FORMULATE THE PROBLEM :
FORMULATE THE PROBLEM VI V2 V3 V4 V5 V6 V7 V8 V9 V10 CONSTRUCT THE CORRELATION MATRIX :
CONSTRUCT THE CORRELATION MATRIX The variables must be correlated
If correlation is small then factor analysis may not be appropriate and vice versa
Two methods to test the correlation matrix
1) Bartlett test of sphercity
2) Kaiser Meyer Olkin measure of sampling . adequacy Output From SPSS for Correlation Matrix :
Output From SPSS for Correlation Matrix BARTLETT TEST OF SPHERICITY :
BARTLETT TEST OF SPHERICITY To test the null hypothesis that the variables are uncorrelated in the population
A large value of test static favors the rejection of null hypothesis
The approximate chi square static is 172.181 with 45 degrees of freedom, which is significant at the 0.05 level. KAISER –MEYER-OKLIN measure of Sampling Adequacy :
KAISER –MEYER-OKLIN measure of Sampling Adequacy The value of KMO static is also large 0.630 (>0.5)
Thus this factor analysis may be considered an appropriate technique for analyzing the correlation matrix COMMUNALITIES :
COMMUNALITIES IT CAN BE DEFINED AS THE PROPORTION OF VARIANCE IN ANY ONE OF THE ORIGINALVARIABLES….
All the values should be greater than 0.5 then only the variables can gel with each other and if any less than one then they won’t gel…
Variable 8 has the value close to .56 so it may be further investigated.
Initial Extraction
VAR00001 1.000 .941
VAR00002 1.000 .969
VAR00003 1.000 .941
VAR00004 1.000 .825
VAR00005 1.000 .871
VAR00006 1.000 .705
VAR00007 1.000 .617
VAR00008 1.000 .569
VAR00009 1.000 .818
VAR00010 1.000 .960
Extraction Method: Principal Component Analysis. DETERMINE THE METHOD OF FACTOR ANALYSIS :
DETERMINE THE METHOD OF FACTOR ANALYSIS Out of the two methods of factor analysis , the Principal Component Analysis is considered
This is because of the primary concern is to determine the minimum number of factors that will account for maximum variance in the provided data and the factors are thereby reduced… DETERMINING THE NUMBER OF FACTORS :
DETERMINING THE NUMBER OF FACTORS FACTOR EXTRACTION PROCESS
The objective is to reduce the variables to a fewer number of factors
Determining the number of factors to be extracted on the basis of Eigen Values.
Assuming Eigen Value = 1, we will retain those factors above Eigen Value so we get (3) factors finally … OUTPUT FOR THE TOTAL VARIANCE AND DETERMINATION OF FACTORS :
OUTPUT FOR THE TOTAL VARIANCE AND DETERMINATION OF FACTORS ROTATE THE FACTORS :
ROTATE THE FACTORS The process of identifying which factors are associated with which original variables.
We get outputs in factor matrix and then we get rotated factor matrix by performing quartimax method of rotation COMPONENT MATRIX :
COMPONENT MATRIX INTERPRETATION :
INTERPRETATION Factor 1 has the loading of variable 1,2,3 & 10 (.96863,.96268,.95977,.97469) can be classified as ECONOMY
Factor 2 has the loading of variable 4 & 5 (.88911,.90771) can be classified as SPACIOUS
Factor 3 has the loading of variable 6 & 7 (..82809,.76951) can be classified as SAFETY ALTERNATIVE SOLUTION :
ALTERNATIVE SOLUTION ALTERNATIVE SOLUTION BY ADDING THE 11TH VARIABLE
VAR0011= The colour of the car should be bright and attractive Communalities :
Communalities Here the value of 11th variable falls below .5 so this variable is less likely to gel with other variables ALTERNATIVE SOLUTION :
ALTERNATIVE SOLUTION Same output in terms of factor determination(3) COMPONENT MATRIX :
COMPONENT MATRIX INTERPRETATION :
INTERPRETATION THIS WILL BE THE SAME
Factor 1 has the loading of variable 1,2,3 & 10 (.96863,.96268,.95977,.97469) can be classified as ECONOMY
Factor 2 has the loading of variable 4 & 5 (.88911,.90771) can be classified as SPACIOUS
Factor 3 has the loading of variable 6 & 7 (..82809,.76951) can be classified as SAFETY
Since the output value of 11th variable is very low so it doesn’t make much of difference on the decision making.