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An environmental scientist has been collecting data for a study on air quality. The scientist is tracking levels of three pollutants: carbon monoxide (CO), nitrogen dioxide (NO₂), and particulate matter (PM2.5). These levels are measured daily for 30 days. The scientist hypothesizes that the levels of these three pollutants are linearly related, meaning that the level of one pollutant can be predicted using the levels of the other two pollutants. However, the data is complicated by the fact that many external variables could be influencing pollutant levels (e.g., wind speed, temperature, human activity, etc.), and these factors may not be consistent from day to day. Here's the data for the first five days (the full data set is provided separately): Day CO Level NO2 Level PM2.5 Level 1 0.8 2 0.6 3 0.7 4 0.9 5 0.6 21 a. Represent the data in matrix form. 20 18 22 23 12 13 14 15 13 b. Write down a system of linear equations that relates CO, NO2, and PM2.5 levels. Assume the relationship can be modeled as a₁CO+a₂NO₂ = PM2.5, where a₁ and a2 are constants to be determined.

An environmental scientist has been collecting data for a study on air quality. The scientist is tracking levels of three pollutants: carbon monoxide (CO), nitrogen dioxide (NO₂), and particulate matter (PM2.5). These levels are measured daily for 30 days. The scientist hypothesizes that the levels of these three pollutants are linearly related, meaning that the level of one pollutant can be predicted using the levels of the other two pollutants. However, the data is complicated by the fact that many external variables could be influencing pollutant levels (e.g., wind speed, temperature, human activity, etc.), and these factors may not be consistent from day to day. Here's the data for the first five days (the full data set is provided separately): Day CO Level NO2 Level PM2.5 Level 1 0.8 2 0.6 3 0.7 4 0.9 5 0.6 21 a. Represent the data in matrix form. 20 18 22 23 12 13 14 15 13 b. Write down a system of linear equations that relates CO, NO2, and PM2.5 levels. Assume the relationship can be modeled as a₁CO+a₂NO₂ = PM2.5, where a₁ and a2 are constants to be determined.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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An environmental scientist has been collecting data for a study on air quality. The scientist is tracking levels of three pollutants: carbon monoxide (CO), nitrogen dioxide (NO₂), and particulate matter (PM2.5). These levels are measured daily for 30 days. The scientist hypothesizes that the levels of these three pollutants are linearly related, meaning that the level of one pollutant can be predicted using the levels of the other two pollutants. However, the data is complicated by the fact that many external variables could be influencing pollutant levels (e.g., wind speed, temperature, human activity, etc.), and these factors may not be consistent from day to day. Here's the data for the first five days (the full data set is provided separately): Day CO Level NO2 Level PM2.5 Level 20 18 3 22 4 23 5 0.6 21 a. Represent the data in matrix form. 0.8 0.6 2 0.7 0.9 12 13 14 15 13 b. Write down a system of linear equations that relates CO, NO2, and PM2.5 levels. Assume the relationship can be modeled as a₁CO+a₂NO₂ = PM2.5, where a₁ and a2 are constants to be determined.
Transcribed Image Text:An environmental scientist has been collecting data for a study on air quality. The scientist is tracking levels of three pollutants: carbon monoxide (CO), nitrogen dioxide (NO₂), and particulate matter (PM2.5). These levels are measured daily for 30 days. The scientist hypothesizes that the levels of these three pollutants are linearly related, meaning that the level of one pollutant can be predicted using the levels of the other two pollutants. However, the data is complicated by the fact that many external variables could be influencing pollutant levels (e.g., wind speed, temperature, human activity, etc.), and these factors may not be consistent from day to day. Here's the data for the first five days (the full data set is provided separately): Day CO Level NO2 Level PM2.5 Level 20 18 3 22 4 23 5 0.6 21 a. Represent the data in matrix form. 0.8 0.6 2 0.7 0.9 12 13 14 15 13 b. Write down a system of linear equations that relates CO, NO2, and PM2.5 levels. Assume the relationship can be modeled as a₁CO+a₂NO₂ = PM2.5, where a₁ and a2 are constants to be determined.
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