1. Lecture note 3-1 Summarizing Relationships among variables ©

2. 4Analyzing a relationship between two (or more) variables is done in many situations. Examples: (i) Relationship between the price of a product and the revenue, (ii) relationship between the promotion cost and revenue, (iii) relationship between the revenue and the rate of price discount. 4We use “Scatter Plot” to represent a relationship between two variables.

3. Using the following data, we will produce scatter plot that shows the relationships between the number of promotions and the revenues from three different products Product AProduct BProduct C Month Number of promoti ons Sales Number of pro mot ions Sales Number of pro mot ion s Sales April5600,0005200,0005400,000 May101,000,00010250,00010200,000 June81,100,0008350,0008150,000 July9900,0009320,00010400,000 August101,500,00011300,00010100,000 September12750,0009200,0001280,000 October202,200,00020900,00020160,000 November182,000,00018600,00015150,000 December171,700,00017700,00015200,000 Scatter plot example

5. From the scatter plot we can learn 4There are positive relationships between the number of promotions and the sales from the product A and product B. 4Promotion seems to be most effective for product A. 4There seems to be no relationship between the number of promotions and the sales from product C. (There is a slight downward trend, but this can happen just by chance)

6. Exercise 4Open the data “Promotion and Sales”, and reproduce the scatter plot.