A political scientist developed a questionnaire to determine political tolerance scores (Y) for a random sample of faculty members at her university. She wanted to compare mean scores adjusted for age (X) in each of three categories: full professors, associate professors, and assistant professors. The data results are given in the accompanying tables (the higher the score, the more tolerant the individual).

a. State an ANACOVA regression model that can be used to compare the three groups, controlling for age.
b. What model should be used to check whether the ANACOVA model in part (a) is appropriate? Carry out the appropriate test. Use α = .01.
c. Using ANACOVA, determine adjusted mean tolerance scores for each group, and test whether these adjusted scores differ significantly from one another. Also, compare the adjusted means with the unadjusted means.
[(overall) = 39.667, (group 1) = 4.10, (group 2) = 4.86, and (group 3) = 5.00.]
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Group 1: Full Professors (ZI 1,22 = 0) 52 49 45 41 41 40 39 Age ) 65 61 47 Tolerance (Y) 3.03 2.70 4.3 2.70 5.09 402 3.71 5.52 5.294.62 1) Group 2: Associate Professors (ZI = 0,22 30 35 49 31 42 39 49 Age C0) 34 31 Tolerance () 4.62 5.22 4.85 4.51 5.12 4.47 4.50 4.88 5.17 5.21 Group 3: Assistant Professors (Z1 = Z2 = 0) 25 30 31 27 Age α) 26 48 32 Tolerance (V) 5.20 5.86 4.61 455 4.47 5.71 4.77 5.82 3.67 5.29 Regression of Tolerance (Y) on Age (X), Faculty Categories (Z1 and Z2) PARAMETER ESTIMATES Parameter Standard Variable DF Estimate Error t Value Pr It 0.61189 Intercept 6.18372 10.11 <.0001 0.03635 0.017412.09 0.0467 0.3398 0.41457 082 04199 10.0557 3234 019 084 21 0.19 08498 Regression of Y on X, Z1, Z2, XZ1, and Xz2 ANALYSIS OF VARIANCE Sum of Mean Source Model Error Corrected Total DF Squares SquareF Value Pr>F 5 10.20934 2.04187 24 9.76275 040678 29 1997210 502 0.0027 Root MSE Dependent Mean Coeff Var 0.63779 4.64967 13.71699 R-Square 0.5112 Adj R-Sq 0.4093 PARAMETER ESTIMATES Parameter Standard Variable DF Estimate Error tValue Pr Type I SS 0.98483 0.02948 045 0.6580 1.51591 Intercept 5.42706 5.51 <,0001648.58200 .20495 0.62494 0.01847 3.14678 073 04751 021420 -0.01321 Z1 2.78490 1 1.84 0.0786 11.223431.50993 081 0.4258 10.07247 0.03779 192 0.0671 0.03022 0.04165