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exam1 - ISYE6414 Summer 2009 Exam I Dr Kobi Abayomi You...

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ISYE6414 Summer 2009 Exam I Dr. Kobi Abayomi June 10, 2009 You must show all work to receive full credit. 1

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1 A climatologist investigates the effect of Solar Radiation, Wind, and Temperature on Ozone levels. She takes n = 153 daily observations from May 1st until September 30th. The multiple regression output is: Coefficient Estimate SE t Pr ( > | t | ) (Intercept) -64.34 -2.791 Solar.R 0.023 2.58 0.013 Wind -3.33 0.65 Temp 0.25 6.51 Fill in the missing values above. Write the estimated linear model. With [,1] [,2] [,3] [,4] [1,] 8.96e-01 7.07e-05 -1.67e-02 -9.40e-03 [2,] 7.07e-05 9.26e-07 -2.04e-06 -2.84e-06 [3,] -1.67e-02 -2.04e-06 7.10e-04 1.28e-04 [4,] -9.40e-03 -2.84e-06 1.28e-04 1.10e-04 as ( X T X ) - 1 : for particular observed values of Solar Radiation, Wind, and Temp: x = (190 , 7 . 4 , 67) what is the confidence interval for the mean response? What is the prediction interval? Say the observed value Ozone value is 41. What can you say about these intervals? 2

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2 For the model Y i = β 0 + β 1 X i + i with i N (0 , σ 2 ) the following statistics are computed: 9 X i =1 x i y i = 243 9 X i =1 x 2 i = 324 = 9 X i =1 y 2 i 9 X i =1 x i = 0 = 9 X i =1 y i
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