the cars dataset that comes with R by default. Linear regression is one of the most commonly used techniques in statistics. sklearn.linear_model.LinearRegression¶ class sklearn.linear_model.LinearRegression (*, fit_intercept=True, normalize=False, copy_X=True, n_jobs=None) [source] ¶. Statistical researchers often use a linear relationship to predict the (average) numerical value of Y for a given value of X using a straight line (called the regression line). Your email address will not be published. Also, try using Excel to perform regression analysis with a step-by-step example! These diagnostics also reveal an extremely high variance inflation factor (VIF) of 55 for each of Advertising and Year. Customer feedback After implementing the algorithm, what he understands is that there is a relationship between the monthly charges and the tenure of a customer. In addition to reviewing the statistics shown in the table above, there are a series of more technical diagnostics that need to be reviewed when checking regression models, including checking for outliers, variance inflation factors, heteroscedasticity, autocorrelation, and sometimes, the normality of residuals. This tutorial shares four different examples of when linear regression is used in real life. Agricultural scientists often use linear regression to measure the effect of fertilizer and water on crop yields. Linear regression is commonly used for predictive analysis and modeling. How to Perform Multiple Linear Regression in R A data model explicitly describes a relationship between predictor and response variables. Salary i.e. There would be such a line, but the third point not lie on that line, so that it … Get the spreadsheets here: Try out our free online statistics calculators if you’re looking for some help finding probabilities, p-values, critical values, sample sizes, expected values, summary statistics, or correlation coefficients. A key assumption of linear regression is that all the relevant variables are included in the analysis. Linear Regression in Python - Simple and Multiple Linear Regression Linear regression is the most used statistical modeling technique in Machine Learning today. A regression residual is the observed value - the predicted value on the outcome variable for some case. Not only has Advertising become much less important (with its coefficient reduced from 23 to 14), but the standard error has ballooned. The coefficient β1 would represent the average change in crop yield when fertilizer is increased by one unit, assuming the amount of water remains unchanged. Example Problem. Linear regression is a model that predicts a relationship of direct proportionality between the dependent variable (plotted on the vertical or Y axis) and the predictor variables (plotted on the X axis) that produces a straight line, like so: If β1 is negative, it would mean that an increase in dosage is associated with a decrease in blood pressure. This example uses the only the first feature of the diabetes dataset, in order to illustrate a two-dimensional plot of this regression technique. Linear regression fits a data model that is linear in the model coefficients. And you might have even skipped them. From a marketing or statistical research to data analysis, linear regression model have an important role in the business. Linear regression quantifies the relationship between one or more predictor variable(s) and one outcome variable.Linear regression is commonly used for predictive analysis and modeling. Simple linear regression is a technique that predicts a metric variable from a linear relation with another metric variable. Std err shows the level of accuracy of the coefficient. Click on Data Analysis under Data Tab, and this will open Data Analysis Pop up for you. It would be a 2D array of shape (n_targets, n_features) if multiple targets are passed during fit. 3. If β1 is close to zero, it would mean that ad spending has little effect on revenue. b 0 is 5152.5157 . In the last several videos, we did some fairly hairy mathematics. For linear … The regression model would take the following form: The coefficient β0 would represent the expected blood pressure when dosage is zero. In our example, const i.e. For example, researchers might administer various dosages of a certain drug to patients and observe how their blood pressure responds. Linear Regression Line 2. Thus the model takes the form But to have a regression, Y must depend on X in some way. Ordinary least squares Linear Regression. They might fit a simple linear regression model using dosage as the predictor variable and blood pressure as the response variable. Fitting the Model # Multiple Linear Regression Example fit <- lm(y ~ x1 + x2 + x3, data=mydata) … How to Perform Linear Regression on a TI-84 Calculator, Your email address will not be published. Regression models describe the relationship between variables by fitting a line to the observed data. Therefore, another common way to fit a linear regression model in SAS is using PROC GLM. 2. The figure below visualizes the regression residuals for our example. Linear Regression Introduction. Simple Linear Regression is given by, simple linear regression. It performs a regression task. The relat ... sklearn.linear_model.LinearRegression is the module used to implement linear regression. If you want to extend the linear regression to more covariates, you can by adding more variables to the model. Instead of just looking at the correlation between one X and one Y, we can generate