Chapter Topics • Types of Regression Models • Determining the Simple Linear Regression Equation • Measures of Variation in Regression and Correlation • Assumptions of Regression and Correlation • Residual Analysis and the Durbin- Watson Statistic • Estimation of Predicted Values • Correlation - Measuring the Strength of the Association
Chapter Topics. Types of Regression Models Determining the Simple Linear Regression Equation Measures of Variation in Regression and Correlation Assumptions of Regression and Correlation Residual Analysis and the Durbin-Watson Statistic Estimation of Predicted Values - PowerPoint PPT Presentation
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Chapter Topics• Types of Regression Models• Determining the Simple Linear Regression
Equation• Measures of Variation in Regression and
Correlation• Assumptions of Regression and Correlation• Residual Analysis and the Durbin-Watson Statistic• Estimation of Predicted Values• Correlation - Measuring the Strength of the
Association
Purpose of Regression and Correlation Analysis
• Regression Analysis is Used Primarily for Prediction
A statistical model used to predict the values of a dependent or response variable based on values of at least one independent or explanatory variable
Correlation Analysis is Used to Measure Strength of the Association Between Numerical Variables
Types of Regression Models
Positive Linear Relationship
Negative Linear Relationship
Relationship NOT Linear
No Relationship
Simple Linear Regression Model
iii XY 10
Y intercept
Slope
• The Straight Line that Best Fit the Data
• Relationship Between Variables Is a Linear Function
Random Error
Dependent (Response) Variable
Independent (Explanatory) Variable
Sample Linear Regression Model
ii XbbY 10
Yi
= Predicted Value of Y for observation i
Xi = Value of X for observation i
b0 = Sample Y - intercept used as estimate ofthe population 0
b1 = Sample Slope used as estimate of the population 1
Simple Linear Regression Equation: Example
You wish to examine the relationship between the square footage of produce stores and its annual sales. Sample data for 7 stores were obtained. Find the equation of the straight line that fits the data best