Chapter 10: Linear Regression and Correlation
Introduction to Chapter 10: Linear Regression and Correlation
Professionals often want to know how two or more numeric variables are related. For example, is there a relationship between the grade on the second math exam a student takes and the grade on the final exam? If there is a relationship, what is the relationship and how strong is it?
In another example, your income may be determined by your education, your profession, your years of experience, and your ability. The amount you pay a repair person for labor is often determined by an initial amount plus an hourly fee.
The type of data described in the examples is bivariate data — “bi” for two variables. In reality, statisticians use multivariate data, meaning many variables.
In this chapter, you will be studying the simplest form of regression, “linear regression” with one independent variable (x). This involves data that fits a line in two dimensions. You will also study correlation which measures how strong the relationship is.
Collaborative Exercises
Section 10.3
Collaborative Exercise
If you know a person’s pinky (smallest) finger length, do you think you could predict that person’s height? Collect data from your class (pinky finger length, in inches).
The independent variable, x, is pinky finger length and the dependent variable, y, is height. For each set of data, plot the points on graph paper. Make your graph big enough and use a ruler.
Then “by eye,” draw a line that appears to “fit” the data. For your line, pick two convenient points and use them to find the slope of the line. Find the y-intercept of the line by extending your line so it crosses the y-axis.
Using the slopes and the y-intercepts, write your equation of “best fit.” Do you think everyone will have the same equation? Why or why not? According to your equation, what is the predicted height for a pinky length of 2.5 inches?
Media Attributions
- Chapter 12 Introduction Figure © OpenStax Introductory Statistics is licensed under a CC BY (Attribution) license
