Question

An independent mail delivery service wants to study factors that affect the daily gas usage of its delivery trucks. Using data collected from different trucks on various days, a company analyst uses a software to fit a regression model of the form =y+52.3+−8.9x14.1x2+5x30.09x4 , where =y volume of gasoline used (in gallons) =x1 weight of truck (in tons) =x2 tire pressure (in psi, pounds per square inch) =x3 weight of initial package load (in hundreds of pounds) =x4 total distance driven while delivering packages (in miles) Answer the following questions for the interpretation of the coefficient of x1 in this model. Holding the other variables fixed, what is the average change in daily fuel used for each additional ton that a truck weighs? gallon(s) Is this change an increase or a decrease? increase decrease

Answer 1

we have the regression equation

y = 52.3+−8.9x1+4.1x2+5x3 + 0.09x4

where =y volume of gasoline used (in gallons) =x1 weight of truck (in tons) =x2 tire pressure (in psi, pounds per square inch) =x3 weight of initial package load (in hundreds of pounds) =x4 total distance driven while delivering packages (in miles)

There is one positive sign in front of x1 coefficient and one negative sign. So, we will check answer for both cases.

CASE (a) When the coefficient of x1 is positive

y = 52.3 + 8.9x1 + 4.1x2 + 5x3 + 0.09x4

Keeping all other variables constant except x1, we can write it as

y = 0 +8.9x1 + 0 + 0 + 0

this shows that for every one unit or one ton increase in the truck's weight, there will be an average change of 8.9 gallons in daily fuel used. Average change depends upon the numerical value of coefficient of x1

There will be an increase in average change in daily fuel used because the coefficient of x1 is positive.

CASE (b) When the coefficient of x1 is negative

y = 52.3 - 8.9x1 + 4.1x2 + 5x3 + 0.09x4

Keeping all other variables constant except x1, we can write it as

y = 0 - 8.9x1 + 0 + 0 + 0

this shows that for every one unit or one ton increase in the truck's weight, there will be an average change of 8.9 gallons in daily fuel used. Average change depends upon the numerical value of coefficient of x1

There will be a decrease in average change in daily fuel used because the coefficient of x1 is negative.