Question

(16 pts) Suppose you have the output from an Excel linear regression. The dependent variable is ntrip, see definitions below Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.534 0.386 0.370 1.414 785 ANOVA df sS MS Regression Residual Total 2 113.5355 56.76777 156.2694 782 284.0761 0.363269 784 397.6116 Standard Coefficients Error tStat P-value Intercept hhsize wrkrcnt 1.500 0.250 0.150 0.049 20.7860.000 0.016 12.857 .000 0.027 5.551 0.000 NAME |Type- ntrip Numeric # of trips made by a household per day hhsize Numeric Total number of persons in household wrkrent Numeric Number of workers in the HH Description a. What i s the probability that a household with 4 members and 2 workers will generate more 4 trips (8 pts)

Answer 1

Solution:

We have to find the probability that a household with 4 members and 2 workers will generate more than 4 trips.

First we have to find average number of trips for the given scenario by using the given regression model.

The regression equation by using given output is given as below:

ntrip = 1.500 + 0.250*hhsize + 0.150*wrkrcnt

We are given hhsize = 4 and wrkrcnt = 2

ntrip = 1.500 + 0.250*hhsize + 0.150*wrkrcnt

ntrip = 1.500 + 0.250*4 + 0.150*2

ntrip = 2.8

Number of trips made by a household per day = 2.8

We have to find P(Xbar>4) and we have µ = 2.8, standard error = 1.414

P(X>4) = 1 – P(X<4)

Z = (Xbar - µ)/Standard error

Z = (4 – 2.8) / 1.414

Z = 1.2/1.414

Z = 0.848656

P(Z<0.848656) = P(X<4) = 0.801964

(by using z-table)

P(X>4) = 1 – P(X<4)

P(X>4) = 1 – 0.801964

P(X>4) = 0.198036

Required probability = 0.198036