文档介绍：CHAPTER 15 Simple Linear Regression and Correlation
to pany
Introduction to Business Statistics
fourth edition, by Ronald M. Weiers
Presentation by Priscilla Chaffe-Stengel
Donald N. Stengel
© 2002 The Wadsworth Group
Chapter 15 - Learning Objectives
Determine the least squares regression equation, and make point and interval estimates for the dependent variable.
Determine and interpret the value of the:
Coefficient of correlation.
Coefficient of determination.
Construct confidence intervals and carry out hypothesis tests involving the slope of the regression line.
© 2002 The Wadsworth Group
Chapter 15 - Key Terms
Direct or inverse relationships
Least squares regression model
Standard error of the estimate, sy,x
Point estimate using the regression model
Confidence interval for the mean
Prediction interval for an individual value
Coefficient of correlation
Coefficient of determination
© 2002 The Wadsworth Group
Chapter 15 - Key Concept
Regression analysis generates a “best-fit” mathematical equation that can be used in predicting the values of the dependent variable as a function of the independent variable.
© 2002 The Wadsworth Group
Direct vs Inverse Relationships
Direct relationship:
As x increases, y increases.
The graph of the model rises from left to right.
The slope of the linear model is positive.
Inverse relationship:
As x increases, y decreases.
The graph of the model falls from left to right.
The slope of the linear model is negative.
© 2002 The Wadsworth Group
Simple Linear Regression Model
Probabilistic Model: yi = b0 + b1xi + ei
where yi = a value of the dependent variable, y
xi = a value of the independent variable, x
b0 = the y-intercept of the regression line
b1 = the slope of the regression line
ei = random error, the residual
Deterministic Model:
= b0 + b1xi where
and is the predicted value of y in contrast to the actual value of y.
© 2002 The Wadsworth Group
Determining the Least Squares Regression Line
Least Square