A testing laboratory studies and compares the relationship between tire tread wear per 1,000 miles (Y) and average driving speed (X) for two competing tire types (denoted A and B). The data shown in the following table were collected for a random sample of 20 tires, 10 of A and 10 of B.

a. Identify a single regression model that uses the data for both tire types and that defines straight-line models relating tread wear (Y) to average speed (X) for each tire.
b. Using the computer output given next, determines and plot the fitted straight lines for each tire type.
c. Test the null hypothesis that the straight lines for the two tire types coincide.
d. Test H0: "The lines are parallel" versus HA: "The lines are not parallel."
e. In light of your answers to parts (c) and (d), comment on differences and similarities in the tread wear-average speed relationship for the two tire types.
Regression of Tread Wear (Y) on Avg. Speed (X), Tire (Z), and XZ
(Z = 0 for Tire A, Z = 1 for Tire B)
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Tread Wear per 100 Miles of Travel (%of tread thickness) Average Speed (mph) Tread Wear per 100 Miles of Travel (% of tread thickness) Average Tire Speed (mph) Tire 0.5 0.4 0.6 0.6 0.6 0,5 0.4 0.3 0.5 0.6 65 70 70 0.7 0.7 0.8 0.7 0.9 0.9 0.5 0.6 0.6 0.8 65 69 70 69 58 62 64 68 64 68 DESCRIPTIVE STATISTICS Standard Deviation Variable Uncorrected S$ 20 00000 83302 10.00000 Sum Mean Variance Intercept 100000 1286.00000 64.30000 50000 655.00000 32 75000 12 20000 061000 20.00000 32 22105 5 5.67636 051299 0.00000 0 26316 430271135 565793369816 0.02621 xz 94000 002621 01610 ANALYSIS OF VARIANCE Sum of Mean DF Squares Square FValue Pr> F Source Model Error Corrected Total 3 047861 0.15954 131.64 0001 16 0.01939 0.00121 19 0.49800 Root MSE Dependent Mean Coeff Var 0.03481 0.61000 5.70697 R-Square Adj R-Sq 09611 0.9538 PARAMETER ESTIMATES Parameter Standard VariableDF Estimate Intercept Error 0 10313 0.00163 t Value Pr>t Type I Ss 0.40752 395 0.0011 885