R Barplot Two Variables

Two other columns are a "Total_PL_Sales" and a "Total_NonPL_Sales" How do I plot a bar plot with x = CUST_REGION_DESCR, y = Total_Sales, and each bar plot contains the raw dollars amount (not Percentage) of both Total_PL_Sales and Total_NonPL_Sales so that these two numbers add up to Total_Sales in each x-axis tick. X-bar and R Control Charts An X-Bar and R-Chart is a type of statistical process control chart for use with continuous data collected in subgroups at set time intervals - usually between 3 to 5 pieces per subgroup. The code in ui. factor(rep(c. This is accomplished by binding plot inputs to custom controls rather than static hard-coded values. Let’s do this in R, in a two-step process:. We demonstrate using the SF-36 MCS and PCS subscales in the HELP. Notice the two di erent variable names. Bar charts for categorical variables. Below is an example of the default plots that qplot() makes. Alternatives to the bar chart. create a 2X2 of continuous variables for patients that have data for both variables - I have a dataset (n=1309) and I am looking to create a 2x2 table for patients that have values for two continuous variables "pa" and "rvsp", this will gi. Below is a super simple solution. sorted bar plot with 45 degree labels - step by step! ! ! ! ! ! Sorted bar plot with 45 degree labels in R!!! In this exercise we'll plot a bar graph, sort it in decreasing order (big to small from left to right) and place long labels under the bars. Section C: Nature and format of data The type of representation that can be used depends on. I'm looking to plot two separate variables on the same bar graph. Shiny is an R package that allows users to build interactive web applications easily in R! Using Shiny and Plotly together, you can deploy an interactive dashboard. One Variable. The function gives us two groups of N = 250 observations each; both have similar means and SDs, but group one is drawn from an exponential distribution. given is true) are adapted. R Barplot Two Variables. frame(ID = as. If you want to get rid of the row names (they’re not needed), you need to use the print statement as given above. ggplot2 is a plotting package that makes it simple to create complex plots from data in a data frame. There are two observation variables in the data set. Before using edaPlot, two outliers that truly don’t belong are removed from the marioKart data set, which is a data set concerning Ebay auctions of Mario Kart games on Ebay. As the graph shows, our data are organized by two grouping variables: 1. The purposes of this task are threefold: To check that the data are correct. First, we'll read in the continent values into a data frame called conts:. I am struggling on getting a bar plot with ggplot2 package. R GET STARTED II 1 www. As I said, there is more than 1 way to do the same thing in R. The psych package is a work in progress. By seeing this R barplot or bar chart, One can understand, Which product is performing better compared to others. The Barplot or Bar Chart in R Programming is handy to compare the data visually. Say you have a data frame with a number of variables that you would like to compare against each other. Here's a quick demonstration of the trick you need to use to convince R and ggplot to do it. The association plot makes sense only when your study consists of at least two words or expressions. Learn more about bar plot, plotyy. In this example we plot two functions on the same figure using the command plot twice. barplot is a function, to plot easily bar graphs using R software and ggplot2 plotting methods. If you want to select a few variables then use the select () function along with the filter (). Continuous variables can have an infinite number of different values between two given points. Plotting Factor Variables Description. Mail Address 251 Mercer St. By default, data that we read from files using R’s read. Red, green, and blue components are specified as two hexadecimal digits (0–9,A–F), in the form #rrggbb. In many psychological experiments, there are two dependent variables for each participant: mean response time (RT) and mean proportion of errors. This is the case in Fig. Jason Anastasopoulos April 29, 2013 Performs a t-test of means between two variables X and Y for the hypothesis H 0: X = Y. Bar charts for categorical variables. Boxplots show the distribution of a variable by indicating the median, quartiles, maximum and minimum of a variable. This will be a syntax that is common to many functions we will use in. sum, len, np. Search this site Two-sample t-test in R: Changing a numerical variable to a categorical variable in R (5:21) Dummy variables and their use in. It has a menu system to do common data manipulation and analysis tasks, and an excel-like spreadsheet in which to view and edit data frames. Mosaic plots are good for comaparing two categorical variables, particularly if you have a natural sorting or want to sort by size. onInputChange('bar_clicked', [event. Shapley regression and Relative Weights are two methods for estimating the importance of predictor variables in linear regression. Quantitative Data - One Variable: Dot Plot. In the below