What information can you gather from a scatter plot?

The most common use of scatter plots is when one performs exploratory factor analysis (EFA) to see the number of factors that a measurement instrument contains . In this case based on eigenvalues greater than 1 we could see how many factors exist. As such a scatter plot provide a visual evidence. The exploratory factor analysis usually is a procedure that we perform to examine structural validity.

Scatter plots come in various flavors, each tailored to specific data types. The bivariate scatter plot, for instance, is akin to a two-character play, where each variable is an actor, and their interaction tells a story. It's straightforward yet profound in its ability to reveal correlations. On the other hand, multivariate scatter plots are like ensemble casts, where multiple variables interact in a complex narrative, offering a richer, more layered understanding of data relationships. Categorical scatter plots add another dimension, akin to introducing a new genre into a film series, where categorical variables bring a different kind of insight, often adding color and texture to the data's story.

A scatter plot allows for the visualization of potential trends and can help in predicting the value of one variable based on the value of another, particularly when fitting a trend line or regression line to the data. Scatter plots are versatile and useful for exploratory data analysis as they provide an intuitive way to assess the relationship between two continuous variables.

This aspect of scatter plots is a crucial lesson in discernment. Correlation in scatter plots can be misleading, like a mirage that suggests a relationship where none exists. It's essential to understand that correlation coefficients, whether positive, negative, or zero, are indicators, not proof, of a relationship. Establishing causation requires a deeper dive, much like a detective looking beyond circumstantial evidence to find the real cause of an event.

Outliers in scatter plots are the anomalies that defy expectations, like unexpected plot points in a story. They challenge our understanding of the data and often lead to new insights or questions. Clusters, on the other hand, are like the recurring themes or motifs in a narrative. They represent groups or patterns within the data that are consistent and tell a part of the story. Both outliers and clusters are critical in painting a complete picture of the data.

Identifying the nature of relationships in scatter plots is akin to understanding the dynamics of different ecosystems. Linear relationships are straightforward, like a well-tended garden with predictable growth patterns. Nonlinear relationships, however, are like wild forests, where growth patterns are diverse and unpredictable. Recognizing these patterns is crucial for choosing the right analytical approach, much like selecting the right tools for gardening or forest management.

Summary statistics in scatter plots act as the executive summary of a complex report. They distill the essence of the data, providing key metrics like mean, median, and standard deviation. These statistics are like the keynotes of a lecture, summarizing the main points and providing a foundation for deeper analysis, such as hypothesis testing or confidence interval estimation.

Scatter plots have a significant flaw : if you have overlapping or closely placed datapoints, they would give a very misleading picture of the distribution of the data. For instance, certain regions with concentration of high number of points may appear similar to sparse regions.

Some ways to supplement your scatterplots: - Plot density in some way; this can be by adjusting transparency (i.e., alpha) of the points themselves, so that overlapping points appear darker than a single point. - Consider use of color to plot another dimension, or to plot separate groups of data in the same space. A control group might be colored black while a treatment group is red. - Similarly, use varying symbols to denote group membership of a given observation. Like before, a control observation might take the shape of a circle while a treatment could be a cross. - Consider accessibility, your audience, and your data. If you are using different shapes, consider how distinguishable from one another they are for readers.