Question

Accountants at the Tucson​ firm, Larry​ Youdelman, CPAs, believed that several traveling executives were submitting unusually high travel vouchers when they returned from business trips.​ First, they took a sample of 200 vouchers submitted from the past year. Then they developed the following​multiple-regression equation relating expected travel cost to number of days on the road ​(x1​) and distance traveled​(x2​) in​ miles:
y= ​$90.00 ​+ $46.50X1​+ ​0.35X 2.

The coefficient of correlation for the model is 0.64.

​a) If Donna Battista returns from a 340​-mile trip that took her out of town for 5 ​days, the expected amount that she should claim as expense =$ __________ (round your response to two decimal​places).

​b) After the 340​-mile and 55​-day ​trip, Battista submitted a reimbursement request for $685​, which is different than the predicted value. The accountant should question/not question the voucher as the request is much higher than expected/within expectations.

c) Additional variables that could be included in the model are​ (select the choice that has all the factors you would​consider)

A. Type of travel (air/car)

B. Gender of the executive (male/female)

C. Dress code (formal/business casual)

The percentage of variation in the trip cost that can be explained by the model​ = ________​% ​(round your

Answer 1

Answer:

a) $Y= 90 +46.50(5) +0.35 (340) =441.50$

b) The accountant should not question the voucher as the request is much higher than expected.

c) We can add the following variables

d) The percentage of variation in the trip cost that can be explained by the model​ = (0.64)^2 =0.4096 or 40.96%

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Step-by-step explanation:

Part a

For this case we have the multiple regression model given by:

$Y= 90 +46.50 x_1 +0.35 x_2$

Where $x_1$ represent the number of days on the road and $x_2$ the distance traveled in miles.

And we want to find the expected amount from a 340​-mile trip that took her out of town for 5 ​days, so we just need to replace x1= 5 and x2=340 and we got:

$Y= 90 +46.50(5) +0.35 (340) =441.50$

Part b

The expected value taking in count that x1 = 5 and y = 340 is:

$Y= 90 +46.50(55) +0.35 (340) =441.50$

And the difference from the obtained value is : 685-441.50=243.5

So then the correct answer would be:

The accountant should not question the voucher as the request is much higher than expected.

Part c

We can add the following variables

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Part d

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

The coefficient of determination "is a measure used in statistical analysis that assesses how well a model explains and predicts future outcomes. It is indicative of the level of explained variability in the data set".

The percentage of variation in the trip cost that can be explained by the model​ = (0.64)^2 =0.4096 or 40.96%