Videos
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?
a.
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:
b.
Write conclusion about the sales of product.
Explanation of Solution
The tree model contains two splits and an
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.
Want to see more full solutions like this?
Chapter 17 Solutions
Basic Business Statistics
- Let X be a random variable with support SX = {−3, 0.5, 3, −2.5, 3.5}. Part ofits probability mass function (PMF) is given bypX(−3) = 0.15, pX(−2.5) = 0.3, pX(3) = 0.2, pX(3.5) = 0.15.(a) Find pX(0.5).(b) Find the cumulative distribution function (CDF), FX(x), of X.1(c) Sketch the graph of FX(x).arrow_forwardA well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.arrow_forward5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.arrow_forward
- 8. Suppose that the moments of the random variable X are constant, that is, suppose that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) = sup P(x ≤ X ≤x+h), h>0. Show that, if X and Y are independent random variables, then Qx+y (h) min{Qx(h). Qr (h)).arrow_forward10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.arrow_forward
- 9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward
- 1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning