 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.