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ST3131 Tutorial 5.pdf - NATIONAL UNIVERSITY OF SINGAPORE...

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1 NATIONAL UNIVERSITY OF SINGAPORE Department of Statistics and Applied Probability 2017/18 Semester 1 ST3131 Regression Analysis Tutorial 5 1. Consider the multiple linear regression model ݕ = ߚ + ߚ ݔ + ߚ ݔ + ߚ ݔ + ߚ ݔ + ߳ The above model can be represented by ݕ = ܺߚ + ߳ or ݕ ݕ ݕ ൲ = ൮ 1 ݔ ଵ,ଵ ݔ ଶ,ଵ ݔ ଷ,ଵ ݔ ସ,ଵ 1 ݔ ଵ,ଶ ݔ ଶ,ଶ ݔ ଷ,ଶ ݔ ସ,ଶ 1 ݔ ଵ,௡ ݔ ଶ,௡ ݔ ଷ,௡ ݔ ସ,௡ ۉ ۈ ۇ ߚ ߚ ߚ ߚ ߚ ی ۋ ۊ + ൮ ߳ ߳ ߳ It is desired to test (i) H 0 : ߚ = 2ߚ , ߚ = ߚ . (ii) H 0 : ߚ − 2ߚ = 4ߚ , ߚ − 3ߚ = 0 . (iii) H 0 : ܥߚ = 0 where ܥ = ൭ 0 2 −1 0 1 0 1 −1 0 0 0 0 1 0 1 and ߚ = ሺߚ ߚ ߚ ߚ ߚ Carry out the test of the hypotheses using the set of data in Question 2 of Tutorial 4. Use α = 0.05. (Data file: “t4q2.txt”) 2. The effectiveness of a new experimental overdrive gear in reducing patrol consumption was studied in 12 trials with a light truck equipped with this gear. In the data that follow, x denotes the constant speed (in mph) on the test track and y denotes miles per gallon obtained. (Data file: “t5q2.txt”) x 35 35 40 40 45 45 50 50 55 55 60 60 y 22 20 28 31 36 38 41 39 34 37 27 30 (i) Fit the data to a straight line model.
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