Practice Midterm

Practice Midterm - GEORGE WASHINGTON UNIVERSITY Department...

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GEORGE WASHINGTON UNIVERSITY Department of Statistics STAT 118, Section 10, Fall 2009 Practice Midterm 1. Express the following system of equations in matrix form. y 1 = β 0 +8 β 1 +4 β 2 + ± 1 y 2 = β 0 +11 β 1 +5 β 2 + ± 2 y 3 = β 0 + β 1 + β 2 + ± 3 y 4 = β 0 +7 β 1 + ± 3 2. Given the matrix X and vector y , Fnd ( X ± X ) - 1 , X ± y and ( X ± X ) - 1 X ± y . X= 2 3 y = 11 10 5 3- 1 7 02 8 45 1 5 01 4 3. Sometimes additives are used to boost the mileage of cars. An automechanic wants to study the effect of a particular additive on mileage. She took a random sample of 11 cars (of similar type) and observed the mileage(mpg)( Y ) obtained for different amounts of additive used(in ml/G)( X ) under similar driving conditions. The results of the study and partial SAS output is reproduced below. Additive amount( x ) 10 13 8 18 15 20 10 5 22 16 6 Mileage(mpg) ( y ) 27.5 28.8 28.1 33.5 29.6 32.6 28.1 26.5 34.9 31.7 24.9 Dependent Variable: mpg Analysis of Variance Sum of Mean Source DF Squares Square F Value Model 1 -------- 89.72299 ------- Error -- 8.20428 -------- Corrected Total -- 97.92727 Root MSE -------- R-Square 0.9162 Dependent Mean 29.65455 Adj R-Sq 0.9069
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This note was uploaded on 11/09/2009 for the course STAT 118 taught by Professor ** during the Fall '09 term at GWU.

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Practice Midterm - GEORGE WASHINGTON UNIVERSITY Department...

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