Chapter 9.2（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 9.2 Linear Regression . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 9.2 Objectives How to find the equation of a regression line How to predict y-values using a regression equation . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Regression lines After verifying that the linear correlation between two variables is significant, the next step is to determine the equation of the line that best models the data. This line is called a regression line, and its equation can be used to predict the value of y for a given value of x. x y . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Residuals For each data point, di represents the difference between the observed y-value and the predicted y-value for a given x-value. These differences are called residuals and can be positive, negative, or zero. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Regression line (line of best fit) The line for which the sum of the squares of the residuals is a minimum. The equation of a regression line for an independent variable x and a dependent variable y is ŷ = mx + b Regression Line Predicted y-value for a given x-value Slope y-intercept . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 7 The Equation of a Regression Line The equation of a regression line for an independent variable x and a dependent variable y is ŷ = mx + b where is the predicted y-value for a given x-value. The slope m and y-intercept b are given by where is the mean of the y-values in the data set, is the mean of the x-values, and n is the number of pairs of data. The regression line always passes through the point (x, y). . 1 Copyright 2019, 2015, 201