204 4.1%2c4.2%2c4.3 lin relationships

204 4.1%2c4.2%2c4.3 lin relationships - R 2 SST = 2 1 ) (...

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CHAPTER 4 RELATIONSHIPS BETWEEN TWO VARIABLES Graphical Display scatter plot Numerical summaries r, r 2 , and y = ax + b 4.1 Scatter Plots and Correlation scatter plot X 1 2 3 4 5 Y 7 3 9 15 11 Y Correlation r - measures the strength of the linear relationship r = ) 1 ( ) )( ( - - - n s s y y x x y x r 2 - measures the fraction of the total variation in the response variable (y) explained by the linear regression. 15 12 9 6 3 1 2 3 4 5
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4.2 1) Calculate the regression equation y = b 1 x + b 0: a) from a set of data using a calculator or computer and b) using b 1 = rs y /s x b 0 = y - b 1 x 2) Calculate a predicted y value for a given x * value y = b 1 x * + b 0 = y predicted 3) Compute the residual for a particular x value e = y observed - y 4) Know the criteria for determining the values of b 0 and b 1 . b 0 and b 1 are the values that will minimize the sum of the squared errors ( 2 e ) for this particular set of data. 0 2 4 6 8 10 12 14 16 0 2 4 6 Series1 4.3 1) Calculate and understand the Coefficient of Determination
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Unformatted text preview: R 2 SST = 2 1 ) ( ∑ =-n i y y = total sum of squares for y (the response variable) SSR = 2 1 ) ( ∑ = ∧-n i y y = sum of squares for the regression SSE = 2 1 ) ( ∑ = ∧-n i y y = sum of the errors squared It can be mathematically shown that SST = SSR + SSE Define r 2 = SST SSR 2) Residual (error) Analysis a) Is the linear model reasonable b) Are the errors: i) normally distributed about the regression line ii) of constant variance for all x values 3) Influential observations - Influential points - points which when removed from the data will result in a significant change in the slope and/or intercept of the regression line Outliers - points outside the general pattern of data...
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This note was uploaded on 12/05/2011 for the course MATH 2040 taught by Professor Raysievers during the Fall '10 term at Utah Valley University.

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204 4.1%2c4.2%2c4.3 lin relationships - R 2 SST = 2 1 ) (...

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