Understanding Mathematical Terms

Refer to the English-Spanish Glossary, which starts on textbook page A39, if you need help with a definition or finding a textbook page with an example for a vocabulary word.

Explorations

Read and work through the Exploration 1 and Communicate Your Answer on page 193. The goal of this lesson is to introduce an analytic method for determining a line of best fit. Be sure to use your graphing calculator. Become familiar with finding a regression line. Then, check your answers below.

Answers to Explorations and Communicate Your Answer

Exploration 1 (page 193)

1. The median age of American women at their first marriage in 1985 was 23.3.
2. Check students' work.
3. y = 0.13x + 19.8; The equations are similar.

Communicate Your Answer (page 193)

2. Use a computer, spreadsheet, or graphing calculator that has a linear regression feature.
3. 
   y = 3.27x + 25.0; about 87.1°F

Section 4-6 Lesson (pages 194-197)

In the last lesson, you used eyesight and quantitative reasoning to calculate a line of fit. Residuals, introduced in this lesson, are used in a more analytic approach to finding a best-fit line. Technology is used to find the regression equation. The lesson ends with a discussion of correlation and causation.

Look over Examples 1 through 5. Examples 1 and 2 both use residuals to see if a given equation models the data. They are very different. Study them. The last three examples show you how easy it is to find the regression line using technology. Practice with the Monitoring Progress problems as you go, and then check your answers below.

Answers to Monitoring Progress (pages 195-197)

1. No

2. a. y = –9.6x + 844.5

   

   b. –0.964; strong negative correlation
   c. The slope of –9.6 means the attendance decreases by about 9600 each year. The y-intercept of 844.5 means the attendance in 2005 was about 844,500.

3. 729,300

4. There may be a negative correlation; A causal relationship is possible because the more time you spend playing video games, the less time you spend studying.