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]