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Unformatted text preview: Forecasting with Simple Forecasting with Simple Regression Regression Learning Objectives To Recognize Different Types of Regression Models To Determine the Simple Linear Regression Equation To Measure Variations To Understand the Assumptions of Regression and Correlation Chapter Topics To Perform Residual Analysis To Measure Autocorrelation To Make Inferences about the Slope To Measure the Strength of the Association To Estimate The Mean and Predicted Individual Values To Understand the Pitfalls in Regression and Ethical Issues (continued) Learning Objectives Purpose of Regression Analysis Regression Analysis is Used Primarily to Model Causality and Provide Prediction Predict the values of a dependent (response) variable based on values of at least one independent (explanatory) variable Explain the effect of the independent variables on the dependent variable Types of Regression Models Positive Linear Relationship Relationship NOT Linear Types of Regression Models Negative Linear Relationship No Relationship Sample regression line provides an estimate estimate of the population regression line as well as a predicted value of Y Linear Regression Equation Population Y Intercept Population Slope Coefficient Residual Sample Regression Equation (Fitted Regression Line, Predicted Value) t t X t Y ε β α + + = b X a Y + = ˆ Simple Linear Regression: Example You wish to examine the linear dependency of the annual sales of super markets on their sizes in square footage. Sample data for 7 Wellcome stores in Hong Kong were obtained. Find the equation of the straight line that fits the data best. Annual Store Square Sales Feet ($1000) 1 1,726 3,681 2 1,542 3,395 3 2,816 6,653 4 5,555 9,543 5 1,292 3,318 6 2,208 5,563 7 1,313 3,760 Scatter Diagram: Example 2000 4000 6000 8000 10000 12000 1000 2000 3000 4000 5000 6000 Square Feet Annual Sales ($000) Excel Output Estimating the Regression Equation: Example ( 29 ( 29 ( 29 2 2 2 1 ) ( ) ( ) )( ( ) ( ∑ ∑ ∑ ∑ ∑ ∑ ∑ = = X X Y Y X X X X n Y X XY n b X b Y n X b n Y b 1 1 =  = ∑ ∑ Estimating the Regression Equation: Example Notice that the slope coefficient is related to the sample correlation coefficient in the following way: ( 29 ( 29 r X X Y Y b 2 2 1 ∑ ∑ = This means that and r are proportional to one another and have the same sign 1 b Simple Linear Regression Equation: Example From Excel Printout: Co efficien ts In te rce pt 1636.414726 X V a ria ble 1.486633657 i i bX a Y + = ˆ i X 487 . 1 415 . 1636 + = Graph of the Simple Linear Regression Equation: Example 2000 4000 6000 8000 10000 12000 1000 2000 3000 4000 5000 6000 Square Feet Annual Sales ($000 Y i = 1 6 3 6 . 4 1 5 + 1 . 4 8 7 X i ∧ Interpretation of Results:...
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This note was uploaded on 05/14/2010 for the course EF 410 taught by Professor Jimchan during the Spring '10 term at Zagazig University.
 Spring '10
 jimchan

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