Chapter 9.3（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Correlation and Regression 9 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 9.1 Correlation 9.2 Linear Regression 9.3 Measures of Regression and Prediction Intervals 9.4 Multiple Regression . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 9.3 Measures of Regression and Prediction Intervals . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 9.3 Objectives How to interpret the three types of variation about a regression line How to find and interpret the coefficient of determination How to find and interpret the standard error of the estimate for a regression line How to construct and interpret a prediction interval for y . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Variation About a Regression Line Three types of variation about a regression line Total variation Explained variation Unexplained variation To find these variations, you must first calculate The total deviation The explained deviation The unexplained deviation For each ordered pair (xi, yi) in a data set. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Variation About a Regression Line . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 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 = . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 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 . 1 Copyright 2019, 2015, 2012, Pearson Educat