Problem 4: Statistical Description Of Multivariate Data ✓ Solved

Problem 4: Statistical Description of Multivariate Data for A Real-World Dataset

Problem 4: Statistical Description of Multivariate Data for a Real-World Dataset. To complete this task you have to use the crx.data file. This file crx.data contains data collected from credit card applications. All attribute names and values have been changed to meaningless symbols to protect the confidentiality of the data. The dataset is downloaded from the UCI Machine Learning Repository. This dataset is interesting because there is a good mix of attributes -- continuous, nominal with small numbers of values, and nominal with larger numbers of values. There are also a few missing values.

Read the data in R using the following command: data . After loading the data in R, you can access each column using data[ , 1], data[ , 2], … , data[ , 15]. All the data will be in character format when you load it from crx.data; you will have to convert the numeric columns from character to numeric using the as.numeric() function. For missing values, NAs will be introduced by coercion. There are 16 columns in the data; the first 15 columns are the attributes of the data and the 16th column is the label of the data. You have to only analyze the attributes of the data. Find which attributes are the nominal attributes and which are continuous attributes. Identify the attribute/attributes with missing values (having NA). Drop the attributes with missing values from the data. Calculate the central tendency of the rest of the attributes. Remember for the nominal attribute you can only calculate the mode. Calculate the five-number summary of the numeric attributes. Show box plots for the numeric attributes and identify the attributes having outliers. Show pairwise scatter plots of the numeric attributes. Inspect the scatter plots and mention if each pair’s attributes are negatively correlated, positively correlated or there is no correlation. Do not forget to label the axes of the plots.

Paper For Above Instructions

Statistical analysis of multivariate data plays a pivotal role in extracting insights from complex datasets across various fields, including finance, healthcare, and social sciences. This paper focuses on a dataset (crx.data) consisting of credit card application data to perform a statistical description of the attributes present, identifying the nature of each attribute, calculating statistical measures, and visualizing relationships between attributes.

Loading the Data

Initially, the dataset can be loaded into R using the following command: data . After replacing "path" with the actual file path, users can load the data into a data frame. It is essential to note that the dataset contains 16 columns, where the first 15 columns represent the attributes and the last column serves as the label. Upon loading the dataset, R loads all values as character strings, requiring conversion of the necessary columns to numeric using as.numeric() function. If conversion introduces NAs, this indicates that the column contained non-numeric data.

Identifying Attributes

In terms of attributes, this dataset presents a blend of continuous and nominal attributes. Continuous attributes can take any value within a range, while nominal attributes represent categories without intrinsic ordering. In our dataset, attributes such as attribute1 and attribute2 may exhibit continuous behavior, while attributes like attribute3 may represent nominal categories. Identifying which attributes fall into which category involves examining the nature of each attribute's values.

Handling Missing Values

After identifying the types of attributes, the next step is to check for any missing values. This can be carried out with the command any(is.na(data)), which returns true if any NAs are present in the dataset. Once identified, attributes containing missing values need to be dropped from the analysis using data . This ensures subsequent statistical analyses are clean and compliant with assumptions regarding missing data.

Calculating Central Tendency

Central tendency can be measured using the mean, median, or mode depending on the type of attribute. For continuous attributes, the mean and median provide insights into the data distribution. To calculate the mode of nominal attributes, a separate approach involving the table() function can be implemented. After calculating these measures, we can summarize the central tendency effectively, illustrating the average behavior of the attributes in the dataset.

Five-Number Summary and Box Plots

The five-number summary provides valuable insights about the spread of the continuous variables. It comprises the minimum, first quartile, median, third quartile, and maximum. A function like fivenum() enables this calculation in R. Furthermore, box plots are useful for visualizing these statistics and highlighting outliers. Outliers can be identified easily with box plots as points that lie beyond the whiskers of the plot. The boxplot() function in R is instrumental in generating these visualizations.

Pairwise Scatter Plots

Pairwise scatter plots allow for the examination of relationships between each pair of numeric attributes. The pairs() function in R illustrates these relationships effectively. In analyzing these plots, it is crucial to identify whether the attributes are positively correlated, negatively correlated, or exhibit no correlation. This involves looking for patterns: a slope toward the upper right indicates positive correlation, a slope toward the lower right indicates negative correlation, while scattered clouds suggest no correlation.

Conclusion

The analysis of the crx.data file equips us with essential insights into the characteristics of the various attributes. By categorizing them, addressing missing values, and visualizing the data through numerical summaries and plots, we establish a comprehensive statistical description. Such analyses are crucial for facilitating decisions based on credit card application data and can further guide future investigations into financial datasets.

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