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Problem 1 Find the population principal components Y1 and Y2 for the covariance matrix . Then, calculate the proportion of the total population variance explained by the first principal component. Answer Find the eigenvalues and the corresponding eigenvectors. (λ-5)(λ-2) –Read More
Manufacturing and service companies attempt to deliver the best products or services to their customers. Manufacturing companies expect that 100% of the goods they produce are non-defective. Also, service companies such as courier services expect that 100% of the packagesRead More
Before we look at the concept of statistical distance, it is worth pointing out first what is meant by distance in mathematics. Definition Suppose that V is a non-empty set and d is a function from V×V to .Read More
While the median splits data into two groups with an equal number of data, the quartiles separate them into four groups with an equal number of data. If a set of data has Q1 as its first quartile and Q3Read More
In the article Introduction to The Measures in Statistics, it is stated that there are several measures of location such as the mean, median, mode, etc. The article also warns us not to apply the mean if the data beingRead More
Suppose that we have collected some sample data and presented them in a frequency distribution table with equal class widths, As a consequence, we can apply the coding method to calculate the variance. By this method, the variance can beRead More
A principal component analysis is concerned with explaining the variance-covariance structure of a set of variables through a few linear combinations of these variables. Hereinafter, each linear combination is referred to as a component. The number of components can beRead More
Is there a significant relationship between ones’ education level and their public speaking skill? Is there a correlation between TOEFL scores and the ability to speak in English? Is there any relatedness between the alumni’s GPAs and their linguistic intelligence?Read More
Quantitative data can be presented in the form of frequency distribution tables. Here is a typical frequency distribution table (FDT). Table 1 shows the duration of 20 conversations. There are five classes (or categories) for the duration. Each class isRead More