The cycling data frame contains the results of a study on the effects of cycling to work among 1,000 participants with asthma, a respiratory illness. Half of the participants, chosen uniformly at random, received a monetary incentive to cycle to work, and the other half did not. The variables in the data frame are:

• miles: the average number of miles cycled per week

• episodes: the number of asthma episodes experienced during the study

• incentive: whether or not a monetary incentive to cycle was given

• history: the number of asthma episodes in the year preceding the study

Consider the $R$ code below and its abbreviated output.

$>\operatorname{lm} .1=\operatorname{lm}$ (episodes miles $+$ history, data=cycling)

$>\operatorname{summary}(1 \mathrm{~lm} .1)$

Coefficients:

Estimate Std. Error $t$ value $\operatorname{Pr}(>|t|)$

(Intercept) $0.66937 \quad 0.07965 \quad 8.404<2 \mathrm{e}-16 * * *$

miles $\quad-0.04917 \quad 0.01839-2.6740 .00761 * *$

history $1.489540 .0481830 .918<2 \mathrm{e}-16 * * *$

$>\operatorname{lm} .2=\operatorname{lm}($ episodes $~$incentive $+$ history, data=cycling)

$>$ summary (lm.2)

Coefficients:

Estimate Std. Error $t$ value $\operatorname{Pr}(>|t|)$

(Intercept) $0.09539 \quad 0.06960 \quad 1.371 \quad 0.171$

incentiveYes $0.91387 \quad 0.06504 \quad 14.051<2 \mathrm{e}-16 * * *$

history $1.46806 \quad 0.04346 \quad 33.782<2 \mathrm{e}-16 * * *$

$>\operatorname{lm} .3=\operatorname{lm}($ miles incentive $+$ history, data=cycling)

$>\operatorname{summary}(\operatorname{lm} .3)$

Coefficients :

Estimate Std. Error t value $\operatorname{Pr}(>|t|)$

(Intercept) $1.47050 \quad 0.11682 \quad 12.588<2 \mathrm{e}-16 * * *$

incentiveYes $1.73282 \quad 0.10917 \quad 15.872<2 \mathrm{e}-16 * * *$

history $\quad 0.47322 \quad 0.07294 \quad 6.487 \quad 1.37 \mathrm{e}-10 * * *$

(a) For each of the fitted models, briefly explain what can be inferred about participants with similar histories.

(b) Based on this analysis and the experimental design, is it advisable for a participant with asthma to cycle to work more often? Explain.