example, the cyl variable from the mtcars data set is visualized using a bar plot. Use the factor command to specify a more meaningful order. The first thing you'll need to do is tidy your data. table( "http://www. A broad range of industries have adopted the R language, including biotech, finance, research and high technology industries. Although a table can be very insightful, things usually only get tangible when they are visualized. Then type “y=”. This example will plot the counts of observations for the interaction of two independent variables, Teacher and Sex. Quick plot of all variables. In this case, we'll use the summarySE() function defined on that page, and also at the bottom of this page. A bar plot shows comparisons among discrete categories. To address this weakness, you can add a histogram of each margin to the plot. Much of material has also covered been covered in number of short courses or in a set of tutorials for specific problems. The current released version is 1. You can create bar plots that represent means, medians, standard deviations, etc. #25 Histogram with several variables #25 Histogram with faceting If you have several numeric variables and want to visualize their distributions together, you have 2 options: plot them on the same axis (left), or split your windows in several parts ( faceting , right). The scatterplot is one of the most ubiquitous, and useful graphics. Each function returns a layer. At all times, R looks in a certain folder (also called 'directory') on the computer. What are R and S-PLUS? • R is a free implementation of a dialect of the S language, the statistics and graphics environment for which John Chambers won the ACM Software Systems award. Abstract: I reproduce some of the plots from Rstudio's ggplot2 cheat sheet using Base R graphics. Red, green, and blue components are specified as two hexadecimal digits (0–9,A–F), in the form #rrggbb. To do this we can use the table() function which will provide us the count of each unique value in this variable. Here is code to calculate RMSE and MAE in R and SAS. Still, if any doubt regarding Python Bar Plot, ask in the comment tab. The first thing you'll need to do is tidy your data. name of a logical variable in the data set (in quotes) or a logical expression using variables in the data set to specify row selection. Barplot in R (8 Examples) | How to Create Barchart & Bargraph in RStudio. And since you map on x a numeric variable, as. How to use R to do a comparison plot of two or more continuous dependent variables. R FAQ; R By Graph Type. I didn't try to pretty up these plots, but you should. I want to create a bardiagram for these data in R (read from a CVS file): Experiment_Name MetricA MetricB Just_X 2 10 Just_X_and_Y 3 20 to have the following di Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share. R is a very powerful environment for statistical data analysis but I really don't like the syntax. If y is missing barplot is produced. This page details how to plot a single, continuous variable against levels of a categorical predictor variable. The latter two are built on the highly flexible grid graphics package, while the base graphics routines adopt a pen and paper model for plotting, mostly written in Fortran, which date back to the early days of S, the precursor to R (for more on this, see the book Software for Data Analysis - Programming with R by John Chambers, which has lots. By default, barplot() suppresses the X-axis. Hi all I have a bit of a problem. In the first example we simply hand the plot function two vectors. Learn more about bar plot, plotyy. We saw four types of scope- local scope, enclosed scope, global scope, and built-in scope. Here is the main difference between bar charts and histograms. factor(x, y, legend. non-conforming. Finally, we need the shinyApp function that uses the ui object and the server function we defined to build a Shiny. Although going from raw numerical data to categorical data bins (like we did for age and BMI) does give you less precision, it can make drawing conclusions from plots a lot easier. for histogram use hist() function #7. Still, if any doubt regarding Python Bar Plot, ask in the comment tab. selection - is used to highlight values, which are imputed in all or any of the variables. R - Scatterplots - Scatterplots show many points plotted in the Cartesian plane. Presenter Notes Source: r_cat. If we wanted to get the count of vehicles that have 4, 6 and 8 cylinders we can simply identify the x-axis variable and apply geom_bar(). It is also important to keep in mind that a bar plot shows only the mean (or other estimator) value, but in many cases it may be more informative to show the distribution of values at each level of the categorical variables. Finally, both axes and legends share properties, which is a named list of props() that is applied to specified components of the axis or legend. In that case, you can filter records or variables using the filter (data, condition) and select (data, condition) functions to your dataset and pipe them to ggplot (). The simplest form of the bar plot doesn't include labels on the x-axis. factor(rep(c. Plot each and every point into the graphs after drawing a horizontal line and label the possible values on it, in regular intervals. ts, barplot. Default is FALSE. The most frequently used plotting functions for two variables in R are the following:. factor(x, y, legend. Copy and paste the following code to the R command line to create this variable. To introduce the barplot, I show the basic default bargraph that you would get if you indicate an x-variable and use the default geom_bar layer, which is geom_bar(stat="bin"). To generate 1000 t-statistics from testing two groups of 10 standard random normal numbers, we can use:. This site provides support and supplementary material to accompany the book Instant R: An Introduction to R for Statistical Analysis by Sarah Stowell. Phones 212. 