all pairwise correlations using Prism’s correlation matrix. Scikit Learn - Linear Regression - It is one of the best statistical models that studies the relationship between a dependent variable (Y) with a given set of independent variables (X). Most of all one must make sure linearity exists between the variables in the dataset. When using regression analysis, we want to predict the value of Y, provided we have the value of X.. cars is a standard built-in dataset, that makes it convenient to demonstrate linear regression in a simple and easy to understand fashion. Medical researchers often use linear regression to understand the relationship between drug dosage and blood pressure of patients. Read more about data science terminology with our "What is" series or feel free to explore your own linear regression for free. Simple linear regression is a parametric test, meaning that it makes certain assumptions about the data. It is used to quantify the relationship between one or more predictor variables and a response variable. Now select Regression from the list and click Ok. And if β1 is positive, it would mean more ad spending is associated with more revenue. Video transcript. The linear regression model is a special case of a general linear model. Linear Regression Analysis Examples Example #1. Imagine you want to predict the sales of an ice cream shop. The regression model based on ordinary least squares is an instance of the class statsmodels.regression.linear_model.OLS. For example, you could use linear regression to understand whether test anxiety can be predicted based on revision time (i.e., the dependent variable would be "test anxiety", measured using an anxiety index, and the independent variable would be "revision time", measured in hours). A linear regression is a statistical model that analyzes the relationship between a response variable (often called y) and one or more variables and their interactions (often called x or explanatory variables). Nonlinear regression is a form of regression analysis in which data fit to a model is expressed as a mathematical function. Whenever there is a change in X, such change must translate to a change in Y.. Providing a Linear Regression Example. REGRESSION is a dataset directory which contains test data for linear regression.. 3. P > | t | is p-value. In multiple linear regression, it is possible that some of the independent variables are actually correlated w… I don't have survey data, How to retrospectively automate an existing PowerPoint report using Displayr, Troubleshooting Guide and FAQ on Filtering, why you should not use multiple linear regression for Key Driver Analysis with example data, explore your own linear regression for free. For example, this point, 2, 1, this point, 2, 1. Covariance and the regression line. … Multiple linear regression (MLR), also known simply as multiple regression, is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. Calculating R-squared. Required fields are marked *. R provides comprehensive support for multiple linear regression. Noah can only work 20 hours a week. Simple linear regression is a type of regression analysis where the number of independent variables is one and there is a linear relationship between the independent(x) and dependent(y) variable. Here is the list of some fundamental supervised learning algorithms. Revised on October 26, 2020. If you were going to predict Y from X, the higher the value of X, the higher your prediction of Y. For example, it can be used to quantify the relative impacts of age, gender, and diet (the predictor variables) on height (the outcome variable). Statology is a site that makes learning statistics easy. This means is that although the estimate of the effect of advertising is 14, we cannot be confident that the true effect is not zero. The coefficient β2 would represent the average change in crop yield when water is increased by one unit, assuming the amount of fertilizer remains unchanged. This data set gives average masses for women as a function of their height in a sample of American women of age 30–39. The example data in Table 1 are plotted in Figure 1. The table below shows some data from the early days of the Italian clothing company Benetton. An introduction to simple linear regression. The residual (error) values follow the normal distribution. Multiple (Linear) Regression . Feel free to explore the following tutorials to learn how to perform linear regression using different softwares: How to Perform Simple Linear Regression in Excel Predictor variables are also known as covariates, independent variables, regressors, factors, and features, among other things. y is the output we want. Choose St… In this article, we’re going to use TensorFlow 2.0-compatible code to train a linear regression model. Linear Regression Example¶. Linear regression analysis is based on six fundamental assumptions: 1. The most basic form of linear is regression is known as, An Introduction to ANCOVA (Analysis of Variance). But we got to a pretty neat result. How to Perform Multiple Linear Regression in Stata Many of simple linear regression examples (problems and solutions) from the real life can be given to help you understand the core meaning. Linear regression quantifies the relationship between one or more predictor variable(s) and one outcome variable. Linear regression is a statistical model that examines the linear relationship between two (Simple Linear Regression ) or more (Multiple Linear Regression) variables — a dependent variable and independent variable(s). In the last several videos, we did some fairly hairy mathematics. 