simple2 - Simple Linear Regression Model The equation that...

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Simple Linear Regression Model y = b 0 + 1 x + e where: 0 and 1 are called parameters of the model , is a random variable called the error term . The simple linear regression model is: The equation that describes how y is related to x and an error term is called the regression model .
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Estimation Process Regression Model y = b 0 + 1 x + e Regression Equation E ( y ) = 0 + 1 x Unknown Parameters 0 , 1 Sample Data: x y x 1 y 1 . . . . x n y n b 0 and b 1 provide estimates of 0 and 1 Estimated Regression Equation Sample Statistics b 0 , b 1 01 ˆ y b b x 
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Estimation Process Unknown Relationship Population Random Sample Y X i i i b b e 0 1 i i i X Y e b ˆ ˆ ˆ 1 0
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Sampling distribution of slope Y Population Line X Sample 1 Line Sample 2 Line b 1 All Possible Sample Slopes Sample 1: 2.5 Sample 2: 1.6 Sample 3: 1.8 Sample 4: 2.1 : : Very large number of sample slopes Sampling Distribution b 1 b 1 S ^ ^ Source: McClave & Sincich (2003)
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Some cautions about the interpretation of significance tests Just because we are able to reject H 0 : b 1 = 0 and demonstrate statistical significance does not enable us to conclude that there is a linear relationship between x and y .
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simple2 - Simple Linear Regression Model The equation that...

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