Download presentation

Presentation is loading. Please wait.

Published byEunice Tate Modified over 6 years ago

1
1 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman C.M. Pascual S TATISTICS Section 9c Variation and Prediction Intervals

2
2 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definitions

3
3 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definitions Total Deviation from the mean of the particular point ( x, y ) the vertical distance y - y, which is the distance between the point ( x, y ) and the horizontal line passing through the sample mean y

4
4 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definitions Total Deviation from the mean of the particular point ( x, y ) the vertical distance y - y, which is the distance between the point ( x, y ) and the horizontal line passing through the sample mean y Explained Deviation the vertical distance y - y, which is the distance between the predicted y value and the horizontal line passing through the sample mean y ^

5
5 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definitions Total Deviation from the mean of the particular point ( x, y ) the vertical distance y - y, which is the distance between the point ( x, y ) and the horizontal line passing through the sample mean y Explained Deviation the vertical distance y - y, which is the distance between the predicted y value and the horizontal line passing through the sample mean y Unexplained Deviation the vertical distance y - y, which is the vertical distance between the point ( x, y ) and the regression line. (The distance y - y is also called a residual, as defined in Section 9-3.) ^ ^ ^

6
6 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Figure 9-9 Unexplained, Explained, and Total Deviation

7
7 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Total deviation ( y - y ) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Unexplained deviation ( y - y ) Explained deviation ( y - y ) (5, 19) (5, 13) (5, 9) y = 3 + 2 x ^ y = 9 ^ ^ y x 0123456789 Figure 9-9 Unexplained, Explained, and Total Deviation

8
8 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman ( y - y ) = ( y - y ) + (y - y ) (total deviation) = (explained deviation) + (unexplained deviation) ^ ^

9
9 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman ( y - y ) = ( y - y ) + (y - y ) (total deviation) = (explained deviation) + (unexplained deviation) (total variation) = (explained variation) + (unexplained variation) ( y - y ) 2 = ( y - y ) 2 + (y - y) 2 ^ ^ ^ ^ Formula 9-5

10
10 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definition Coefficient of determination the amount of the variation in y that is explained by the regression line

11
11 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definition r 2 = explained variation total variation Coefficient of determination the amount of the variation in y that is explained by the regression line

12
12 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definition r 2 = explained variation. total variation r 2 = b SS xy /Ss yy Where b = SS xy /SS xx Coefficient of determination the amount of the variation in y that is explained by the regression line

13
13 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Prediction Intervals Definition Standard error of estimate

14
14 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman a measure of the differences (or distances) between the observed sample y values and the predicted values y that are obtained using the regression equation Prediction Intervals ^ Definition Standard error of estimate

15
15 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Standard Error of Estimate

16
16 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Standard Error of Estimate s e = ( y - y ) 2 n - 2 y 2 - b 0 y - b 1 xy s e = n - 2 or Formula 9-6 ^

17
17 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Standard Error of Estimate s e = ( y - y ) 2 n - 2 ^ = [SS yy – b SS xy /(n – 2)] 0.5

18
18 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Example 3 Using the problem in Chapter 9, determine the standard error (Se) and coefficient of determination (r 2 ) Solution: Getting the following data: SSxx = 362 ; SSxy = 22.7 ; SSyy = 2.78 b = 0.063 Solving for standard error (Se) Se = [(SSyy-b*SSxy)/(n-2)] 0.5 Se = [((2.78 – (0.063)(22.7))/(8-2) ] 0.5 = 1.59

19
19 Chapter 9. Section 9-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Example 3 Solution: Getting the following data: SSxx = 362 ; SSxy = 22.7 ; SSyy = 2.78 b = 0.063 Solving for Coefficient of determination (r 2 ) r 2 =(b*SSxy)/(SSyy) = (0.063*22.7)/(2.78) = 0.514

Similar presentations

© 2021 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