A Trucking Company Considered a Multiple Regression Model for Relating $x _ { 1 }$

Essay

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 $x _ { 1 }$ =distance traveled (miles) and $x _ { 2 }$ the number of deliveries made. Suppose that the model equation is $Y = - .800 + .062 x _ { 1 } + .900 x _ { 2 } + \varepsilon$
a. What is the mean value of travel time when distance traveled is 50 miles and three deliveries are made?
b. How would interpret $\beta _ { 1 } = .060 \text {, }$
the coefficient of the predictor $x _ { 1 }$
? What is the interpretation of $\beta _ { 2 } = .900 ?$
c. If $\sigma = .5$
hour, what is the probability that travel time will be at most 6 hours when three deliveries are made and the distance traveled is 50 miles?