Chapter 5: Linear Models PDF

Chapter 5 : Linear Models This week, you’ll learn about how we can define a linear model to make predictions about one variable (the DV) from another (the IV). You’ll then learn about R2 (read : “R-squared”) - professor’s favorite statistic - and how this quantifies the amount of error in a model. Y...

Chapter 5 : Linear Models This week, you’ll learn about how we can define a linear model to make predictions about one variable (the DV) from another (the IV). You’ll then learn about R2 (read : “R-squared”) - professor’s favorite statistic - and how this quantifies the amount of error in a model. You’ll then learn how our good friend the z-score can be used to calculate a correlation coefficient. Wow! Table of Contents 1. Part 1 : Making Predictions with Linear Models a. RECAP : The Mean (and Linear Model) as Prediction b. The Linear Model : It’s Just a Line c. Check-In : Intercepts and Slopes 2. Part 2 : Evaluating Error in Our Predictions a. R2 (“R Squared”) b. Video Example : Age and Narcissism c. Check-In : Understanding R2 3. Part 3 : The Z-Score and Correlations a. Why Z-Score in a Model b. Video Example : Age and Narcissism (Z-Scored) c. Check-Out : Understanding Z-Scores in a Linear Model 4. Quiz 5 : Defining and Interpreting Linear Models, R2, and Z-Scores 1 Part 1 : Making Predictions with Linear Models At the beginning of the semester, we talked about how the goal of psychological science is to make predictions about people, while recognizing that our predictions will not perfectly match what actually happens (which we call error). Conceptually, we can think of a person's actual score on y (some variable) as the sum of our prediction and the error in our prediction (with the goal to minimize error as much as possible). As an equation, we would write this as: 𝑎𝑐𝑡𝑢𝑎𝑙. 𝑠𝑐𝑜𝑟𝑒 = 𝑜𝑢𝑟. 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛 + 𝑒𝑟𝑟𝑜𝑟 Great! But the real question is WHAT should define our prediction? RECAP : The Mean (and Linear Model) as Prediction Previously, we learned how the mean was a simple way to make a prediction about individuals. For example, if you wanted to know whether it would rain today, you might look at the average rainfall for today’s date, and use that average for your prediction. Let's review this idea, and set up the linear model, by working with a classic dataset in teaching statistics - the Prestige dataset. These data are contained in the car package, and are used in one of the classic R textbooks - John Fox' Applied Regression Analysis and Generalized Linear Models (2nd Edition). (These data are also posted online as a.csv file to Canvas.) Below is some code that you can copy into your own R script and run. The output of this code (what you would see if you submitted this code) follows the ##. install.packages(‘car’) # this installs a package - you only need to do this ONCE library(car) # loading the library - make sure you installed it first! presto