It seems like taxi's with CMT displays had greater tip percentages after February $9,2011,$ than they did before. This might be because CMT increased their default tip suggestions, but it also might be the case that tip percentages just increase over time. One way to try to understand which of these two hypothesis is correct is to use taxi's with VTS displays as a comparison group. To do that, use the entire taxi dataframe, instead of just CMT$\_$taxi, and run the OLS regression in which the depenent variable is tip$\_$percentage and the independent variables are CMT$,$ post$\_$feb, and CMTxpost. The dummy variable CMT will control for differences between CMT and VTS$.$ The dummy variable post$\_$feb will control for differences in the pre$-$period and the post$-$period. Finally, the dummy variable CMTxpost will be the variable of interest$--$ the difference between CMT in the post$-$period and VTS in the pre$-$period while controlling CMT$-$VTS differences and pre$-$post differences. To run an OLS regression with more than one independent variable, use a list of column names when defining your X variable.

If the average fare amount is $$47,$ how much does increasing default tip suggestions increase the predicted dollar value of a tip on the average fare? Store your answer in the variable predicted$\_$tip$\_$increase. Remember to look at the units of the variable tip$\_$percentage $($in the output of taxi.head$()$ above$)$ in order to set the interpret the coefficients correctly. My code: import statsmodels.api as sm

# OLS Regression

x $=$ sm$.$add$\_$constant$($taxi$[[\text{'}$CMT$\text{'},$ 'post$\_$feb', 'CMTxpost'$]])$

y $=$ taxi$[\text{'}$tip$\_$percentage'$]$

model $=$ sm$.$OLS$($y$,$ x$)$

results $=$ model.fit$()$

average$\_$fare$\_$amount $=47$

predicted$\_$tip$\_$increase $=$ results.params$[\text{'}$CMTxpost$\text{'}]*$ average$\_$fare$\_$amount

print$($predicted$\_$tip$\_$increase$)$

# Logistic Regression

x$\_$logit $=$ sm$.$add$\_$constant$($taxi$[[\text{'}$CMT$\text{'},$ 'post$\_$feb', 'CMTxpost'$]])$

y$\_$logit $=$ taxi$[\text{'}$default$\_$option'$]$

logit$\_$model $=$ sm$.$Logit$($y$\_$logit$,$ x$\_$logit$)$

results$\_$logit $=$ logit$\_$model.fit$()$

marginal$\_$effects $=$ results$\_$logit$.$get$\_$margeff$($at$=$'mean'$)$

effect$\_$on$\_$default$\_$selection $=$ marginal$\_$effects.summary$().$tables$[1][1][0]$

p$\_$value $=$ results$\_$logit$.$pvalues$[-1]$

alpha $=0\mathrm{.}05$

stat$\_$sig $=$ "yes" if p$\_$value $<$ alpha else $"$no$"$

print$($effect$\_$on$\_$default$\_$selection$)$

print$($stat$\_$sig$)$ error code: You have failed this test due to an error. The traceback has been removed because it may contain hidden tests. This is the exception that was thrown:

AssertionError: Problem $3\mathrm{.}3$: Your answer for predicted$\_$tip$\_$increase does not match the official answer.