Download presentation

Presentation is loading. Please wait.

Published byRosa Norris Modified over 6 years ago

1
Linear Models and Scatter Plots 2015

2
Objectives Interpret correlation Use a graphing calculator to find linear models and make predictions about data. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2

3
HWQ 8/11/15 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 3

4
Extra practice: Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 4

5
Interesting result: Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 5

6
6 x 24 –2–2 – 4 y 2 4 6 A scatter plot represents data graphically using points plotted on a rectangular coordinate system. Example: (x, y) (1, – 4) (2, – 2) (3, – 1) (4, 0) (5, 2) (6, 4) Definition: Scatter plot

7
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 7 In a collection of ordered pairs (x, y), if y tends to increase as x increases, the collection has a positive correlation. Correlation x y x y x y If y tends to decrease as x increases, the collection has a negative correlation. positive correlation no correlation negative correlation

8
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 8 Example: The average salary S (in millions of dollars) for professional baseball players from 1996 through 2002 is shown in the table. Let t = 6 represent the year 1996. Draw the scatter plot. Example: Scatter Plot YearSalary, S 19961.1 19971.3 19981.4 19991.6 20001.8 20012.1 20022.3 S 4 t 8 1 2 Year (6 1996) Salary (in millions of dollars)

9
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 9 Graphing Utility: Scatter Plot YearSalary, S 19961.1 19971.3 19981.4 19991.6 20001.8 20012.1 20022.3 Graphing Utility: Draw the scatter plot that describes the data. Stat Plot Menu: Zoom Menu: Stat Edit Menu:

10
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 10 Finding a linear model to represent the relationship described by a scatter pot is called fitting the line to data. Example: Fitting a Line to Data YearSalary, S 19961.1 19971.3 19981.4 19991.6 20001.8 20012.1 20022.3 4 t 8 S 1 2 Example: The table and scatter plot for the average salary S (in millions of dollars) for professional baseball players from 1996 through 2002 is shown. Let t = 6 represent the year 1996. Find the equation of the line. Example continues.

11
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 11 Continued Example: Fitting a Line to Data YearSalary, S 19961.1 19971.3 19981.4 19991.6 20001.8 20012.1 20022.3 4 t 8 S 1 2 (6, 1.1) (12, 2.3) The equation of this line is S = 0.2t – 0.1. This line approximates the data. Example continued:

12
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 12 Graphing Utility: Finding a Liner Model YearSalary, S 19961.1 19971.3 19981.4 19991.6 20001.8 20012.1 20022.3 Graphing Utility: Find a linear model that describes the data. Stat Menu: A linear model for this data is S = 0.2t – 0.14. This equation is very close to the equation found using two data points. What does the model predict Baseball players salaries to be in 2015? Stat Edit:

13
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 13 Correlation Coefficient The correlation coefficient (or r-value) of the data gives the measure of how well the model fits the data. The closer |r| is to 1, the better the points can be described by a line. r = 0.99 strong positive correlation r = – 0.93 negative correlation 0 13 2 0 52.6 52.3 0 13 r = 0.66 weak correlation 50 90 50 100

14
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 14 Graphing Utility: Finding a Liner Model YearRadio Stations, R 19706,760 19757,744 19808,566 198510,359 199010,788 199511,834 200013,058 A linear model for this data is R = 209.257t +6733.857. 15,104 You Try: The number R of U.S. radio stations for selected years is shown in the table. Use a graphing utility to find a linear model that describes the data. Let t=0 correspond to 1970. For the year 2010, how many radio stations does the model predict?

15
Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 15 Homework Pg. 77 3-6 all, 7-15 odds, 27-37 odds

Similar presentations

© 2022 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google