Question: This problem is a study of air pollution. One component of air pollution is airborne particulate matter such as dust & smoke. To measure particulate pollution, a vacuum motor draws air through a filter for 24 hours. Weight the filter at the beginning & end of the period. The weight gained is a measure of a concentration of particles in the air. A study of air pollution made measurements every 6 days with identical instruments in the center of a small city & at a rural location ten miles southwest of the city. Because the prevailing winds blow from the west, we suspect that the rural readings will be generally lower than the city readings, but that the city readings can be predicted from the rural readings. The table below gives readings taken every six days over a seven month period. The entry NA means that the reading for that date is not available, usually because of equipment failure.

Missing data are common, especially in field studies like this one. We think that equipment failures are not related to pollution levels. If that is true, the missing data do not introduce bias. We can work with the data that are not missing as if they are a random sample of days. We can analyze these data in different ways to answer different questions. For each of the three parts below, do a careful descriptive analysis with graphs & summary statistics & whatever formal inference is called for. Then present & interpret your findings.

We hope to use the rural particulate level to predict the city level on the same day. Make a graph to examine the relationship. Does the graph suggest that using the least-square regression line for prediction will give approximately correct results over the range of values appearing in the data? Calculate the least-squares line for predicting city pollution from rural pollution. What percent of the observed variation in the city pollution levels does this straight-line relationship account for? On the fourteenth date in the series, the rural reading was eighty-eight & the city reading was not available. What do you estimate the city reading to be for that date?