= Solution
For participants with the same recorded history, the first <linear regression> estimates that one additional average mile cycled per week is associated with $0.04917$ fewer asthma episodes. The corresponding $p$-value is $0.00761$, giving evidence against a zero conditional association.
The second model estimates that, among participants with the same history, receiving the incentive is associated with $0.91387$ more episodes. The third estimates that receiving the incentive is associated with $1.73282$ more miles cycled per week. Both incentive coefficients have very small <p-values>. Because the incentive was assigned in a <randomized controlled trial>, these last two comparisons estimate a <causal effect> of the incentive.
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