Chapter_14(1)
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Set up, interpret, and apply an ANOVA table Compute and interpret the multiple standard error of estimate, the
coefficient of multiple determination, and the adjusted coefficient of multiple determination. Conduct a test of hypothesis to determine whether regression coefficients differ from zero. Conduct a test of hypothesis on each of the regression coefficients. Use residual analysis to evaluate the assumptions of multiple regression analysis. Evaluate the effects of correlated independent variables. Use and understand qualitative independent variables. Understand and interpret the stepwise regression method. Understand and interpret possible interaction among independent variables.
3
Multiple Regression Analysis
For two independent variables, the general form of the multiple regression equation is:
•X1 and X2 are the independent variables. •a is the Y-intercept •b1 is the net change in Y for each unit change in X1 holding X2 constant. It is called a partial regression coefficient, a net regression coefficient, or just a regression coefficient.
2
Multiple Regression Analysis
The general multiple regression with k independent variables is given by:
The least squares criterion is used to develop this equation. Because determining b1, b2, etc. is very tedious, a software package such as Excel or MINITAB is recommended.
To investigate, Salsberry’s research department selected a random sample of 20 recently sold homes. It determined the cost to heat each home last January, as well
6
Multiple Linear Regression - Example
7
Multiple Linear Regression – Minitab Example
8
Multiple Linear Regression – Excel Example
Multiple Linear Regression and Correlation Analysis
Chapter 14
McGraw-Hill/Irwin
©The McGraw-Hill Companies, Inc. 2008
GOALS
Describe the relationship between several independent variables and a dependent variable using multiple regression analysis.
Three variables are thought to relate to the heating costs: (1) the mean daily outside temperature, (2) the number of inches of insulation in the attic, and (3) the age in years of the furnace.
4
Regression Plane for a 2-Independent Variable Linear Regression Equation
5
Multiple Linear Regression - Example
Salsberry Realty sells homes along the east coast of the United States. One of the questions most frequently asked by prospective buyers is: If we purchase this home, how much can we expect to pay to heat it during the winter? The research department at Salsberry has been asked to develop some guidelines regarding heating costs for single-family homes.
coefficient of multiple determination, and the adjusted coefficient of multiple determination. Conduct a test of hypothesis to determine whether regression coefficients differ from zero. Conduct a test of hypothesis on each of the regression coefficients. Use residual analysis to evaluate the assumptions of multiple regression analysis. Evaluate the effects of correlated independent variables. Use and understand qualitative independent variables. Understand and interpret the stepwise regression method. Understand and interpret possible interaction among independent variables.
3
Multiple Regression Analysis
For two independent variables, the general form of the multiple regression equation is:
•X1 and X2 are the independent variables. •a is the Y-intercept •b1 is the net change in Y for each unit change in X1 holding X2 constant. It is called a partial regression coefficient, a net regression coefficient, or just a regression coefficient.
2
Multiple Regression Analysis
The general multiple regression with k independent variables is given by:
The least squares criterion is used to develop this equation. Because determining b1, b2, etc. is very tedious, a software package such as Excel or MINITAB is recommended.
To investigate, Salsberry’s research department selected a random sample of 20 recently sold homes. It determined the cost to heat each home last January, as well
6
Multiple Linear Regression - Example
7
Multiple Linear Regression – Minitab Example
8
Multiple Linear Regression – Excel Example
Multiple Linear Regression and Correlation Analysis
Chapter 14
McGraw-Hill/Irwin
©The McGraw-Hill Companies, Inc. 2008
GOALS
Describe the relationship between several independent variables and a dependent variable using multiple regression analysis.
Three variables are thought to relate to the heating costs: (1) the mean daily outside temperature, (2) the number of inches of insulation in the attic, and (3) the age in years of the furnace.
4
Regression Plane for a 2-Independent Variable Linear Regression Equation
5
Multiple Linear Regression - Example
Salsberry Realty sells homes along the east coast of the United States. One of the questions most frequently asked by prospective buyers is: If we purchase this home, how much can we expect to pay to heat it during the winter? The research department at Salsberry has been asked to develop some guidelines regarding heating costs for single-family homes.