9. 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:

Question

9. 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:

What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?

Answer 1

To find the percentage of the variation in y that can be explained by the corresponding variation in x and the least-squares line, we need to calculate the coefficient of determination, often denoted as R^2.

The coefficient of determination, R^2, measures the proportion of the variation in the dependent variable (y) that can be explained by the independent variable (x) and the least-squares line. It ranges from 0 to 1, where 0 indicates no linear relationship and 1 indicates a perfect linear relationship.

To calculate R^2, we need to perform a linear regression analysis on the given data. The linear regression analysis will provide us with the equation of the least-squares line and the sum of squares of the residuals.

Once we have the sum of squares of the residuals (SSR) and the total sum of squares (SST), we can calculate R^2 using the formula:

R^2 = 1 - (SSR / SST)

Where SSR is the sum of squares of the residuals and SST is the total sum of squares.

Now let's assume that the data provided for the collection of archaeological sites in New Mexico is missing in your question. To proceed with the calculation, we would need the elevation (x) and the corresponding percentage of unidentified artifacts (y) for each archaeological site.

So, to find the percentage of the variation in y that can be explained by x and the least-squares line, we need the actual data. Once we have the data, we can perform a linear regression analysis and calculate R^2 using the formula mentioned above.

awaiting

To find the percentage of the variation in y that can be explained by the corresponding variation in x and the least-squares line, we need to calculate the coefficient of determination, often denoted as R^2.