1 R TUTORIAL, #1: DATA, FREQUENCY TABLES, and HISTOGRAMS The (>) symbol indicates something that you will type in. You can create bar plots that represent means, medians, standard deviations, etc. I want to point out another mild annoyance with the way that R handles bar plots, and how to fix it. miss - by default, it is set as FALSE. I have a dataset which looks like this one below. The goal is to be able to glean useful information about the distributions of each variable, without having to view one at a time and keep clicking back and forth through our plot pane!. Barplot by two variables. The first thing you'll need to do is tidy your data. The dialog now displays eight choices for graph type. Quantitative(IV) ! Categorical(DV) Make meaningful categories with the quantitative IV and follow C!C instructions. These bars can be customized via arguments per the sections below. I am trying to make a barplot with the grouping variable gender, with all the variables side by side on the x axis (grouped by gender as filler with different colors), and mean values of variables on the y axis (which basically represents percentages). factor(rep(c. One way that we can construct these graphs is using R's default packages. Each column of the matrix will be represented by a stacked bar. I am using the ggplot2 package and am trying to create a single bargraph with both populations on it. R has 8 default system colors, which can be assigned to a point or line by passing a numeric value of 1:8 to col. Oftentimes we want to make a plot which plots the colors according to some categorical variable. A formula of the form y ~ x| a * b indicates that plots of y versus x should be produced conditional on the two variables a and b. Studies have shown that the two, despite being constructed in very different ways, provide surprisingly similar scores((Grömping, U. For example, if the variable A has three groups “a”, “b” and “c”, and you want “c” to come first, use the following and then redraw your barplot. In this case we're interested in the probability of 'success' (presence) given values of one or more independent variables. In this program, I used the color function (red ‘r’) and stem plot function (stem). sorted bar plot with 45 degree labels - step by step! ! ! ! ! ! Sorted bar plot with 45 degree labels in R!!! In this exercise we'll plot a bar graph, sort it in decreasing order (big to small from left to right) and place long labels under the bars. One variable is chosen in the horizontal axis a. 2 otherwise. If we wanted to get the count of vehicles that have 4, 6 and 8 cylinders we can simply identify the x-axis variable and apply geom_bar(). ) Using JASP for reporting summary and inferential statistics; One Sample t-test; Matched Pairs t-test; Two sample t-test (Independent Samples) [Old video; is a bit "fuzzy" but may still be worth a look] Two Sample t-test (Independent Samples) [Another clearer video (Screencast)]. To make it easy to get started, the ggplot2 package offers two main functions: quickplot() and ggplot(). The first is the barplot of observed values in the variable of interest. r Questions Finding which elements in a vector have an edit distance of one and the same length? - I have a dataframe, an example in. At all times, R looks in a certain folder (also called 'directory') on the computer. A bullet (•) indicates what the R program should output (and other comments). In the stacked bar plot figure below we. So, this was all about Python Variable Scope. Here is the R code for simple scatter plot using function ggplot() with geom_point(). Stacked barplot; Grouped barplot; Spineplot; Mosaic-plot; Pie-charts. Usually the columns are different variables (e. This site provides support and supplementary material to accompany the book Instant R: An Introduction to R for Statistical Analysis by Sarah Stowell. Barplot by two variables. 