3. A company markets its products by direct mail. An experiment was conducted to

Question

3. A company markets its products by direct mail. An experiment was conducted to study the effects of three factors on the customer response rate for a particular product. The three factors are A = type of mail used (3rd class, 1st class), B-type of descriptive brochure (color, black-and-white), and C offer price ($19.95, $24.95). The mailings are made to two groups of 8,000 randomly selected customers, with 1,000 customers in each group receiving each treatment combination. Each group of customers is considered as a replicate. The response variable is the number of orders placed. The experimental data is shown below. Analyze the data from this experiment. Which factors siginificantly affect the customer response rate? Use -0.05. Coded Factors Number of Orders Run licate 2 54 42 48 43 46 45 48 54 Replicate 1 50 Factor Levels Low (-1 High (+1 46 42 49 48 47 56 A (class) 3rd B (type BW C (S) 1st Color $24.95 4 $19.95

Explanation / Answer

Consider (a) only. Ignore (b), (c)

Factorial Regression: Rep1 versus rep, A, B, C

* NOTE * This design is not orthogonal.

Method

Analysis of Variance

Model Summary

(a)

a p-value for B and A*B*C is higher than 0.05 so it's a significantly affect the model.

(b)

here,

hence, a model is better as R2 and adj R2 both is high for the model.

(c)

the only brochure color effect the company sells, hence company have to expend money only on it.

Source DF Adj SS Adj MS F-Value P-Value Model 8 290.686 36.336 13.87 0.002 Blocks 1 0.286 0.286 0.11 0.752 Linear 3 67.911 22.637 8.64 0.013     A 1 27.161 27.161 10.37 0.018     B 1 1.786 1.786 0.68 0.441     C 1 30.754 30.754 11.74 0.014 2-Way Interactions 3 192.386 64.129 24.49 0.001     A*B 1 64.286 64.286 24.55 0.003     A*C 1 127.504 127.504 48.68 0.000     B*C 1 43.754 43.754 16.71 0.006 3-Way Interactions 1 0.004 0.004 0.00 0.968     A*B*C 1 0.004 0.004 0.00 0.968 Error 6 15.714 2.619 Total 14 306.400

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