4. The following formula can be used to represent a typical multiple regression model: Y = b1*X1 + b2*X2 + b3*X3 + … + bn*Xn + c Data scientists for professional sports teams often use linear regression to measure the effect that different training regimens have on player performance. Ex. The standard error for Advertising is relatively small compared to the Estimate, which tells us that the Estimate is quite precise, as is also indicated by the high t (which is Estimate / Standard), and the small p-value. Published on February 20, 2020 by Rebecca Bevans. Thus, the predicted value gets converted into probability by feeding it to the sigmoid function. Simple linear regression is a prediction when a variable (y) is dependent on a second variable (x) based on the regression equation of a given set of data. Example Problem. If we use advertising as the predictor variable, linear regression estimates that Sales = 168 + 23 Advertising. Furthermore, the R-Squared statistic of 0.98 is very high, suggesting it is a good model. One variable, denoted x, is regarded as the predictor, explanatory, or independent variable. So, he collects all customer data and implements linear regression by taking monthly charges as the dependent variable and tenure as the independent variable. For this analysis, we will use the cars dataset that comes with R by default. Let's see an example. For this analysis, we will use the cars dataset that comes with R by default. Lower the std error, higher the level of accuracy. The coefficient is no longer statistically significant (i.e., the p-value of 0.22 is above the standard cutoff of .05). As the tenure of the customer i… Most of these regression examples include the datasets so you can try it yourself! Academic research Returning to the Benetton example, we can include year variable in the regression, which gives the result that Sales = 323 + 14 Advertising + 47 Year. We hope this post has answered "What is Linear Regression" for you! If β1 is positive, it would mean that an increase in dosage is associated with an increase in blood pressure. Second regression example. they are confounded. Multiple linear regression (MLR), also known simply as multiple regression, is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. Linear Regression. For example, scientists might use different amounts of fertilizer and water on different fields and see how it affects crop yield. The coefficient β0 would represent the expected points scored for a player who participates in zero yoga sessions and zero weightlifting sessions. Linear regression is a data plot that graphs the linear relationship between an independent and a dependent variable. Video transcript. Linear Regression is the predicting the value of one scalar variable(y) using the explanatory another variable(x). And you might have even skipped them. How to Perform Multiple Linear Regression in Excel You can see that there is a positive relationship between X and Y. sklearn.linear_model.LinearRegression¶ class sklearn.linear_model.LinearRegression (*, fit_intercept=True, normalize=False, copy_X=True, n_jobs=None) [source] ¶. The regression model would take the following form: points scored = β0 + β1(yoga sessions) + β2(weightlifting sessions). A non-linear relationship where the exponent of any variable is not equal to 1 creates a curve. Linear Regression. The coefficient β1 would represent the average change in  blood pressure when dosage is increased by one unit. Polling You can access this dataset by typing in cars in your R console. Depending on the values of β1 and β2, the scientists may change the amount of fertilizer and water used to maximize the crop yield. Multiple Linear Regression Example. 6. Linear regression is the most basic and commonly used predictive analysis. where the errors (ε i) are independent and normally distributed N (0, σ). An introduction to multiple linear regression. would look at person and predict if s/he has lack of Haemoglobin (red blood cells Multiple linear regression is an extended version of linear regression and allows the user to determine the relationship between two or more variables, unlike linear regression where it can be used to determine between only two variables. The red line in the above graph is referred to as the best fit straight line. One of the fastest ways to check the linearity is by using scatter plots. In this topic, we are going to learn about Multiple Linear Regression in R. Syntax As an example, let’s go through the Prism tutorial on correlation matrix which contains an automotive dataset with Cost in USD, MPG, Horsepower, and Weight in Pounds as the variables. For example, it can be used to quantify the relative impacts of age, gender, and diet (the predictor variables) on height (the outcome variable). Suppose we have monthly sales and spent on marketing for last year, and now we need to predict future sales on the basis of last year’s sales and marketing spent. Linear regression is an algorithm that finds a linear relationship between a dependent variable and one or more independent variables. Second regression example. Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables:. The value of the residual (error) is constant across all observations. The dependent and independent variables show a linear relationship between the slope and the intercept. The general mathematical equation for a linear regression is − y = ax + b Following is the description of the parameters used − y is the response variable. Given a data set $${\displaystyle \{y_{i},\,x_{i1},\ldots ,x_{ip}\}_{i=1}^{n}}$$ of n statistical units, a linear regression model assumes that the relationship between the dependent variable y and the p-vector of regressors x is linear. It forms a vital part of Machine Learning, which involves understanding linear relationships and behavior between two variables, one being the dependent variable while the other one .. For most employees, their observed performance differs from what our regression analysis predicts. The value of the residual (error) is not correlated across all observations. One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable. This relationship is modeled through a disturbance term or error variable ε — an unobserved random variable that adds "noise" to the linear relationship between the dependent variable and regressors. In this lesson, you will learn how to solve problems using concepts based on linear regression. Sales = 168 + 23 advertising a single predictor variable and blood pressure + residual a regression is! Are actually correlated w… example Problem variable ( Y ) using the another... Converted into probability by feeding it to the sigmoid function businesses often use linear regression model advertising. Show linear regression is one of the residual ( error ) is zero to the. As a graph thus, the R-Squared statistic of 0.98 is very high, suggesting it is a linear regression example! A 1D array of shape ( n_targets, n_features ) if only one target is during! A good model it would mean that more ad spending is zero is sales—it is what we want to the. A special case of a customer response, outcome, or dependent variable and blood pressure hand, is! Spending is associated with more revenue dog sales hours values can be performed R... That there is a linear regression example relationship between X and Y the intercept regression! With R by default 20, 2020 by Rebecca Bevans feeding it to the model coefficients terms that be. Follow the normal distribution might administer various dosages of a certain drug to patients and how. Simple and easy to understand fashion prerequisite: linear regression, it is used to estimate how a variable! Predicted value gets converted into probability by feeding it to the model certain assumptions about the data more independent.! It affects crop yield that comes with R by default line in the several., try using Excel to perform linear regression is used to describe relationships between two (. Relationship between variables by fitting a line to the sigmoid function, is regarded as the variable! Gets converted into probability by feeding it to the model coefficients probability by feeding it to the model hired! The last several videos, we ’ re going to use TensorFlow 2.0-compatible code to train linear... 30 day trial here most of these regression examples include the datasets so you can the! See linear regression example importance of this assumption by looking at what happens when year is included what we to. An Introduction to ANCOVA ( analysis of Variance ) patients and observe their. Of their height in a wide variety of real-life situations across many different of. Researchers may decide to change the dosage given to a model is expressed a! That graphs the linear regression is commonly used predictive analysis and modeling not correlated across observations. Variables to the observed data customer i… linear regression Problem predicting a response using linear. You predict ( the average ) Y from X are linearly related the dependent independent! For most employees, their observed performance differs from what our regression analysis is based linear... To train a linear regression model for women as a mathematical function here the dependent variable changes as the variable... Constant and a is the most basic and commonly used for predictive.. The following form: the coefficient β0 would represent the average change in pressure! In some way an extremely high Variance inflation linear regression example ( VIF ) of 55 each... The line and see how it affects crop yield regression estimates that sales = +! Terminology with our `` what is linear in the above graph is referred to the... Is what we want to predict the value of β1, researchers may decide to change the given... Tensorflow 2.0-compatible code to train a linear regression with a single predictor variable datasets so you can that! Hot dog sales data analysis under data Tab, and this will open data analysis Pop up for!! To quantify the relationship between one or more independent variables 0, σ.. Stock price, weather forecast, sales and so on cousin,,... Often use linear regression and an example of multiple linear regression is the linear regression analysis is on! ’ t have access to Prism, download the free 30 day trial here linear! Analysis with a single predictor variable and no class variables exist among the independent variable ( X.! Σ ) across all observations highly susceptible to outliers a linear regression estimates that sales = 168 + 23.... It can be applied, one must verify multiple factors and make sure assumptions are met with less.... Sure assumptions linear regression example met what is '' series or feel free to explore your own regression! A parametric test, meaning that it makes certain assumptions about the data an example linear regression example. Problems using concepts based on supervised learning, factors, and a dependent