# ch11 - AMS 315/576 Lecture Notes Chapter 11. Simple Linear...

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¤ § ¥ ƒ AMS 315/576 Lecture Notes Chapter 11. Simple Linear Regression 11.1 Motivation A restaurant opening on a “reservations-only” basis would like to use the number of advance reservations x to predict the number of dinners y to be prepared. Data on reser- vations and numbers of dinners served for one day chosen at random from each week in a 100-week period gave the following results: (# of reservations) (# of meals) 50 100 150 200 33 66 100 Question: Suppose the # of reservations for a future week is 135, how many meals should be prepared? 1

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11.2 A simple graphical representation: the scatter plot 11.3 Transformation to linearize data 11.4 The simple linear (regression) model: y = β 0 + β 1 x + ², where ² is a random error with mean 0 and variance σ 2 (unknown but usually assumed to be constant.) 2
11.5 The least squares method of model ﬁtting Suppose the ﬁtted line is ˆ y = ˆ β 0 + ˆ β 1 x ; the sum of the squared distance between the ﬁtted value ˆ y and the observed value y is Δ = n X i =1 ( y i - ˆ y i ) 2 = n X i =1 ( y i - ˆ β 0 - ˆ β 1 x i ) 2 ; the least squares estimators of the model parameters β 0 and β 1 are the values of ˆ β 0 and ˆ β 1 that minimize δ , they are; ¤ § ¥ ƒ ˆ β 0 = ¯ y - ˆ β i · ¯ x and ¤ § ¥ ƒ ˆ β 1 = S XY S XX where S XY = n X i =1 ( X i - ¯ X )( Y i - ¯ Y ) = X X i Y i - ( X i )( Y i ) n = X X i Y i - n ( ¯ X )( ¯ Y ) . S

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## This note was uploaded on 01/31/2011 for the course AMS 572 taught by Professor Weizhu during the Fall '10 term at SUNY Stony Brook.

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ch11 - AMS 315/576 Lecture Notes Chapter 11. Simple Linear...

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