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Exercises 11 and 12 provide two data sets from “Graphs in Statistical Analysis,” by F. J. Anscombe, the American Statistician, Vol. 27. For each exercise,





a. Construct a scatterplot.

Verified step by step guidance

1. Step 1: Begin by identifying the data points from the table. Each pair of (x, y) values represents a coordinate in the scatterplot. For example, the first pair is (10, 9.14), the second pair is (8, 8.14), and so on.
2. Step 2: Set up a graph with an x-axis and y-axis. Label the x-axis with the values of 'x' and the y-axis with the values of 'y'. Ensure the axes cover the range of the data provided (x values range from 4 to 14, and y values range from 3.10 to 9.26).
3. Step 3: Plot each data point on the graph. For example, plot (10, 9.14) by locating 10 on the x-axis and 9.14 on the y-axis, then marking the point where these values intersect. Repeat this for all pairs in the table.
4. Step 4: After plotting all points, visually inspect the scatterplot to observe any patterns, trends, or clusters. This will help in understanding the relationship between x and y.
5. Step 5: Optionally, add a title to the scatterplot and label the axes to make the graph more informative. For example, the title could be 'Scatterplot of x vs. y', and the axes could be labeled 'x values' and 'y values'.

Key Concepts

Scatterplot

A scatterplot is a graphical representation of two variables, where each point represents an observation in the dataset. The x-axis typically represents the independent variable, while the y-axis represents the dependent variable. This visualization helps identify relationships, trends, or patterns between the variables, such as correlation or clustering.

Correlation

Correlation measures the strength and direction of a linear relationship between two variables. It is quantified using the correlation coefficient, which ranges from -1 to 1. A value close to 1 indicates a strong positive correlation, while a value close to -1 indicates a strong negative correlation. Understanding correlation is essential for interpreting scatterplots and assessing the relationship between the x and y values.

Data Sets

A data set is a collection of related data points, typically organized in a table format with rows and columns. In this context, the data set consists of paired x and y values, which can be analyzed to explore relationships. Understanding how to interpret and manipulate data sets is fundamental for statistical analysis, including creating visualizations like scatterplots.