The data listed in the table on the following page are from an unpublished study by Harbin and others (1985). Subjects were young (ages 18 through 29) or old (ages 60 through 86) men. Each subject was exposed to 0 or 100 parts per million (ppm) of carbon monoxide (CO) for a period before and during testing. Median reaction times for 30 trials are reported for two different tasks: (1) simple reaction time (no choice), REACTIM1; (2) two-choice reaction time, REACTIM2. Pilot data analysis from an earlier study established that this dependent variable followed an appropriate Gaussian distribution. For this problem, consider only REACTIM1 as a dependent variable. Use a = .01.
a. Observe the cross-tabulation of AGEGROUP and PPM_CO in the accompanying SAS PROC FREQ computer output. Why might this be called a nearly orthogonal two-way design? Any missing data were due to technical problems unrelated to the response variable or treatments.
b. Using dummy variables coded -1 and 1 for AGEGROUP = young and old, respectively, and coded €” 1 and 1 for PPM_CO = 0 and 100, respectively, define dummy variables and a corresponding multiple regression model for a two-way ANOVA.
c. Use an appropriate computer program to fit the regression model in part (b). Report appropriate tests of the AGEGROUP × PPM_CO interaction and tests of their main effects in an appropriate summary source table.
d. SAS's PROC GLM procedure automatically codes dummy variables (and properly treats unequal sample sizes). The accompanying PROC GLM computer output shows the two-way ANOVA results for this problem. Complete the F statistics in the ANOVA table, and report the results of the same tests as in part (c). Compare the results to those in part (c), and explain any differences.

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Observation AGEGROUP PPM CO REACTIM REACTIM2 Young Young Young Young oung Young Young Young Young Young Young 291.5 471.0 692.0 376.0 372.5 307.0 501.0 466.0 375.0 25.0 343.0 632.0 607.5 859.0 484.0 501.0 381.0 59.0 632.0 434.0 454.0 10 50000050500 .0 50550 5554 556577886 88688 0000555550500000 0005500 1.5 500050050 005500 30343344 34 3 4436453434 000000000 100 100 100 100 Old Old Old Old Old Old Old Old Old Old Old Old Old Old Old Old Old Old Old Old Old 5 245 26 27 28 29 30 31 32 33 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 678 234 15 16 17 18 19 20