Group members- DEEPAK, SHUBHAM, MAHAK AGARWALL
Batch- M2
From- ITM Business school, Kharghar, Navi Mumbai
Cluster Membership or Anova analysis-
Introduction-
Our topic is Maruti Suzuki car in this study, we talk about Maruti Suzuki car features and aim to analyze a dataset that categorizes various cases into distinct clusters based on their attributes and distances to cluster centroids.
Objective-
The primary objective is to investigate whether there are significant differences in various features among these clusters using Analysis of Variance (ANOVA). By understanding the relationships between cluster membership and the specified attributes, we can derive insights into the characteristics that differentiate the clusters.
Data Collection-
The dataset we collect through conduct the google from and taken the survey from collage, hostel and outside area.
- Cluster Membership Data: This data includes 100 cases, each assigned to one of four clusters based on their distances from the cluster centroids. The distance metric indicates how closely related each case is to its assigned cluster.
- ANOVA Results: The ANOVA analysis was conducted on several features, including fuel efficiency, features, air bags, easily modifiable, affordable price, bright lighting, high technology, comfort, and extra boot space. The analysis aimed to determine whether there are statistically significant differences in these features across the different clusters.
Data Analysis-
The data analysis form SPSS (IBM) software.
- Cluster Membership Analysis-
The cluster membership data indicates the distribution of cases across the four clusters, with distances varying significantly among them. Each case’s distance from the cluster centroid provides insight into how well it fits within its assigned cluster.
|
Cluster Membership |
||
|
Case Number |
Cluster |
Distance |
|
1 |
3 |
7.958 |
|
2 |
2 |
7.020 |
|
3 |
3 |
8.453 |
|
4 |
4 |
5.888 |
|
5 |
4 |
8.569 |
|
6 |
3 |
7.131 |
|
7 |
1 |
8.423 |
|
8 |
1 |
8.209 |
|
9 |
2 |
8.921 |
|
10 |
1 |
8.533 |
|
11 |
1 |
7.603 |
|
12 |
3 |
6.367 |
|
13 |
3 |
8.922 |
|
14 |
2 |
8.209 |
|
15 |
3 |
6.257 |
|
16 |
3 |
8.604 |
|
17 |
2 |
8.935 |
|
18 |
4 |
8.785 |
|
19 |
3 |
8.354 |
|
20 |
3 |
4.960 |
|
21 |
2 |
8.702 |
|
22 |
4 |
5.874 |
|
23 |
3 |
9.249 |
|
24 |
4 |
8.282 |
|
25 |
4 |
8.530 |
|
26 |
1 |
6.935 |
|
27 |
3 |
7.610 |
|
28 |
2 |
8.236 |
|
29 |
2 |
8.666 |
|
30 |
3 |
9.896 |
|
31 |
4 |
9.605 |
|
32 |
2 |
7.972 |
|
33 |
3 |
7.990 |
|
34 |
3 |
6.764 |
|
35 |
3 |
10.397 |
|
36 |
2 |
9.386 |
|
37 |
1 |
7.835 |
|
38 |
2 |
6.026 |
|
39 |
4 |
8.016 |
|
40 |
3 |
9.490 |
|
41 |
3 |
8.176 |
|
42 |
1 |
8.499 |
|
43 |
1 |
7.316 |
|
44 |
3 |
9.637 |
|
45 |
2 |
8.026 |
|
46 |
2 |
7.887 |
|
47 |
4 |
7.901 |
|
48 |
1 |
7.027 |
|
49 |
2 |
8.481 |
|
50 |
4 |
7.594 |
|
51 |
4 |
8.006 |
|
52 |
2 |
6.946 |
|
53 |
1 |
8.033 |
|
54 |
4 |
8.661 |
|
55 |
2 |
5.376 |
|
56 |
1 |
7.118 |
|
57 |
2 |
8.298 |
|
58 |
2 |
9.814 |
|
59 |
2 |
8.305 |
|
60 |
2 |
7.506 |
|
61 |
3 |
5.980 |
|
62 |
3 |
8.191 |
|
63 |
3 |
9.055 |
|
64 |
2 |
8.015 |
|
65 |
4 |
10.658 |
|
66 |
3 |
8.057 |
|
67 |
4 |
8.063 |
|
68 |
2 |
8.875 |
|
69 |
3 |
8.844 |
|
70 |
4 |
8.083 |
|
71 |
3 |
8.611 |
|
72 |
2 |
8.319 |
|
73 |
2 |
8.822 |
|
74 |
3 |
8.283 |
|
75 |
3 |
10.072 |
|
76 |
3 |
8.307 |
|
77 |
2 |
10.627 |
|
78 |
3 |
8.692 |
|
79 |
3 |
8.721 |
|
80 |
4 |
9.047 |
|
81 |
1 |
8.415 |
|
82 |
2 |
8.660 |
|
83 |
4 |
6.764 |
|
84 |
4 |
9.074 |
|
85 |
2 |
6.167 |
|
86 |
3 |
10.000 |
|
87 |
1 |
7.934 |
|
88 |
4 |
8.675 |
|
89 |
1 |
5.576 |
|
90 |
4 |
6.590 |
|
91 |
4 |
6.953 |
|
92 |
2 |
4.828 |
|
