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

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"1212032011 a-5122776299 1240134205 ja-3661680220 Xi 4 8 2 1 714025 Xi ay 2 3 4 5 6 7 8 9 0 ANALYSIS OF VARIANCE Sum of DF Squares Mean Source Model Error Corrected Total Square F Value Pr> F 3 31.33952 10.44651 19.87 0001 16 8.41048 0.52565 19 39.75000 Root MSE Dependent Mean Coeff Var 0.72502 1.75000 41 42974 R-Square Adj R-Sq 0.7884 0.7487 PARAMETER ESTIMATES Standard Error Parameter Variable DF Estimate intercept t Value Pr>t Type 1 ss 0.43196 4.65 0.0003 -1.94 0.0708 -2 42792 0.61773 -3.93 0.0012 .0001 2.00856 61.25000 4.83482 4.61660 21.88810 0,03915 0.02023 xz 0.19506 0.03023 6.45