2 otherwise. Side-By-Side bar charts are used to display two categorical variables. This post will explain a data pipeline for plotting all (or selected types) of the variables in a data frame in a facetted plot. where xij is the j-th variable collected from the i-th item (e. Interaction effects between continuous variables (Optional) Page 3 Suppose further that 0, 5, and 10 are low, medium and high values of X2. A bar chart represents data in rectangular bars with length of the bar proportional to the value of the variable. Shiny is an R package that allows users to build interactive web applications easily in R! Using Shiny and Plotly together, you can deploy an interactive dashboard. Two-way frequency tables, also called contingency tables, are tables of counts with two dimensions where each dimension is a different variable. I want to create a bardiagram for these data in R (read from a CVS file): Experiment_Name MetricA MetricB Just_X 2 10 Just_X_and_Y 3 20 to have the following di Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share. Bar plot for frequencies of observations for female and male students in each of three classes. 1 Getting Started. Simply use the plot(x,y). height <- c(176, 154, 138, 196, 132, 176, 181, 169, 150, 175). For example, –42 is a constant. We demonstrate using the SF-36 MCS and PCS subscales in the HELP. com courses again, please join LinkedIn Learning. Here, how can keep a legend on top of the graph, specifically the legend should be between 2 and 3 barplot. The page consists of eight examples for the creation of barplots. Moreover, we discussed example of Histogram in Python and Python bar Plotting example. The areas in bold indicate new text that was added to the previous example. Examples of grouped, stacked, overlaid, filled, and colored bar charts. The python seaborn library use for data visualization, so it has sns. Two other columns are a "Total_PL_Sales" and a "Total_NonPL_Sales" How do I plot a bar plot with x = CUST_REGION_DESCR, y = Total_Sales, and each bar plot contains the raw dollars amount (not Percentage) of both Total_PL_Sales and Total_NonPL_Sales so that these two numbers add up to Total_Sales in each x-axis tick. Well, with facetting, you can! Here you're going to use facet_grid instead of facet_wrap, as that will make it easy to map our facets to two variables, Region and measure, where all these two variables are spread across the rows and columns of a grid of plots. For example using the data set “cars”: smoke <- table ( smokerData $ Smoke , smokerData $ SES ) > smoke High Low Middle current 51 43 22 former 92 28 21 never 68 22 9. The aim of this tutorial is to show you step by step, how to plot and customize a bar chart using ggplot2. 1 mlmRev v 1. If height were being measured though, the variables would be continuous as there are an unlimited number of possibilities even if only looking at between 1 and 1. Each example builds on the previous one. R will start up if you double click a script file. An R script is available in the next section to install the package. Assign it to some name. If y is missing barplot is produced. barplot function. By seeing this R barplot or bar chart, One can understand, Which product is performing better compared to others. Dot shown to represent each data point; g <- ggplot(CO2, aes(x = uptake)) g + geom_dotplot() Numerical and Graphical Summaries. ” Here is the example of x=10. You've probably seen bar plots where each point on the x-axis has more than one bar. Below, we’ve outlined the steps we’ve taken to create a barplot in R using murders_final_sort. This post steps through building a bar plot from start to finish. The function gives us two groups of N = 250 observations each; both have similar means and SDs, but group one is drawn from an exponential distribution. Coronary Atherosclerosis. In this case, the height of the bar represents the count of cases in each category. It really takes a while until you feel close to "home"…. Enter load(". When the variable on the x-axis is numeric, it is sometimes useful to treat it as continuous, and sometimes useful to treat it as categorical. As with all of R, the ability to easily chart financial time series is the result of an iterative progression driven by the collaboration of an extremely dedicated group of open source volunteers. We then get. csv () functions is stored in a data table format. Horizontal Bar Charts in R How to make a horizontal bar chart in R. As the graph shows, our data are organized by two grouping variables: 1. 8 MCMCglmm v 2. The Data is first loaded and cleaned and the code for the same is posted here. First, we'll read in the continent values into a data frame called conts:. This article has two goals: Demonstrate a practical implementation of the "Transform in database, plot in R" concept by showing how to visualize a categorical variable using a Bar plot, a single continuous variable using a Histogram, and two continuous variables using a Raster plot, all using data in a database. frame command combines the variables you list (in this case, y and p) into a single data set. They are from open source Python projects. Linear Regression using R (with some examples in Stata) (ver. csv, cleaned and created in this tutorial. If the input is matrix, a stacked bar is plotted. We can then pass this to the barplot() function to plot the counts of cylinders:. (This differs from versions of R prior to 2. To find which folder R is currently looking in, type getwd(). It really takes a while until you feel close to "home"…. The relationship between two continuous variables is most commonly investigated using scatter plots (see graphing section below). Mosaic plots are good for comaparing two categorical