We just saw how to get the value of the intercept and the slope of a regression line from the estimate column of a regression table generated by the get_regression_table() function. Now, let’s say we want information on individual observations instead. For example, let’s focus on the 21st of the 463 courses in the evals_ch5 data frame in the table below:

What is the value $\hat y$ on the regression line corresponding to this instructor’s bty_avg beauty score of 7.333? In the figure below, we mark three values corresponding to the instructor for this 21st course and give their statistical names:

Circle: The observed value 𝑦 = 4.9 is this course’s instructor’s actual teaching score.
Square: The fitted value $\hat y$ is the value on the regression line for 𝑥 = bty_avg = 7.333. This value is computed using the intercept and slope in the previous regression table:

Getting Started with Data in R

Data Visualization

Data Wrangling

Data Importing and “Tidy” Data

Basic Regression

Multiple Regression

Statistical Inference with the infer Package

Bootstrapping and Confidence Intervals

Hypothesis Testing

Inference for Regression

Price Prediction With Regression Analysis in R

Tell a Story with Data

Appendix

Uber Data Analysis Using the R Language

Observed/Fitted Values and Residuals on Numerical Variables

Data for the 21st Course Out of 463

`ID`	`score`	`bty_avg`	`age`
21	4.9	7.33	31