Transcript
Chapter 3:
Describing Relationships
Section 3.2
Least – Squares Regression
Regression Lines
summarize the relationship between two variables, but only in settings where one of the variables helps explain or predict the other (We must have an explanatory variable and a response variable.)
describe how a response variable y changes as an explanatory variable x changes
We often use a regression line to predict the value of y for a given value of x.
Example – Tapping on cans
Don’t you hate it when you open a can of soda and some of the contents spray out of the can? Two AP®Statistics students, Kerry and Danielle, wanted to investigate if tapping on a can of soda would reduce the amount of soda expelled after the can has been shaken. For their experiment, they vigorously shook 40 cans of soda and randomly assigned each can to be tapped for 0 seconds, 4 seconds, 8 seconds, or 12 seconds. Then, after opening the can and cleaning up the
mess, the students measured
the amount of soda left in each
can (in ml). Here are the data
and a scatterplot. The scatterplot
shows a fairly strong, positive
linear association between the
amount of tapping time and the
amount remaining in the can. The
line on the plot is a regression line for
predicting the amount remaining
from the amount of tapping time.
Interpreting a Regression Line
A regression lines is a model for the data and provides a compact mathematical description between the variables.
Example – Tapping on cans
For the soda example, the equation of the regression line is
