p.33 #14-19, p. 34 #32-34, 45-48

p.33 #14-19, p. 34 #32-34, 45-48

p.33 #14-19, p. 34 #32-34, 45-48

Lesson 1.5 - Scatter Plots and Least-Squares Lines

“Line of Best Fit” “Linear Regression Line” “Least Squares Line”

Three terms that mean the same thing

In many real-world problems, you will find data that relate 2 variables such as time and distance or age and height. You can view the relationship between 2 variables with a scatter plot.

There is a correlation between 2 variables when there appears to be a line about which the data points cluster. The diagram below shows some possible correlations.

Finding the Least-Squares Line

A scatter plot can help you see patterns in data involving 2 variables. If you think there maybe a linear correlation between the variables, you can use a calculator to find a linear-regression line, also called a least-squares line, that best fits the data.

STAT (L1, L2)

STAT / CALC / LINREG

Find and graph the least-squares line.

Correlation and Prediction

• The correlation coefficient, denoted by r, indicates how closely the data points cluster around the least-squares line.

• The correlation coefficient can vary from -1, which is a perfect fit for a negative correlation, to +1, which is a perfect fit for a positive correlation.

Ex. 2 Olympic Freestyle Swimming Event Data

Each day last week, the manager of a movie theater recorded how many people attended a movie. He also recorded how many bags of popcorn were sold.

1) Is there is a correlation between these two sets of data?

Number of people

attending a movie

Number of bags of

popcorn sold

175 76

100 43

213 101

249 133

362 197

331 185

250 148

y = .62x – 23.46 r = .99

2) Use your regression model to predict the attendance at a movie during which 198 bags of popcorn were sold.

Practice - p. 41 #13-20

Homework

Sheet 1.5

OR

pp. 42 & 43: Do any two problems from among #22 to 25

• Quiz Tomorrow on Lessons 1.1 to 1.5