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Keywords: multiple regression, daily trend, harmonics.

Hourly carbon monoxide (CO) averages were recorded on summer weekdays at a measurement station in Los Angeles. The station was established by the Environmental Protection Agency as part of a larger study to assess the effectiveness of the catalytic converter. It was located about 25 feet from the San Diego Freeway, which in this particular area is located at 145 degrees north. It was located such that winds from 145 to 325 degress (which in the summer are the prevalent wind directions during the daylight hours) transport the CO emissions from the highway toward the measurement station. Aggregate measurements were recored for each hour of the day 1 to 24.

Hour | - | hour of the day, from midnight to midnight |

CO | - | average summer weekday CO concentration (parts per million) |

TD | - | average weekday traffic density (traffic count/traffic speed) |

WS | - | average perpendicular wind-speed component, wind speed x cos(wind direction - 235 degrees) |

It would be interesting to have wind speed and direction recorded separately.

Data File (tab-delimited text)

Ledolter, J., and Tiao, G. C. (1979). Statistical methods for ambient air pollutants with special reference to the Los Angeles Catalyst Study (LACS) Data. Environmental Science and Technology, 13, 1233-1240. |

Hogg, R. V., and Ledolter, J. (1992). Applied Statistics for Engineers and Physical Scientists, Second Edition. Macmillan, New York. Exercise 1.5-6. |

> summary(lm.co,cor=F) Call: lm(formula = CO ~ Traffic + Wind + Wind^2 + sin((2 * pi)/24 * Hour) + cos((2 * pi)/24 * Hour) + sin((4 * pi)/24 * Hour) + cos((4 * pi)/24 * Hour)) Residuals: Min 1Q Median 3Q Max -0.3477 -0.1078 0.0059 0.1407 0.3994 Coefficients: Value Std. Error t value Pr(>|t|) (Intercept) 1.7523 0.7793 2.2484 0.0390 Traffic 0.0179 0.0013 13.7864 0.0000 Wind 0.3178 0.3447 0.9220 0.3702 I(Wind^2) -0.0774 0.0268 -2.8851 0.0108 sin((2 * pi)/24 * Hour) -0.5437 0.9324 -0.5831 0.5680 cos((2 * pi)/24 * Hour) -0.7300 0.6574 -1.1106 0.2832 sin((4 * pi)/24 * Hour) 0.3664 0.4331 0.8460 0.4100 cos((4 * pi)/24 * Hour) 0.3110 0.1424 2.1838 0.0442 Residual standard error: 0.2298 on 16 degrees of freedom Multiple R-Squared: 0.9918 F-statistic: 277.5 on 7 and 16 degrees of freedom, the p-value is 1.776e-015 > anova(lm.co) Analysis of Variance Table Response: CO Terms added sequentially (first to last) Df Sum of Sq Mean Sq F Value Pr(F) Traffic 1 95.87547 95.87547 1815.139 0.00000000 Wind 1 2.35721 2.35721 44.627 0.00000528 I(Wind^2) 1 1.40893 1.40893 26.674 0.00009402 sin((2 * pi)/24 * Hour) 1 0.82150 0.82150 15.553 0.00116174 cos((2 * pi)/24 * Hour) 1 0.87639 0.87639 16.592 0.00088470 sin((4 * pi)/24 * Hour) 1 1.01972 1.01972 19.306 0.00045302 cos((4 * pi)/24 * Hour) 1 0.25191 0.25191 4.769 0.04420810 Residuals 16 0.84512 0.05282

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