A trucking company considered a multiple regression model for relating thedependent variable y = total daily travel time for one of its drivers (hours) tothe predictors x, = distance traveled (miles) and x, = the number ofdeliveries made. Suppose that the model equation isY = -0.800 + 0.060x, + 0.900x2 + €(a) What is the mean value of travel time when distance traveled is 50miles and four deliveries are made?5.8v hr(b) How would you interpret ß1= 0.060, the coefficient of the predictorX1?o When the number of deliveries is held fixed, the average changein travel time associated with a one-mile (i.e. one unit) increase indistance traveled is 0.060 hours.O The total daily travel time increases by 0.060 hours when thedistance traveled increases by 1.O When the number of deliveries is constant, the average change intravel time associated with a ten-mile (i.e. one unit) increase indistance traveled is 0.060 hours.O The average change in travel time associated with a one-mile (i.e.one unit) increase in distance traveled is 0.060 hours.What is the interpretation of ß, = 0.900?O The average change in travel time associated with one extradelivery is 0.900 hours.o When the distance traveled is held fixed, the average change intravel time associated with one extra delivery is 0.900 hours.O When the distance traveled is constant, the change in travel timeassociated with one delivery is 0.900 hours.O The total daily travel time increases by 0.900 hours with one extradelivery.(c) If o = 0.5 hour, what is the probability that travel time will be atmost 6 hours when four deliveries are made and the distance traveled is50 miles? (Round your answer to four decimal places.)

Solution: The estimated regression equation is y^=-0.800+0.060×x1+0.900×x2 a) The mean value of travelled time when distance travel x1= 50 miles and number of deliveries x2=4 is μy^=-0.800+0.060×50+0.900×4μy^=-0.800+3+3.6μy^=5.8 hours b) Interpretation of β1=0.060 When the number of deliveries is held fixed , the average change in travel time associated with a one miles ( that is one unit) increase in distance traveled is 0.060 hours. Option A is correct Interpretation of β2=0.900 When the distance traveled is held fixed the average change in travel time associated with one extra delivery is 0.900 hours. Option B is correct. c) Given σ=0.5 μy^=5.8 The mean value of travelled time when distance travel x1= 50 miles and number of deliveries x2=4 To find the probability that the travel time is at most 6 hours. that is to find P(y≤6) P(y≤6)=P(y-μy^σ≤6-μy^σ)=P(N(0,1)≤6-5.80.5)=P(Z≤0.20.5)= P(Z< 0.40)= 0.6554 From Z tableP(y≤6)=0.6554 The probability that the travel time is at most 6 hours when 4 deliveries are made and the distance traveled 50 miles is 0.6554

Math

Statistics

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 + 0.060x, + 0.900x2 + E

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 + 0.060x, + 0.900x2 + E

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

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 x, = distance traveled (miles) and x, = the number of
deliveries made. Suppose that the model equation is
Y = -0.800 + 0.060x, + 0.900x2 + €
(a) What is the mean value of travel time when distance traveled is 50
miles and four deliveries are made?
5.8
v hr
(b) How would you interpret ß1
= 0.060, the coefficient of the predictor
X1?
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 total daily travel time increases by 0.060 hours when the
distance traveled increases by 1.
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 average change in travel time associated with a one-mile (i.e.
one unit) increase in distance traveled is 0.060 hours.
What is the interpretation of ß, = 0.900?
O The average change in travel time associated with one extra
delivery is 0.900 hours.
o When the distance traveled is held fixed, the average change in
travel time associated with one extra delivery is 0.900 hours.
O When the distance traveled is constant, the change in travel time
associated with one delivery is 0.900 hours.
O The total daily travel time increases by 0.900 hours with one extra
delivery.
(c) If o = 0.5 hour, what is the probability that travel time will be at
most 6 hours when four deliveries are made and the distance traveled is
50 miles? (Round your answer to four decimal places.)

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