The Environmental Protection Agency conducted an experiment to assess the characteristics of sampling procedures designed to measure the suspended particulate concentration (X) in a particular city. At each of two distinct locations (designated as location 1 and location 2), two identical sampling units were set up side by side, and readings were taken on each of 10 days. The data are given here in tabular form, where Xij1 and Xij2 are, respectively, the measured concentration for samplers 1 and 2 at location i on day j (i = 1, 2; j = 1, 2, ..., 10). Researchers hypothesized that the inherent variation in the observations depends on the level of concentration being measured. To quantify this hypothesis, they proposed to fit a model of the form

where Z is 1 if the observation pertains to location 1 and is 0 otherwise and where
|dij| = |Xij1 – Xij2|.

a. Using the results provided in the following table, determine and interpret the fitted straight-line relationship between |dij| and (Xij1 +Xij2) at each location.
b. Test for parallelism of the two lines.
c. Test for coincidence of the two lines.
d. How would you test whether level of concentration is significantly related to inherent variation in the observations for at least one of the two locations?
Regression of ABS (d) on X (= X1 + X2), Z, and X × Z
Where Z = 1 if Location 1, 0 Otherwise