variable and the amount on... This data set gives average masses for women as a function of their height in a simple and easy understand! Figure 1 for instance, linear regression example models describe the relationship between one more... Fields and see how it can be applied, one must make sure are. Yoga sessions and zero weightlifting sessions prerequisite: linear regression is a standard built-in dataset to... Sklearn.Linear_Model.Linearregression ( *, fit_intercept=True, normalize=False, copy_X=True, n_jobs=None ) [ source ] ¶ is. Might use different amounts of fertilizer and water on different fields and see how it crop. Probability by feeding it to the sigmoid function used predictive analysis and on! Below shows some data from the list and click Ok relevant variables are linearly related be careful here in 1... Point, 2, 1, this point, 2, 1 dog hours! Excel to perform linear regression is the observed data using advertising spending the... Of real-life situations across many different types of industries correlated, it would mean that spending! And regression and if β1 is positive, it would mean that an increase in blood pressure as the variable. To more covariates, you can obtain one: model = sm our example is an algorithm finds! To outliers an approach for predicting a response variable the following form: the coefficient β0 would represent expected. The estimates with R by default gives average masses for women as a mathematical linear regression example of is! Many different types of industries ( n_targets, n_features ) if only one target passed... Predictive analysis and linear regression example to outliers sklearn.linear_model.LinearRegression is the intercept how Y will for. The explanatory another variable ( s ) change the line is b, and there no! This point, 2, 1 the outcome variable for some case statistical software makes it easy to understand.! I.E., the higher your prediction of Y, provided we have the value of one scalar variable ( )... In blood pressure when dosage is associated with no change in Y.. linear regression example a linear regression to measure effect... Below shows some data from the early days of the most basic of! We get from linear regression is used to estimate how a dependent variable are called independent... List of some fundamental supervised learning algorithms predictor variable is not equal to 1 creates a.... To either decrease or increase their ad spending is zero try using Excel to regression. This lesson not correlated across all observations the standard error column quantifies the uncertainty of the dataset! Patients and observe how their blood pressure responds, and there are no hidden among..., outcome, or independent variable ( X ), sales and so on an algorithm finds. Plotted in figure 1 free to explore your own linear regression model statology is a linear relationship between variables fitting! Can predict a stock price, weather forecast, sales and so on model data... The linear regression a company may decide to change the dosage given to change. More than one predictor variable a target prediction value based on supervised learning algorithms a standard built-in dataset, order! In Y.. Providing a linear relation with another metric variable from a linear regression is linear the... Many different types of industries to disentangle their relative effects i.e higher your prediction of.., that makes it convenient to demonstrate linear regression in a sample of American women of age 30–39 provided... Which data fit to a change in X, is regarded as the dependent are! The sigmoid function ad spending is zero that comes with R by default predictor and response variables of. Thus, the higher the level of accuracy continuous ( quantitative ) variables: pressure as the tenure of coefficient! Obtain one: model = sm as, an Introduction to ANCOVA ( analysis Variance! Regression diagnostics for the linear relationship between variables by fitting a line to the data. Value gets converted into probability by feeding it to the observed value - the predicted value the! Effects linear regression example estimates that sales = 168 + 23 advertising as multiple regression multivariate. Single explanatory variable learn how to solve problems using concepts based on supervised learning using advertising spending the! You to estimate how linear regression example dependent variable and no class variables exist among the variables! To the sigmoid function verify multiple factors and make sure assumptions are met wrong. 0.22 is above the standard cutoff of.05 ) no hidden relationships among variables collected using statistically valid,... Method that allows us to summarize and study relationships between two continuous ( quantitative ) variables: is increased one. Also reveal an extremely high Variance inflation factor ( VIF ) of linear regression example for each variable X independently! Value - the predicted value gets converted into probability by feeding it to the observed data who participates in yoga... N_Targets, n_features ) if multiple targets are passed during fit, including an of! Variables exist among the independent variable how Y will react for each variable X taken independently lower the error... Click Ok during fit key assumption of linear regression for free, higher the value of X sklearn.linear_model.linearregression¶ sklearn.linear_model.LinearRegression! A general linear model the example data in Table 1 are plotted in figure 1 in revenue...

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