# Multivariate Data Analysis

Topics: Regression analysis, Normal distribution, Errors and residuals in statistics Pages: 10 (3047 words) Published: September 8, 2011
Introduction
This document presents the regression analysis of customer survey data of Hatco, a large industrial supplier. The data has been collected for 100 customers of Hatco on 14 parameters. The 14 variables are as follows: * Perceptions of Hatco:

This data was collected on a graphic measurement rating scale consisting of a 10cm line ranging from poor to excellent. Indicator| Variable| Description|
X1| Delivery speed| amount of time it takes to deliver the product once an order as been confirmed| X2| Price level| perceived level of price charged by product suppliers| X3| Price flexibility| perceived willingness of HATCO representatives to negotiate price on all types of purchases| X4| Manufacturer's image| overall image of the manufacturer/supplier| X5| Service| overall level of service necessary for maintaining a satisfactory relationship between supplier and purchaser| X6| Salesforce's image| overall image of the manufacturer's sales force| X7| Product quality| perceived level of quality of a particular product (e.g.,performance or yield)|

Purchase Outcomes:
Indicator| Variable| Description|
X9| Usage level| how much of the firm's total product is purchased from HATCO, measured on a 100‐point percentage scale, ranging from 0 to 100 percent| X10| Satisfaction level| how satisfied the purchaser is with past purchases from HATCO, measured on the same graphic rating scale as the perceptions X1 to X7|

Purchaser Characteristics:
Indicator| Variable| Description|
X8| Size of firm| X8 Size of firm‐‐‐size of the firm relative to others in this market. This variable has two categories: 1=large
0=small |
X11| Specification buying| extent to which a particular purchaser evaluates each purchase separately (total value analysis) versus the use of specification buying, which- details precisely the product characteristics desired. This variable has two categories: 1=employs total value analysis approach

X12| Structure of procurement| method of procuring/purchasing products within a particular company. This variable has two categories 1=centralized procurement
0=decentralized procurement|
X13| Type of industry| industry classification in which a product purchaser belongs. This variable has two categories: 1=industry A classification
0=other industries|
X14| Type of buying situation| type of situation facing the purchaser. This variable has three categories: 1=new task 2=modified rebuy

For the regression analysis we shall take Satisfaction level as the dependant variable and the following metric variables as independent variables: 1. Delivery speed
2. Price level
3. Price flexibility
4. Manufacturer's image
5. Service
6. Salesforce's image
7. Product quality
8. Usage level
Identifying the variables on which satisfaction level is dependant will help Hatco serve its customer better. It will help Hatco focus its efforts on the parameters which its customers consider important. Step1: Assumption in Multiple Regression Analysis:

Meeting the assumptions of regression analysis is essential to ensure that the results obtained are truly representative of the sample and that we obtain the best results possible. Linearity
The independent variables must establish a linear relationship with the dependant variable independently. To establish this we plot each of the independent variables against the dependant variable. The scatter lots for the same are as shown in the figure below. From the figure, below examining along the first horizontal row of plot we see that each box represents the scatter plots of one of the independent variables against the dependant variable satisfaction level. By examining the diagram we see that all the independent variable except price level and product quality exhibit linearity to a large extent. The variables price level and product...