Chapter_13 - Chapter 13 Simple Linear Regression Click to...

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Click to edit Master subtitle style 1Chap 13-1 Chapter 13 Simple Linear Regression
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2Chap 13-2 Correlation vs. Regression n A scatter plot can be used to show the relationship between two variables n Correlation analysis is used to measure the strength of the association (linear relationship) between two variables n Correlation is only concerned with strength of the relationship n No causal effect is implied with correlation n Scatter plots were first presented in Ch. 2 n Correlation was first presented in Ch. 3
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3Chap 13-3 Introduction to Regression Analysis n Regression analysis is used to: n Predict the value of a dependent variable based on the value of at least one independent variable n 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
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4Chap 13-4 Simple Linear Regression Model n Only one independent variable , X n Relationship between X and Y is described by a linear function n Changes in Y are assumed to be related to changes in X
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5Chap 13-5 Types of Relationships Y X Y X Y Y X X Linear relationships Curvilinear relationships
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6Chap 13-6 Types of Relationships Y X Y X Y Y X X Strong relationships Weak relationships (continued)
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7Chap 13-7 Types of Relationships Y X Y X No relationship (continued )
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8Chap 13-8 i i 1 0 i ε X β β Y + + = Linear component Simple Linear Regression Model Population Y intercept Population Slope Coefficient Random Error term Dependent Variable Independent Variable Random Error component
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9Chap 13-9 (continued) Random Error for this Xi value Y X Observed Value of Y for Xi Predicted Value of Y for Xi i i 1 0 i ε X β β Y + + = Xi Slope = β1 Intercept = β0 εi Simple Linear Regression Model
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10Chap 13-10 i 1 0 i X b b Y ˆ + = The simple linear regression equation provides an estimate of the population regression line Simple Linear Regression Equation (Prediction 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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11Chap 13-11 The Least Squares Method b0 and b1 are obtained by finding the values of that minimize the sum of the squared differences between Y and : 2 i 1 0 i 2 i i )) X b (b (Y min ) Y ˆ (Y min + - = - Y ˆ
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12Chap 13-12 n b0 is the estimated average value of Y when the value of X is zero n b1 is the estimated change in the average value of Y as a result of a one-unit change in X Interpretation of the Slope and the Intercept
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13Chap 13-13 Simple Linear Regression Example n A real estate agent wishes to examine the relationship between the selling price of a home and its size (measured in square feet) n A random sample of 10 houses is selected n Dependent variable (Y) = house price in $1000s n Independent variable (X) = square feet
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14Chap 13-14 0 50 100 150 200 250 300 350 400 450 0 500 1000 1500 2000 2500 3000 Square Feet House Price ($1000s)
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Chapter_13 - Chapter 13 Simple Linear Regression Click to...

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