# Air pollution control speciali

Air pollution control specialists in southern California monitorthe amount of ozone, carbon dioxide, and nitrogen dioxide in theair on an hourly basis. The hourly time series data exhibitseasonality, with the levels of pollutants showing patterns thatvary over the hours in the day. On July 15, 16, and 17, thefollowing levels of nitrogen dioxide were observed for the 12 hoursfrom 6:00 A.M. to 6:00 P.M.

Click on the datafile logo to reference the data.

 July 15: 25 28 35 50 60 60 40 35 30 25 25 20 July 16: 28 30 35 48 60 65 50 40 35 25 20 20 July 17: 35 42 45 70 72 75 60 45 40 25 25 25
Use a multiple linear regression model with dummy variables asfollows to develop an equation to account for seasonal effects inthe data:
Hour1 = 1 if the reading was made between 6:00 A.M. and7:00A.M.; 0 otherwise
Hour2 = 1 if the reading was made between 7:00 A.M. and 8:00A.M.; 0 otherwise
.
.
.
Hour11 = 1 if the reading was made between 4:00 P.M. and 5:00P.M., 0 otherwise
Note that when the values of the 11 dummy variables are equalto 0, the observation corresponds to the 5:00 P.M. to 6:00 P.M.hour.
If required, round your answers to three decimal places. Forsubtractive or negative numbers use a minus sign even if there is a+ sign before the blank. (Example: -300) Do not round intermediatecalculation.
Value =  +  Hour1 +  Hour2+  Hour3 +  Hour4 +  Hour5+  Hour6 +  Hour7 +  Hour8+  Hour9 +  Hour10 +  Hour11
(c) Using the equation developed in part (b), compute estimates ofthe levels of nitrogen dioxide for July 18.
If required, round your answers to three decimal places. Do notround intermediate calculation.
 6:00 a.m. – 7:00 a.m. forecast 7:00 a.m. – 8:00 a.m. forecast 8:00 a.m. – 9:00 a.m. forecast 9:00 a.m. – 10:00 a.m. forecast 10:00 a.m. – 11:00 a.m. forecast 11:00 a.m. – noon forecast noon – 1:00 p.m. forecast 1:00 p.m. – 2:00 p.m. forecast 2:00 p.m. – 3:00 p.m. forecast 3:00 p.m. – 4:00 p.m. forecast 4:00 p.m. – 5:00 p.m. forecast 5:00 p.m. – 6:00 p.m. forecast
(d) Let t = 1 to refer to the observation in hour 1 onJuly 15; t = 2 to refer to the observation in hour 2 ofJuly 15; …; and t = 36 to refer to the observation inhour 12 of July 17. Using the dummy variables defined in part (b)and ts, develop an equation to account forseasonal effects and any linear trend in the time series.
If required, round your answers to three decimal places. Forsubtractive or negative numbers use a minus sign even if there is a+ sign before the blank. (Example: -300)
Value =  +  Hour1 +  Hour2+  Hour3 +  Hour4 +  Hour5+  Hour6 +  Hour7 +  Hour8+  Hour9 +  Hour10 +  Hour11+  t
(e) Based on the seasonal effects in the data and linear trendestimated in part (d), compute estimates of the levels of nitrogendioxide for July 18.
 6:00 a.m. – 7:00 a.m. forecast 7:00 a.m. – 8:00 a.m. forecast 8:00 a.m. – 9:00 a.m. forecast 9:00 a.m. – 10:00 a.m. forecast 10:00 a.m. – 11:00 a.m. forecast 11:00 a.m. – noon forecast noon – 1:00 p.m. forecast 1:00 p.m. – 2:00 p.m. forecast 2:00 p.m. – 3:00 p.m. forecast 3:00 p.m. – 4:00 p.m. forecast 4:00 p.m. – 5:00 p.m. forecast 5:00 p.m. – 6:00 p.m. forecast
(f) Is the model you developed in part (b) or the model youdeveloped in part (d) more effective?
 Model developed in part (b) Model developed in part (d) MSE
– Select your answer -Model developed in part (b)Modeldeveloped in part (d)Item 54

Step-1

Forecasting is a technique which helps inpredicting the future data based on the present data or situation.It is analyzed by trend analysis. Time series is a set ofobservation measured at successive points in time or oversuccessive period of time.

Step-2

a.

Construct the time series plot using XLMINER software, theprocedure to make the time series plot is given as below:

1. Write down the provided data into spreadsheet, the screenshotis shown below:

2. Select the provided data range and then click on the“XLMMINER” Platform tab in the ribbon.

3. From the “Data Analysis” table select the “Explore” option.In the Explore option select the “Chart wizard” option.

A new dialog box will appear, select the “Line chart” option andpress “Next” option. Now select the “level and time period” press“level” tab. Select “time period” then press “Next” and select“level” and again press “Next”. Press “Finish” option, thescreenshot of the obtained time series plot is shown below:

The above time series plot indicate seasonal pattern in thelevel of ozone, carbon dioxide and nitrogen dioxide.

Step-3

b.

The multiple linear regression models given as:

1

Here, the intercept isthe predicted value of when areequal to zero, and arethe slope coefficients. According to the provided criteriaintroduce the dummy variables for 11 hours for three days levels.Thus the obtained dummy variables for the 11 hours will be:

Step-4

Cosider “Hour1…Hour11” as explnatory variables and “level” asdependent variable, regressing level on explanatory variable inExcel as follows:

1. Select the provided data range and then click on the“XLMINER” Platform tab in the ribbon.

2. Select the “Predict” in the “Data Mining” group and selectthe “Multiple Liner Regression” option.

3. A new dialog box will appear, select the explanatory variablein the “Selected variables” box. And select the dependent variablein the “Output variable” box. The screenshot is shown below:

Step-5

4. Click “Next” option in the above dialog box, a new dialog boxwill appear. Select the options as shown below:

5. Press “Finish” option in the above dialog box, the screenshotof the obtained regression analysis is shown below:

According to the above output, the multile regression equationfor the seasonal effects is given as:

Step-6

c.

Predict estimates of the level of nitrogen dioxide for july 18,use the multile regression line obtained in the part (b). Calculatthe forecast for each hour as shown below:

step-7

Step-8

Step-9

Step-10

Step-11

Step-12

Step-13

Step-14

Step-15

Step-16

d.

Now, introduce new variable to account the seasonal effect inthe data for, for this add new explanatory variable “Time(t)” in the data. The screenshot of the data file is shownbelow:

Step-17

Now, follow the same procedure as done in the part (b), thescreenshot of the output is shown below:

According to the above output, the multile regression equationto predict the seasonal effects and liner trend is given as:

Step-18

e.

Predict hourly forcast for July 18, use the multile regressionline obtained in the part (d). The forecast for the each hour forJuly 18 is calculated as below:

Step-19

Step-20

Step-21

f.

According to the results obtained in the part (b), the minimumMSE for the hour is calculated as

According to the results obtained in the part (d), the minimumMSE for the hour is calculated as:

Hence, the mean squared error for the model from the part (d),which include the seasonal effects and linear trend is smaller thanthe mean squared error for the model from the part (b), whichinclude the seasonal effects. So, the model obtained in the part(d) will be more effective. This supports initial decisions gottenin review of the time series plot created in part (a) and the datashow a linear trend with seasonality.

##### "Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
Calculate the price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with brilliantassignmenthelp.com
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat