Statistics

Posted: December 10th, 2013

1. For each of the following business performance measures (Y), identify factors (Xs)

that might be useful in building a predictive model. Explain why each of the Xs is a

potentially useful predictor.

a. Daily absentee rate for sales associates at a large retailer employing 100 sales

associates for each of two shifts (early and late).

b. Number of new businesses started annually in a county.

c. Data collected by the biomechanical engineering department of a university on the

type and severity of injuries treated at ski resort First Aid stations. The data are

used to design safer ski equipment.

2. For each of the following situations, discuss the appropriate boundaries and scope of

models.

a. A producer of packaged food items would like to predict sales of a new fruit drink

based on data taken from a focus group of boys and girls aged 6–16 from a

suburban community.

b. An organic strawberry farmer wishes to forecast yield for the next two weeks

based on meteorological forecasts. He wants to determine how much temporary

help to hire.

c. A print media publication wants to determine the amount of advertising sold,

measured in dollars.

3. Sketch potential models for the uncertainty in the following processes.

a. Five members of a town council are each equally likely to be appointed to fill a

vacancy on a regional planning commission.

b. An investment firm wants to predict the number of sick days taken by office

workers.

4. Moore’s Law is an empirical model that states that the transistor count on a computer

chip doubles about every two years. Kryder’s Law was similarly derived and states

that the density of information the can be stored on a hard disk increases by a factor

of 1000 every 10.5 years.

a. Use the Internet to find estimates of the current transistor count on a computer

chip and the current storage density for a hard disk.

b. How long might these laws expected to be valid? What factors might cause these

laws to become no longer applicable?

c. Use Moore’s Law and Kryder’s Law to predict the transistor count and storage

density, respectively, in five years.

d. Discuss how Moore’s Law and Kryder’s Law might be of use in budgeting

information technology needs.

5. Sketch a model of the distribution of household income for the U.S. Compare the

model to data given on the U.S. Census Bureau Web site. How does your model,

compare to the facts?

6. A bakery makes handmade French bread. The costs and revenues associated with the

number of loaves produced are given in the following table.

a. Plot cost and revenue on the same Y-axis against the number of units produced.

b. Sketch a model for the cost function.

c. Sketch a model for the revenue function.

d. Use the two models to estimate the breakeven point from the graphs.

7. Explore the field of financial engineering. Prepare a written summary including a

brief overview of the field and a description of two examples where models are

applied in this field. Explain the purpose of these models and how they are applied.

(It is not necessary to include mathematical descriptions of the models.)

4.6 Case Study: Models of Advertising Effectiveness

Business Problem

A company must decide how many minutes of television advertising to purchase each

day. They have 15- and 30-second commercials available to air.

Tasks

Perform the following tasks:

1. Sketch a possible relationship between the number of seconds of daily advertising

and sales (in number of units). Place advertising time on the X-axis and sales on the

Y-axis. Write a brief description explaining the relationship.

2. Sketch an alternative relationship between the number of seconds of daily advertising

and sales and write a brief description explaining this relationship.

3. The following table gives data from the past five TV advertising campaigns.

a. Plot the data and sketch a model that you think adequately represents the

data.

b. Using your model, quantify the relationship between advertising time and

sales.

c. Use your model to predict the number of units sold for 180 seconds.

d. What would you expect sales to be for 300 seconds of advertising time? Do

you have any reservations about this prediction?