Graph 1: Scatter plot of the relationship between attraction (a) and the Body Mass Index (b). This shows that the data has no real relationship and appears to be random. Graph 2: Scatter plot of the relationship between attraction and the Waist to Hip Ratio (h). This also shows that there does not seem to be any apparent relationship between the data and is random. Graph 3: The relationship between attraction and BMI using the average attractiveness rating for the BMI (abg) and the group values (gval).
This shows that images with either extremely high BMI values (overweight) or extremely low BMI values (underweight) are considered to be unattractive, whereas, images with an optimum BMI value are considered to be normal and attractive. This gives the graph an apparent parabola shaped curve. Graph 4: The relationship between the average attractiveness rating for the WHR (ahg) and the group values. This shows that as image’s WHR increases, the average attractiveness rating decreases, suggesting that subjects find low WHRs more attractive.
This gives the data a linear relationship. Graph 5: Dotplot for the attractiveness rating Residuals showing that they are roughly normally distributed; there are only a few outliers. This allows for a valid regression analysis. Graph 6: Showing that the distribution of the residuals and the fitted values is roughly linear, but there is a high amount of variance. Graph 7: The residuals for the WHI showing that they too are roughly normal, about zero and there are fewer outliers. Regression analysis is valid.
Graph 8: This could be considered as a linear relationship between the WHI residuals and fitted values, however this also has a large variance as the data is spread quite widely on the graph. Graph 9: BMI residuals are also approximately normally distributed, but have some extreme outliers. Regression analysis is valid. Graph 10: The residuals and fitted values for the BMI are clearly not linearly related. This does not allow a simple linear regression analysis to be applied to the data. The shape of the curve is roughly a parabola, so the regression equation will have to be in the form of:
Y = aX – bX2 + c So, in order to prove this, values of Y were calculated where X takes the values 1 to 20. This formula was used: Y = 20 X – X2 The values found for Y and the values for X were then plotted against one another: Graph 11: Values found for Y when using the values 1 to 20 for X, giving a much smoother parabola than in graph 3. This has given a curvilinear fit rather than straight lines joining up the points. It can be seen that the relationship is linear between the WHR, i. e. the lower the WHR value the more attractive the image is considered to be.
Whereas, the BMI the data is not linearly related and that the lower the BMI score the image seems to be unattractive and the higher the BMI score the image is also considered to be unattractive. As the BMI is not linearly related a quadratic formula had to be used in order to better predict the rating. Therefore the residuals had to be analysed in order to justify this. Graphs 5 and 6 show the distribution of the residuals for the attractiveness rating and the relationship of them with the fitted values, respectively. The residuals were distributed normally and the relationship seemed linear, but seemed to have a high variance.
Similarly with the residuals of WHR (graphs 7 and 8), residuals were normally distributed and an approximate linear relationship with the fitted values. However, the residuals for the BMI, although normally distributed (graph 9), did not have a linear relationship with their fitted values (graph 10). So a quadratic formula was used which resulted in a much smoother parabola (graph 11) showing the same relationship from graph 3 but more clearly. As all the residuals were approximately normally distributed regression analysis was valid and applied (table 1) using the quadratic (BMI2) as one of the predictors.
This resulted in only just under 30% (R-sq = 29. 0%) of the variance being explained by the three predictors. This was probably due to other contributing factors that were not taken into account during the experiment such as the gender of the subjects, cultural differences e. t. c. An analysis of the variance was applied and resulted in a very highly significant variance ratio (874. 55) suggesting that both the BMI and WHR were significant contributing factors. The first table of best subsets (table 3) shows that the WHR is the more influential of the two factors.
However, only 29% of the variance has been explained and this is not much, so could be inaccurate. So, a cubic formula was tried and this resulted in a more accurate regression equation (table 4) and a greater proportion of the variance was explained (46. 4%). The best subsets (table 6) showed that the BMI was the best contributing factor with the WHR second. The analysis of variance (table 5) confirmed that the significance of the two factors in predicting the attractiveness rating had increased (variance ratio = 1390. 05). The same test was done to discover if using a formula with the power 4 would make a more accurate predictor.
This was true and R-sq = 48. 8%, so the accuracy was beginning to plateau off at around 50%. The best subsets of the power four attempted, however was impossible to compute as the correlation was too high. Using firstly, the quadratic allowed a relationship between the three values WHR, BMI and attractiveness to be formulated and plotted against one another (graph 12). This shows that the relationship between the BMI and the attractiveness is always curved, however, the height and elevation of the curve always depends upon the WHR. The values are greatest for attractiveness where WHR is high and the BMI is in the middle of the range.
This contradicts graph 4 where the lower the WHR the more attractive the image is considered to be. However, graph 4 only takes into account the influence of WHR alone, not the joint influence of both factors together like graph 12. Greater information could be been obtained if the subjects were asked their gender before rating the images. This would have allowed insight into whether males perception of attractiveness if different to that of women’s. Also the age of the subjects could have been varied to see if the age of the individual has an affect on their perception of attractiveness.
This has been researched by Fallon and Rozin (1989, cited in Singh 1994) as women’s perception is thinner than that of men’s ideal. This also works the opposite way, as the age and gender of the images could have been varied to see if either one has an effect upon attractiveness. Cultural differences both of the subject and of the image should be investigated. If the culture of the subject influences their perception, or if, for example, the colour of the person in the image matters to the subject. Are coloured people considered to be less, more or indifferent in their attractiveness to other different coloured people?
Also, geographical differences, whether the ideal image of attractiveness varies between the populations of different countries. Yu and Shepard (1998, cited in Tovee & Cornelissen 1999) have investigated this and among their findings concluded that Americans prefer higher WHRs to the English. Possibly a more important and more interesting factor could be eating disorders and the effect that they have upon the individual’s perception of attractiveness. With the media’s representation and obsession with supermodels there has been a steady increase of eating disorders among the population.
This rise was predicted by the studies of Agras (1987 cited in Morris et al 1989) when the change in the body shape of women began to appear in fashion magazines. To conclude at first the WHR seemed to be the more important contributing factor (table 3) however, when using a cubic and the power of 4 the accuracy began to increase and it became apparent that the BMI was quite considerably the more influential of the two factors (BMI = 11. 3% and WHR = 9. 8%). This is supported by other research; however, there are many other contributing factors such as, age, culture and eating disorders, which need further investigation.
References
Morris, A. et al (1989). The changing shape of female fashion Models. Journal of Eating Disorders. 8: 593-596. Singh, D. (1994) Ideal female Body Shape: The role of body weight and Waist-to-Hip Ratio. Journal of Eating Disorders 16:283-288. Singh, D. (1994) Is thin really beautiful and good? Relationship between Waist-to-hip ratio (WHR) and female attractiveness. Personal and Individual Differences 16: 123-132 Tovee, M. J. & Cornelissen, P. L (1999). The mystery of Female beauty Journal of Nature 399, 215-216