Chapter 17, Problem 1PS

The business problem facing a consumer products company is to measures the effectiveness of difference types of advertising media in the promotion of its products. Specifically, the company is interested in the effectiveness of ratio advertising and newspaper advertising (including the cost of discount coupons). During a one-month test period, data were collected from a sample of 22 cities with approximately equal populations. Each city is allocated a specific expenditure level for radio advertising and for newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded and stored a Advertise.

a. Using all the data as the training sample, develop a regression tree model to predict the sales of the product.

b. What conclusions can you reach about the sales of the product?

To determine

Develop a regression tree model to predict the sales of product.

Explanation of Solution

Use JMP to develop a regression tree model.

Software procedure:

Step by step by procedure to develop regression tree is given below:

Open Advertise file in JMP.

Select Analyze > Predictive Modelling > Partition.

Drag Sales to the Y, Response box.

Drag Radio to the X, Factor box.

Drag Newspaper to the X, Factor box.

Click Ok.

Click Split. Repeat this step until clicking Split no longer has any effect on the tree diagram.

The JMP result is shown below:

To determine

Write conclusion about the sales of product.

Explanation of Solution

The tree model contains two splits and an $AI{C}_c$ value is 293.653.

At the root node, the data has been split based on whether the radio expenditure is less than 45000 dollars or not. The subset less than 45000 dollars has a count of 10 cities with mean sales of 944.5 thousand dollars, which is less than the other subset having a count of 12 cities with mean 1459 thousand dollars.

The subset radio expenditure greater than 45000 dollars has been further split into two based on whether the newspaper expenditure is less than 35000 dollars or not and each further split has a count of 6 cities. The mean sales of newspaper expenditure less than 35000 dollars is less than the newspaper expenditure of 35000 or more.