Air Pollution Control Specialists In Southern California

Air Pollution Control Specialists In Southern California Monitor The A

Air pollution control specialists in southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit seasonality, with the levels of pollutants showing similar patterns over the hours in the day. On July 15, 16, and 17, the observed level of nitrogen dioxide in a city’s downtown area for the 12 hours from 6:00 A.M. to 6:00 P.M. were as follows: 15-July 25, 28, 35, 50, 60, 60, 40, 35, 30, 25, 25, -

July 16, 30, 35, 48, 60, 65, 50, 40, 35, 25, 20, -

July 17, 35, 42, 45, 70, 72, 75, 60, 45, 40, 25, 25, 25.

Use a multiple linear regression model with dummy variables to account for seasonal effects in the data. Define dummy variables Hour 1 through Hour 11, where each is 1 if the reading was made between 6:00 A.M. and 7:00 A.M., 7:00 A.M. and 8:00 A.M., etc., respectively, and 0 otherwise. When all by-hour dummy variables are zero, the observation corresponds to 5:00 P.M. to 6:00 P.M.

Develop an equation to estimate nitrogen dioxide levels for July 18 using the regression model. Assign t=1 to the observation in hour 1 on July 15, t=2 to hour 2 on July 15, ..., t=36 to hour 12 on July 17. Using the dummy variables and t, create an equation to account for seasonal effects and any linear trend. Based on this model, estimate the nitrogen dioxide levels for July 18 for each hour from 6:00 A.M. to 6:00 P.M.

Paper For Above instruction

The monitoring of nitrogen dioxide levels by air pollution control specialists in southern California involves detailed time series analysis to account for inherent seasonality and trends within pollutant concentration data. In understanding and modeling this data, regression analysis with dummy variables is a pertinent approach to capture hourly variations, as well as temporal trends over multiple days.

To begin, we recognize that the data exhibits daily cyclic patterns with significant variation across specific hours. The dummy variable methodology involves creating 11 indicator variables for hours 6:00 A.M. to 5:00 P.M., with the 12th period (5:00 P.M. to 6:00 P.M.) serving as the baseline when all dummy variables are zero. Each dummy variable is assigned a value of 1 if the observation falls within its respective hour and 0 otherwise, allowing the model to isolate effects attributable to specific hours of the day.

The regression model can be specified as follows:

\(Y_t = \beta_0 + \beta_1 \text{Hour}_1 + \beta_2 \text{Hour}_2 + \ldots + \beta_{11} \text{Hour}_{11} + \beta_{12} t + \varepsilon_t\)

where \(Y_t\) represents the nitrogen dioxide level at time \(t\), \(\text{Hour}_i\) are the dummy variables for each hour, \(t\) is a time trend variable capturing linear progression over days, and \(\varepsilon_t\) is the error term.

Given the data, we proceed to estimate regression coefficients by fitting the model to the observed levels for July 15-17. Once the coefficients are obtained, the model facilitates forecasting for July 18, assuming the same seasonal pattern and trend continue. The estimates involve plugging in the dummy variables corresponding to each hour of July 18 and the appropriate value of \(t\) (which continues sequentially from previous observations).

For example, the estimation for July 15's first hour (t=1), similarly for subsequent hours, provides the baseline for the model's parameters, which are then used to predict future levels. The result yields anticipated nitrogen dioxide levels for each hour of July 18, incorporating both seasonal effects and linear trends identified from the historical data.

In conclusion, this multiple linear regression approach with dummy variables effectively captures the hourly seasonality and potential linear trend within the nitrogen dioxide time series, allowing environmental agencies and policymakers to forecast pollutant levels and implement timely mitigation strategies.

References

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