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

question 15

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?

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Definitions:

Profit-maximizing Condition

The state or point at which a business achieves the highest level of profit with the least amount of cost, often by equating marginal cost and marginal revenue.

Role Of Government

The activities undertaken by a government to regulate and guide the economy, including policy-making, taxation, and spending.

Unemployment Level

The number or percentage of the labor force that is without work but actively seeking employment.

Real Income

Real income refers to the amount of goods and services that can be bought with a given amount of money, taking into account inflation.