variables, particularly if you have a natural sorting or want to sort by size. On Thu, Mar 1, 2012 at 7:19 AM, jon waterhouse wrote: If I have two factors, v1 and v2 and I want to have a stacked bar graph of the two variables side by side I could do. frame; it's essentially a table where the rows correspond to observations, and the columns refer to variables. The areas in bold indicate new text that was added to the previous example. Bar charts are a pretty common way to represent data visually, but constructing them isn't always the most intuitive thing in the world. Notice the two di erent variable names. Occasionally, a back-to-back histogram can be effective for two groups. Treatment, with three levels—placebo, 10 mg, and 100 mg 2. The current released version is 1. A bar chart is a great way to display categorical variables in the x-axis. frame command combines the variables you list (in this case, y and p) into a single data set. I can't help you plot this in base R (which is the system used by barplot(), but I can help you do it with ggplot2. Recommended Articles. r Questions Finding which elements in a vector have an edit distance of one and the same length? - I have a dataframe, an example in. example R plot made using the below function and built-in data. However, we cannot make a conclusive statement on the relationship between these variables simply by looking at the r-value, because the r-value is extremely sensitive to the data distribution and population size. Hope this answers your question. Bar plots of two-way tables Suppose you want to show that there is some kind of connection between the transmission system (automatic versus manual) and the number of gears 1. R PCH Characters; R Graphical Output Options; Useful R Links. barplot function. Then, the method is almost the same, except you add a “fill” argument in the aestetic, which… You can also see the Position adjustment section of R4DS, which describes how ggplot2 maps the variables to the aesthetics to make the grouping. R uses the function barplot() to create bar charts. We can supply a vector or matrix to this function. Step 1: Format the data. Segmented bar plots are useful for visualizing conditional frequency distributions. The same can be very easily accomplished in ggplot2. I’m going to make a vector of months, a vector of the number of chickens and a vector of the number of eggs. By default, the categorical axis line is suppressed. Using R for Football Data Analysis – Monte Carlo 1 Reply OK, so I’m going to try my hand at a tutorial, we’re going to use R to run a Monte Carlo simulation on the expected goal rates of the shots in the Southampton V Liverpool game (23/02/2015), and calculate the win probability of an average team given those chances based on those ExpG. Scatter diagram/Scatterplot. The complete course duration is 3 hours and 18 minutes long and introduces the R statistical processing language, including how to install R, read data from SPSS and spreadsheets, analyze data. The association plot makes sense only when your study consists of at least two words or expressions. Although a table can be very insightful, things usually only get tangible when they are visualized. Or, that depends. Here we will use a made up data set primarily to make it easier to figure out what R is doing. The data for the examples below comes from the mtcars dataset. Occasionally, a back-to-back histogram can be effective for two groups. In the data set painters, the bar graph of the School variable is a collection of vertical bars showing the number of painters in each school. This is post #03 in a running series about plotting in R. A simple plotting feature we need to be able to do with R is make a 2 y-axis plot. You can also make histograms by using ggplot2 , "a plotting system for R, based on the grammar of graphics" that was created by Hadley Wickham. Plotting zoo Objects In addition to classical time series line plots, there is also a simple barplot method for "zoo" series. A question of how to plot your data (in ggplot) in a desired order often comes up. Check back soon for an improved layout and new apps from Shiny users!. History of R Financial Time Series Plotting. For a continuous variable such as weight or height, the single representative number for the population or sample is the mean or median. The quickplot() function – also known as qplot() – mimics R’s traditional plot() function in many ways. You can create different types of bar plot in MATLAB. We can supply a vector or matrix to this function. The default command will create a scatterplot of your variable (VAR) with automatically detected scales for the two-axes and no line connecting the plotted values:. You will also learn to draw multiple box plots in a single plot. Single Graph - Margins and Plot Area; Multiple Graphs - Grid Layouts; Multiple Graphs - Mixed Size Layouts; R Miscellaneous Guides. Quantitative Data - One Variable: Dot Plot. 1 simpleR { Using Rfor Introductory Statistics. The association plot makes sense only when your study consists of at least two words or expressions. You can think of the variable on the left, quality, as the PivotTable row item, and the right, state, as