Tut5-1 - NATIONAL UNIVERSITY OF SINGAPORE Department of...

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1 NATIONAL UNIVERSITY OF SINGAPORE Department of Statistics and Applied Probability 2012/13 Semester 2 ST3131 Regression Analysis Tutorial 5 1. The following data represent the heat evolved in calories per gram of cement ( y ) as a function of the amount of each of four ingredients in the mix: tricalcium aluminate ( x 1 ), tricalcium silicate ( x 2 ), tetracalcium alumino ferrite ( x 3 ) and dicalcium silicate ( x 4 ). Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 y 78.5 74.3 104.3 87.6 95.9 109.2 102.7 72.5 93.1 115.9 83.8 113.3 109.4 x 1 7 1 11 11 7 11 3 1 2 21 1 11 10 x 2 26 29 56 31 52 55 71 31 54 47 40 66 68 x 3 6 15 8 8 6 9 17 22 18 4 23 9 8 x 4 60 52 20 47 33 22 6 44 22 26 34 12 12 (i) What are the least squares estimates of the regression coefficients in the multiple regression model y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + β 4 x 4 + ε ? (ii) Test whether or not the overall regression is significant. (Use α = 0.05). (iii) Compute the coefficient of multiple determination for the model in (i). (iv) Determine a 95% confidence interval for the true mean response when x 1 = 7, x 2 = 52, x 3 = 6 and x 4 = 33.
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