PROBABILITY & STATS FOR ENGINEERING &SCI
9th Edition
ISBN: 9781285099804
Author: DEVORE
Publisher: CENGAGE L
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Chapter 13.1, Problem 1E
Suppose the variables x = commuting distance and y = commuting time are related according to the simple linear regression model with σ = 10.
a. If n = 5 observations are made at the x values x1 = 5, x2 = 10, x3 =15, x4 = 20, and x5 = 25, calculate the standard deviations of the five corresponding residuals.
b. Repeat part (a) for x1 = 5, x2 = 10, x3 = 15, x4 = 20, and x5 = 50.
c. What do the results of parts (a) and (b) imply about the deviation of the estimated line from the observation made at the largest sampled x value?
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3. (a). Differentiate the different types of linear regression and describe the use of regression in geographical study.
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A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is
Y = -0.800+ 0.060x₁ +0.900x₂ + e
(a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made?
hr
(b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁?
O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours.
O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1.
O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours.
O The average change in travel time associated with a one-mile (i.e.…
Chapter 13 Solutions
PROBABILITY & STATS FOR ENGINEERING &SCI
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