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STAT 319 1 King Fahd University of Petroleum and Minerals College of Sciences Quiz #6 St. ID: St. Name: Serial#: Q1. Davidson (1993) studied the ozone levels in the South Coast Air Basin of California for the years 1976-1991. He believes that the number of days the ozone levels exceeded 0.20 ppm (the dependent variable y ) depends on the seasonal meteorological index, which is the seasonal average 850-millibar temperature (the independent variable x ). The following table gives the data. The Ozone Year 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 Data Days 91 105 106 108 88 91 58 82 81 65 61 48 61 43 33 36 Index 16.7 17.1 18.2 18.1 17.2 18.2 16 Given that 16 xi 277.5, i 1 16 yi 1157, i 1 16 17.2 18 xi 2 4819.27 , i 1 16 17.2 16.9 17.1 18.2 17.3 17.5 16.6 yi2 =93085, i 1 16 x y =20164.3 . i 1 i i a. Estimate the expected number of days the ozone level exceeded 0.2ppm when the seasonal meteorological index is 16. [6 Marks] b. Calculate MSE (TSS SSR ) /(n 2) . What does it indicate?. [2 Marks] 2 c. Calculate the 95% confidence interval for the expected number of days the ozone level exceeded 0.2 ppm when the seasonal meteorological index is 16. [4 Marks] d. Test, at 1% level of significance, the hypothesis that the seasonal meteorological index affects the expected number of days the ozone level exceeded by 0.2 ppm. Does the correlation coefficient indicate anything about the test you performed? [3+1 Marks] e. Compute the coefficient of determination, and write a comment about its value. [4 marks]