Question 3
a) Although all the ratings are measured based on the same scale (thus, same unit), the scores of the variables have various means and standard deviations, indicating that the rating of each variable distributes differently from one another on the scale. Standardizing the data makes the means of the variables equal to zero and standard deviations to one. The standardization realizes the subsequent analysis of the correlation matrix and makes it easier to interpret the principal components derived later.
b) The large correlations between each pair of the ratings are listed in the table below. The variables are defined as follows: Diversions: the diversity of the residents in terms of race and ethnicity. House: the cost of housing …show more content…
This principal component is more correlated with Diversions (a = 0.45), Education (a = 0.38), House (a = -0.38), and Transportation (a = 0.42). These variables are also correlated with each other as mentioned in b) and their relationship describes some features of living in a college town. For the 2nd principal component, I would label it as “entertainment-related”. This principal component have higher factor loadings on Diversions (a = -0.48), Safety (a = 0.45), and Urban (a = 0.43). Urban areas offer more kinds of entertainment and they are also more reachable when compared to countryside. Safety becomes another concern when people go out seeking entertainment, especially the nightlife. The negative coefficient of Diversions could be due to worries on conflicts between different cultures at entertaining places. For the 3rd principal component, I would label it as “comfortable level of living”. This principal component have higher loadings on Climate (a = 0.54), Economic (a = 0.44), and Health (a = 0.46). In general, people tend to participate in exercise and outdoor activities during good weather and when they can afford to do so. Most of time, the physical activity benefits health mentally and physiologically. These factors may affect the quality of