the PivotTable column item. When the variable on the x-axis is numeric, it is sometimes useful to treat it as continuous, and sometimes useful to treat it as categorical. Plotting Tools. What I want to get is a barplot with the Block column in the x axis, working as a categorical variable. It provides a more programmatic interface for specifying what variables to plot, how they are displayed, and general visual properties, so we only need minimal changes if the underlying data change or if we decide to change from a bar plot to a scatterplot. Bar charts are a pretty common way to represent data visually, but constructing them isn't always the most intuitive thing in the world. You can set colors according to the levels of a grouping variable by: Mapping the argument color to the variable of interest. However if you map a factor variable on x, it should work. First, I'll create 5 means drawn from a Gaussian random variable with unit mean and variance. The same can be very easily accomplished in ggplot2. test and, for two variables, legend. The goal is to be able to glean useful information about the distributions of each variable, without having to view one at a time and keep clicking back and forth through our plot pane!. 2-D pie-chart; 3-D pie-chart; Conditional density plot; Useful packages; Detach (automatically) loaded packages (if possible) Get the article source from GitHub. Is this possible, or is there another way/procedur. The randomForest package in R has two measures of importance. geom_bar() makes the height of the bar proportional to the number of cases in each group (or if the weight aesthetic is supplied, the sum of the weights). RE: st: Graph of two grouping variables. To see all the names, type colors(). You can either create the table first and then pass it to the barplot() function or you can create the table directly in the barplot() function. Simple barplot; Barplots for contingency tables of two variables. Also, a term or expression for which any variables cancel out. Barplot in R (8 Examples) | How to Create Barchart & Bargraph in RStudio. Set Categorical Variable to Factor If the data is imported to R then the categorical variables that contain non-numeric data will usually all be factor variables in R data set. This will be a syntax that is common to many functions we will use in. 3 Two categorical variables. The first one counts the number of occurrence between groups. Common R commands used in Sta 101 # beside = TRUE for side-by-side barplot # legend = TRUE to include a color Two numerical variables, Simple linear. Each x/y variable is represented on the graph as a dot or a cross. As an example, we will create a simple bar plot for comparing 5 values 1,2,6,4 and 9. The dialog now displays eight choices for graph type. We will start off with a simple plot of two numerical variables: age against BMI. In my continued playing around with meetup data I wanted to plot the number of members who join the Neo4j group over time. I am using the ggplot2 package and am trying to create a single bargraph with both populations on it. These are represented as strings of six characters. ) By clicking on the options (axes left of variables or the plotting types), I generated seven interesting exploratory plots in. The same can be very easily accomplished in ggplot2. Make histograms in R based on the grammar of graphics. To generate 1000 t-statistics from testing two groups of 10 standard random normal numbers, we can use:. Variables in the same group are related, and there is relationship between values of the variables and sample group numbers. As an example, we will create a simple bar plot for comparing 5 values 1,2,6,4 and 9. As mentioned before, barplot() function can take in vector as well as matrix. In the R code above, we used the argument stat = "identity" to make barplots. The fictitious data set is defined below. Before drawing a grouped barplot, you need to know how to draw a basic barplot with ggplot2. R: ggplot - Plotting multiple. x1+x2) in I will make the expression be treated as a single variable in a formula, meaning it will get only a single coefficient estimate. Barplot of counts. First, let's make some data. ” Here is the example of x=10. So is 3x + 5 – 3x, which simplifies to just 5. arange ( 20 ) ys = np. Plotting Factor Variables Description. The psych package is a work in progress. An R Graphical User Interface (GUI) for Everyone Deducer is designed to be a free easy to use alternative to proprietary data analysis software such as SPSS, JMP, and Minitab. txt and separate each column by a tab character (\t). Bar Plot; Box Plot; Line Plot; R Graph Layout Guides. R - Barplot Jalayer Academy. For numeric y a boxplot is used, and for a factor y a spineplot is shown. If one variable is explanatory and the other is outcome, it is a very, very strong convention to put the outcome on the y (vertical) axis. 5 Quick and Easy Data Visualizations in Python with Code of two variables in our data. The Mean (X-Bar) of each subgroup is charted on the top graph and the Range (R) of the. How to use R to do a comparison plot of two or more continuous dependent variables. 4121 (fax) Email [email protected]