. A trucking company is interested to create a model that can predict daily trav
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Question
. A trucking company is interested to create a model that can predict daily travel time of its trucks. The manager has decided that the travel time depends on miles traveled and the number of deliveries. A simple random sample of 10 driving assignments provided the following: (Use = 0.05 throughout the problem.)
Driving Miles Number of Travel
Assignment Traveled Deliveries Time
1 105 4 9.5
2 60 3 5.2
3 100 4 7.6
4 50 2 4.3
5 80 2 6.3
6 75 3 7.5
7 65 4 6.0
8 90 3 7.7
9 90 2 6.2
10 100 3 8.2
e) Test whether miles traveled
contributes information for
the prediction of travel time?
f) Test whether the model as a
whole contributes information
for prediction of travel time?
g) What is the standard error of estimate and what does it mean?
h) Predict the travel time in a day in which the truck has to make 4 deliveries and travel 110 miles?
Driving Miles Number of Travel
Assignment Traveled Deliveries Time
1 105 4 9.5
2 60 3 5.2
3 100 4 7.6
4 50 2 4.3
5 80 2 6.3
6 75 3 7.5
7 65 4 6.0
8 90 3 7.7
9 90 2 6.2
10 100 3 8.2
Explanation / Answer
The regression equation is
Travel Time = - 5.6 + 1.14 Mile Traveled - 7.97 No of Deliveries
Predictor Coef SE Coef T P
Constant -5.60 28.94 -0.19 0.852
Mile Traveled 1.1362 0.3327 3.42 0.011
No of Deliveries -7.968 7.626 -1.04 0.331
S = 17.4006 R-Sq = 62.6% R-Sq(adj) = 51.9%
e) Test whether miles traveled contributes information for the prediction of travel time?
Ans: The estimated p-value of miles travelled is 0.011 and less than 0.05 level of significance. Hence, we can conclude that miles travelled contributes information for the prediction of travel time at 0.05 level of significance.
f) Test whether the model as a whole contributes information for prediction of travel time?
Ans: The estimated R-Sq value is 0.626. Hence only 62.6% information for prediction of travel time is contributed by the model.
g) What is the standard error of estimate and what does it mean?
Ans: The standard deviation of the sampling distribution of a statistic (estimate) is known as its Standard error. It gives the precision of the estimated value.
h) Predict the travel time in a day in which the truck has to make 4 deliveries and travel 110 miles?
Ans: If you consider the deliver in the model (actually the No of deliveries is not significant at 0.05 level of significance)
Travel Time = - 5.6 + 1.14 *110 - 7.97 *4 =-5.6+125.4 - 31.88= 87.92
If delivery is not include in the model, the new model is
The regression equation is
Travel Time = - 19.2 + 1.01 Mile Traveled
Predictor Coef SE Coef T P
Constant -19.20 26.00 -0.74 0.481
Mile Traveled 1.0098 0.3117 3.24 0.012
S = 17.5003 R-Sq = 56.7% R-Sq(adj) = 51.3%
Travel Time = - 19.2 + 1.01 *110=91.9.
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