It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:

X= 5.0, 5.75, 6.25, 7.25, 8.25
Y= 6, 16, 22, 68, 82

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To analyze the relationship between elevation and the percentage of unidentified artifacts in the given data set, we can plot a scatter plot.

Step 1: Open a spreadsheet program or a graphing tool.

Step 2: Create two columns, one for the elevation (X) and one for the percentage of unidentified artifacts (Y).

Step 3: Enter the given data points:

X: 5.0, 5.75, 6.25, 7.25, 8.25
Y: 6, 16, 22, 68, 82

Step 4: Plot the data points on a scatter plot. Use the X values for the horizontal axis and the Y values for the vertical axis.

Step 5: Connect the data points with a line to visualize the overall trend.

Step 6: Based on the scatter plot, observe the relationship between elevation and the percentage of unidentified artifacts:

- As the elevation increases, the percentage of unidentified artifacts also tends to increase.

Step 7: To further analyze the relationship, calculate the correlation between elevation and the percentage of unidentified artifacts. The correlation coefficient ranges from -1 to 1, where -1 indicates a strong negative correlation, 1 indicates a strong positive correlation, and 0 indicates no correlation.

Step 8: Use a statistical software or a spreadsheet program that calculates the correlation coefficient to find the correlation between X and Y. If you don't have access to such software, you can use an online calculator or the built-in functions in spreadsheet programs like Excel or Google Sheets.

Based on the provided data points, the correlation between elevation (X) and the percentage of unidentified artifacts (Y) can be calculated to determine the strength and direction of the relationship.