Ch14 - Chapter 14 Simple Linear Regression Learning...

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14 - 1 Chapter 14 Simple Linear Regression Learning Objectives 1. Understand how regression analysis can be used to develop an equation that estimates mathematically how two variables are related. 2. Understand the differences between the regression model, the regression equation, and the estimated regression equation. 3. Know how to fit an estimated regression equation to a set of sample data based upon the least- squares method. 4. Be able to determine how good a fit is provided by the estimated regression equation and compute the sample correlation coefficient from the regression analysis output. 5. Understand the assumptions necessary for statistical inference and be able to test for a significant relationship. 6. Know how to develop confidence interval estimates of y given a specific value of x in both the case of a mean value of y and an individual value of y . 7. Learn how to use a residual plot to make a judgement as to the validity of the regression assumptions, recognize outliers, and identify influential observations. 8. Know the definition of the following terms: independent and dependent variable simple linear regression regression model regression equation and estimated regression equation scatter diagram coefficient of determination standard error of the estimate confidence interval prediction interval residual plot standardized residual plot outlier influential observation leverage
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Chapter 14 14 - 2 Solutions: 1 a. b. There appears to be a linear relationship between x and y. c. Many different straight lines can be drawn to provide a linear approximation of the relationship between x and y; in part d we will determine the equation of a straight line that “best” represents the relationship according to the least squares criterion. d. Summations needed to compute the slope and y-intercept are: 2 15 40 ( )( ) 26 ( ) 10 ii i i i x y xxyy xx Σ= Σ− −= Σ− = 1 2 () 26 2.6 10 i b == = by b x 01 82 6 30 2 =− =− = (.) . ˆ 0.2 2.6 yx =+ e. ˆ 0.2 2.6(4) 10.6 y = 0 2 4 6 8 10 12 14 16 0123456 x y
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Simple Linear Regression 14 - 3 2. a. b. There appears to be a linear relationship between x and y . c. Many different straight lines can be drawn to provide a linear approximation of the relationship between x and y ; in part d we will determine the equation of a straight line that “best” represents the relationship according to the least squares criterion. d. Summations needed to compute the slope and y -intercept are: 2 19 116 ( )( ) 57.8 ( ) 30.8 ii i i i x y xxyy xx Σ= Σ − − = Σ − = 1 2 () 57.8 1.8766 30.8 i b Σ− == = by b x 01 232 18766 38 30 3311 =− = −− = .( . ) ( . ) . ± .. yx =− 30 33 188 e. ± ( ). y = 30 33 188 6 19 05 0 5 10 15 20 25 30 35 02468 1 0 x y
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Chapter 14 14 - 4 3. a. b. Summations needed to compute the slope and y -intercept are: 2 26 17 ( )( ) 11.6 ( ) 22.8 ii i i i x y xxyy xx Σ= Σ− −= Σ− = 1 2 () 11.6 0.5088 22.8 i b == = by b x 01 34 05088 2 07542 =− = − = .( . ) ( 5 .
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This note was uploaded on 03/01/2012 for the course ECON 371 taught by Professor Staff during the Spring '08 term at UVA.

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Ch14 - Chapter 14 Simple Linear Regression Learning...

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