Problem $1$

Data provided on BB for this problem are estimated trips generated from $120$ traffic analysis zones.

These data were collected to understand the mobility pattern during off$-$peak hours. The definition of

the attributes in the dataset is as follows:

Average zonal income in thousands $($income$),$

Zonal population in thousands $($pop$),$

Average number of vehicles in the household $($veh$),$

Average number of children in a household $($children$)$

Average trip rates during off$-$peak period $($Trips$\_$rates$).$

Task: Use Python particularly statsmodels packoge to calibrate linear regression models that estimate

triprates.

e$.$g$.,$ import statsmodels.formula.api as smf

Im$\_$m $=$ smf$.$ols$($formula$="....",...)$

a$)$ Fit a regression between trip rate and income $(2$ Points$)$

b$)$ Fit a regression between trip rate and pop $(2$ Points$)$

c$)$ Fit a multiple linear regression between trip rate with all the attributes in a table. Identity which

attributes are significant at $95\%$ confidence interval $(2$ Points$)$

d$)$ Use the calibrated model in part c to develop a prediction function for the average trip rates.

Test the function for prediction using a traffic analysis zone with the number of pop $=20,000,$

income $=65,000,$ average children $=2,$ and vehicle per household $=2(5$ Points$)$

def Trip$\_$Rates$(....)$:

e$.$g$.,$

$.......$

return pred$\_$trip$\_$rates

e$)$ In each of the three models, comment on the quality of the fitted model and identify all the

significant factors in the models. $(5$ Points$)$

f$)$ Among the three fitted models, which regression equation would you recommend for use for

planning purposes? Why? $(5$ Points$)$