Download presentation

Presentation is loading. Please wait.

Published byPauline Carroll Modified over 2 years ago

1
Statistics Measures of Regression and Prediction Intervals

2
Warm-up What value of “r” below best describes the scatterplot below? a) 0.9 b) -0.9 c) 0.3 d) -0.3 e) 0

3
Warm-up A least squares regression equation was created from last year’s students data to predict Exam 3 scores based on Exam 1 scores. The equation was: a) 69.70 b) 79.89 c) 85.53 d) 89.33 e) 90.53 Predict the score on Exam 3 for a student that scored an 80 on Exam 1.

4
Objectives Interpret the three types of variation about a regression line Find and interpret the coefficient of determination Find and interpret the standard error of the estimate for a regression line

5
Variation About a Regression Line Three types of variation about a regression line Total variation Explained variation Unexplained variation To find the total variation, you must first calculate The total deviation The explained deviation The unexplained deviation

6
Variation About a Regression Line (x i, ŷ i ) x y (x i, y i ) Unexplained deviation Total deviation Explained deviation Total Deviation = Explained Deviation = Unexplained Deviation =

7
Total variation The sum of the squares of the differences between the y-value of each ordered pair and the mean of y. Explained variation The sum of the squares of the differences between each predicted y-value and the mean of y. Variation About a Regression Line Total variation = Explained variation =

8
Unexplained variation The sum of the squares of the differences between the y-value of each ordered pair and each corresponding predicted y-value. Variation About a Regression Line Unexplained variation = The sum of the explained and unexplained variation is equal to the total variation. Total variation = Explained variation + Unexplained variation

9
Coefficient of Determination Coefficient of determination The ratio of the explained variation to the total variation. Denoted by r 2

10
Example: Coefficient of Determination About 83.4% of the variation in the company sales can be explained by the variation in the advertising expenditures. About 16.9% of the variation is unexplained. The correlation coefficient for the advertising expenses and company sales data as calculated is r ≈ 0.913. Find the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? Solution :

11
The Standard Error of Estimate Standard error of estimate The standard deviation of the observed y i -values about the predicted ŷ-value for a given x i -value. Denoted by s e. The closer the observed y-values are to the predicted y- values, the smaller the standard error of estimate will be. n is the number of ordered pairs in the data set

12
The Standard Error of Estimate 1.Make a table that includes the column heading shown. 2.Use the regression equation to calculate the predicted y-values. 3.Calculate the sum of the squares of the differences between each observed y-value and the corresponding predicted y-value. 4.Find the standard error of estimate. In WordsIn Symbols

13
Example: Standard Error of Estimate The regression equation for the advertising expenses and company sales data is ŷ = 50.729x + 104.061 Find the standard error of estimate. Solution: Use a table to calculate the sum of the squared differences of each observed y-value and the corresponding predicted y-value.

14
Solution: Standard Error of Estimate xyŷ iŷ i (y i – ŷ i ) 2 2.4225225.81(225 – 225.81) 2 = 0.6561 1.6184185.23(184 – 185.23) 2 = 1.5129 2.0220205.52(220 – 205.52) 2 = 209.6704 2.6240235.96(240 – 235.96) 2 = 16.3216 1.4180175.08(180 – 175.08) 2 = 24.2064 1.6184185.23(184 – 185.23) 2 = 1.5129 2.0186205.52(186 – 205.52) 2 = 381.0304 2.2215215.66(215 – 215.66) 2 = 0.4356 Σ = 635.3463 unexplained variation

15
Standard error of Estimate Related to unexplained variation (residuals) It is a measurement of the variation of the points about the regression line. s e = 0, r = 1 or -1, a perfect relation exists. The larger the s e, the more variability exists and the lower the quality of the relationship.

16
Solution: Standard Error of Estimate n = 8, Σ(y i – ŷ i ) 2 = 635.3463 The standard error of estimate of the company sales for a specific advertising expense is about $10.29.

17
Summary Interpreted the three types of variation about a regression line Found and interpreted the coefficient of determination Found and interpreted the standard error of the estimate for a regression line

18
Homework Pg 490-492; # 2-16 even

Similar presentations

Presentation is loading. Please wait....

OK

Simple Linear Regression Analysis

Simple Linear Regression Analysis

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on carburetors Ppt on cross docking distribution Download ppt on festivals of france Ppt on automobile related topics about global warming Ppt on hard disk drive download Download ppt on p block elements class 11 Ppt on fair and lovely Ppt on law against child marriage in africa Ppt on linear equations in two variables answers Ppt on computer malwares anti-malware