R Tutorial: Background on modeling for explanation

Key Takeaways

hello welcome to modeling with data in the tidy verse in this course you'll leverage the data wrangling and visualization toolbox you developed in previous courses to learn about modeling the ideas behind modeling are crucial to many fields including statistics causal inference machine learning and artificial intelligence you'll start by equipping yourself with some theory and terminology related to modeling in chapters 2 & 3 you'll learn one of the most widely used techniques for modeling linear regression you'll end by assessing the quality of models for example how well does a model fit given data or how good are a models predictions let's start with the general modeling framework as expressed by the following formula where you have Y an outcome variable the phenomenon you wish to model X a set of explanatory or predictive variables used to inform your model the arrow on the X indicates that X can be a vector in other words a series of values F a mathematical function making explicit the relationship between y and X f of X is also called the signal and finally epsilon and unsystematic error component epsilon is also called the noise let's first focus only on y and X and revisit F and epsilon later previously I called X both explanatory and predictor variables which term you use when depends roughly on which modelling scenario you're addressing if you want to explain what factors are associated with or cause the outcome variable you are modeling for explanation and thus X are explanatory variables if you want to make predictions of the outcome variable you are modeling for prediction and thus X are predictor variables let's start with an example of modeling for explanation at the end of academic terms at many universities and colleges instructors are given teaching evaluation scores by students a study conducted at the University of Texas Austin investigated whether differences in scores could be explained by differences in instructor attributes the outcome variable is average teaching score for different courses explanatory variables include rank gender which at the time of the study was recorded as a binary variable male or female age and even the instructors beauty score BTY average we'll talk more about that later the evals data frame included in the modern dive package contains this data the modern dive package is used in modern dive comm an open source written and published electronic textbook on statistical and data sciences that Chester s may of data command I have co-authored this package includes other data and functions you'll be using in this course let's preview the data using the glimpse function from the deep liar package observe that there are 463 instructors and 13 variables in this data frame a crucial first step is an exploratory data analysis or EDA EDA gives you a sense of your data and it can help inform model construction there are three basic steps to an EDA most fundamentally looking at the data via spreadsheet viewer or using glimpse as I did earlier creating visualizations computing summary statistics let's do this for the outcome variable score since score is numerical let's construct a histogram to visualize its distribution by using a GM histogram from the ggplot2 package where the exes Tet is met to score let's also set a bin width of 0.25 observe the largest score is 5 and most scores are between about 3 & 5 but what's the average let's perform the third step in our EDA computing summary statistics summary statistics summarize many values with a single value called a statistic let's compute three such summary statistics using the summarized function the mean or average score is four point one seven whereas the median of four point three indicates about half the instructors had scores below four point three and about half above the standard deviation a measure of spread and variation is 0.5 for four in our first exercise you'll be performing an EDA on a different numerical variable this time instructor age