BUS152-Ch13 - BUS152 Statistics for Social Sciences Spring...

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Chapter 13: Simple Linear Regression Chap 13-1 BUS152 - Statistics for Social Sciences Spring 2011
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Correlation vs. Regression A scatter plot can be used to show the relationship between two variables Correlation analysis is used to measure the strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the relationship No causal effect is implied with correlation Scatter plots were first presented in Ch. 2 Correlation was first presented in Ch. 3 Chap 13-2
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Introduction to Regression Analysis Regression analysis is used to: Predict the value of a dependent variable based on the value of at least one independent variable Explain the impact of changes in an independent variable on the dependent variable Dependent variable: the variable we wish to predict or explain Independent variable: the variable used to predict or explain the dependent variable Chap 13-3
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Simple Linear Regression Model Only one independent variable , X Relationship between X and Y is described by a linear function Changes in Y are assumed to be related to changes in X Chap 13-4
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Types of Relationships Chap 13-5 Y X Y X Y Y X X Linear relationships Curvilinear relationships
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Types of Relationships Chap 13-6 Y X Y X Y Y X X Strong relationships Weak relationships (continued)
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Types of Relationships Chap 13-7 Y X Y X No relationship (continued)
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Simple Linear Regression Model Chap 13-8 i i 1 0 i ε X β β Y + + = Linear component Population Y intercept Population Slope Coefficient Random Error term Dependent Variable Independent Variable Random Error component
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Simple Linear Regression Model Chap 13-9 (continued) Random Error for this X i value Y X Observed Value of Y for X i Predicted Value of Y for X i i i 1 0 i ε X β β Y + + = X i Slope = β 1 Intercept = β 0 ε i
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Simple Linear Regression Equation (Prediction Line) Chap 13-10 i 1 0 i X b b Y ˆ + = The simple linear regression equation provides an estimate of the population regression line Estimate of the regression intercept Estimate of the regression slope Estimated (or predicted) Y value for observation i Value of X for observation i
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The Least Squares Method b 0 and b 1 are obtained by finding the values of that minimize the sum of the squared differences between Y and : Chap 13-11 2 i 1 0 i 2 i i )) X b (b (Y min ) Y ˆ (Y min + - = - Y ˆ
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Finding the Least Squares Equation The coefficients b 0 and b 1 , and other regression results in this chapter, will be found using Excel or SPSS Chap 13-12 Formulas are shown in the textbook for those who are interested
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Interpretation of the Slope and the Intercept b 0 is the estimated average value of Y when the value of X is zero b 1 is the estimated change in the average value of Y as a result of a one-unit change in X Chap 13-13
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Simple Linear Regression Example A real estate agent wishes to examine the relationship between the selling price of a home and its size (measured in square feet)
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This note was uploaded on 12/22/2011 for the course BUSINESS bus 152 taught by Professor Çeşmecibaşı during the Spring '11 term at Middle East Technical University.

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BUS152-Ch13 - BUS152 Statistics for Social Sciences Spring...

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