93 |
4 |
7.709 |
|
94 |
3 |
6.862 |
|
95 |
2 |
7.247 |
|
96 |
2 |
7.154 |
|
97 |
3 |
5.901 |
|
98 |
4 |
7.649 |
|
99 |
3 |
5.303 |
|
100 |
4 |
5.846 |
- ANOVA Analysis-
|
Feature |
Between Groups SS |
df |
Mean Square |
F |
Sig. |
|
Fuel efficiency |
54.463 |
9 |
6.051 |
0.672 |
0.732 |
|
Features |
23.222 |
9 |
2.580 |
0.324 |
0.965 |
|
Air bags |
140.211 |
9 |
15.579 |
1.910 |
0.060 |
|
Easily modifiable |
36.735 |
9 |
4.082 |
0.480 |
0.885 |
|
Affordable price |
71.037 |
9 |
7.893 |
0.956 |
0.482 |
|
Bright lighting |
44.360 |
9 |
4.929 |
0.571 |
0.817 |
|
High technology |
39.638 |
9 |
4.404 |
0.515 |
0.860 |
|
Comfort |
103.782 |
9 |
11.531 |
1.582 |
0.133 |
|
Extra boot space |
58.379 |
9 |
6.487 |
0.645 |
0.755 |
|
ANOVA |
||||||
|
|
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
|
Fuel efficiency |
Between Groups |
54.463 |
9 |
6.051 |
.672 |
.732 |
|
Within Groups |
810.447 |
90 |
9.005 |
|
|
|
|
Total |
864.910 |
99 |
|
|
|
|
|
Feautures |
Between Groups |
23.222 |
9 |
2.580 |
.324 |
.965 |
|
Within Groups |
715.738 |
90 |
7.953 |
|
|
|
|
Total |
738.960 |
99 |
|
|
|
|
|
Air bags |
Between Groups |
140.211 |
9 |
15.579 |
1.910 |
.060 |
|
Within Groups |
733.979 |
90 |
8.155 |
|
|
|
|
Total |
874.190 |
99 |
|
|
|
|
|
Easily modifie |
Between Groups |
36.735 |
9 |
4.082 |
.480 |
.885 |
|
Within Groups |
765.305 |
90 |
8.503 |
|
|
|
|
Total |
802.040 |
99 |
|
|
|
|
|
Affordable price |
Between Groups |
71.037 |
9 |
7.893 |
.956 |
.482 |
|
Within Groups |
743.153 |
90 |
8.257 |
|
|
|
|
Total |
814.190 |
99 |
|
|
|
|
|
Bright lighting |
Between Groups |
44.360 |
9 |
4.929 |
.571 |
.817 |
|
Within Groups |
776.550 |
90 |
8.628 |
|
|
|
|
Total |
820.910 |
99 |
|
|
|
|
|
High technology |
Between Groups |
39.638 |
9 |
4.404 |
.515 |
.860 |
|
Within Groups |
770.152 |
90 |
8.557 |
|
|
|
|
Total |
809.790 |
99 |
|
|
|
|
|
Comfort |
Between Groups |
103.782 |
9 |
11.531 |
1.582 |
.133 |
|
Within Groups |
656.218 |
90 |
7.291 |
|
|
|
|
Total |
760.000 |
99 |
|
|
|
|
|
Extraboot space |
Between Groups |
58.379 |
9 |
6.487 |
.645 |
.755 |
|
Within Groups |
904.581 |
90 |
10.051 |
|
|
|
|
Total |
962.960 |
99 |
|
|
|
|
Interpretation-
The ANOVA results indicate that none of the features show statistically significant differences between the groups at the conventional alpha level of 0.05.
- The Air bags feature comes closest to significance with a p-value of 0.060, suggesting a potential trend that may warrant further investigation.
- All other features, including fuel efficiency, features, easily modifiable, affordable price, bright lighting, high technology, comfort, and extra boot space, have p-values well above the significance threshold, indicating no significant differences among the clusters for these attributes.
The high p-values suggest that the variation in these features is largely due to random chance rather than the effects of cluster membership.
Conclusion-
In conclusion, the analysis of cluster membership and ANOVA results indicates that there are no significant differences in the assessed features across the identified clusters. While the air bags feature approaches significance, it does not meet the conventional threshold, and further research may be needed to explore this trend. The findings imply that the clusters may not be distinctly characterized by the features analyzed, suggesting that other factors or additional features may be necessary to effectively differentiate between the clusters. Future studies could include a broader range of features or utilize different clustering techniques to gain deeper insights into the data.