STA2020FTest2_08 - STA2020F Class Test 2 Date: 16 April...

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STA2020F Class Test 2 Date: 16 April 2008 Time: 1 hour SECTION A (20) Question 1. In multiple regression, why is it necessary to test the hypothesis that at least one of the β ’s differs from 0 before testing each individual β for difference from 0? [2] Question 2. Suppose that you have at your disposal the information below for each of 30 drivers. Propose a model (including a very brief indication of notation used to represent the variables) to explain how fuel consumption varies from driver to driver on the basis of the factors measured. Information: 1. km driven per day 2. mass of car 3. number of cylinders in car 4. average speed 5. fuel consumption (litres per 100 km) 6. number of passengers [3] Question 3. It is believed that the production rate Y in an industrial process is linearly related to the amount of salt X 1 and the amount of chlorine dioxide X 2 used during a critical part of the process. Production rates (in litres per minute) were recorded along with the values of X 1 and X 2 on eight occasions: Rate (Y) Salt (X 1 ) Chlorine Dioxide (X 2 ) 5.0 9.6 1.5 3.5 9.4 2.3 2.0 9.0 2.0 2.5 9.4 4.2 4.0 9.5 1.5 3.0 9.4 2.5 2.5 9.2 2.5 3.0 9.5 3.3 A portion of computer output is given below: ANOVA df SS MS F P-value Regression 2 6.1070 3.0535 42.20 0.001 Residual 5 0.3618 0.0724 Total 7 6.4687 Coefficient SE t-stat P-value Intercept -33.023 5.009 -6.59 0.001 SALT 4.0128 0.5328 7.53 0.001 CL-DIOX -0.5696 0.1116 -5.11 0.004
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a) Write down the equation of the fitted model. (1) b) Find the standard error of the estimate and explain what this number means. (2) c) What is R 2 ? How do we interpret this figure? (2) d) What conclusion can be drawn about the overall fit of the model? (2) e) What conclusions can be drawn about the individual variables in the model? (3)
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STA2020FTest2_08 - STA2020F Class Test 2 Date: 16 April...

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