Exam 4: Correlation and Regression

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 5.50 6.25 6.75 7.25 8.00 y 22 44 85 98 84 Find the value of the coefficient of determination r².

Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. Suppose a random sample of earthquakes gave the following information. Would you say the correlation is low, moderate, or strong? Positive or negative? If necessary, draw a scatter diagram of the given data. x 2.5 4 3.4 4.4 2.4 y 5.2 10.3 10.8 10.3 8.3

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 5.00 5.75 6.50 7.25 8.25 y 40 40 67 71 98 Find b for the equation of the least-squares line . $\hat { y } = a + b x$

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 5.75 6.75 7.25 7.50 8.25 y 69 60 92 92 94 Find a for the equation of the least-squares line . $\hat { y } = a + b x$

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 5.75 6.50 7.50 7.75 8.00 y 35 50 79 59 94 Find . $\bar x$

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 5.75 6.00 6.50 7.25 8.25 y 28 33 20 70 58 What percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line?

Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. Suppose a random sample of earthquakes gave the following information. Draw the line that best fits the data whose scatter diagram is given below. x 2.5 4 3.4 4.4 2.4 y 5.2 10.3 10.8 10.3 8.3

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 6.00 6.50 7.25 7.50 8.50 y 52 64 54 67 78 Find . $\bar { y }$

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 5.50 6.00 6.50 7.25 8.00 y 32 18 31 68 62 What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?

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 5.50 6.00 6.50 7.50 8.50 y 33 24 41 87 83 Calculate the sample correlation coefficient r.

How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms). Suppose a random sample of ponies gave the following information. x 4 7 14 19 21 y 50 85 130 160 175 Make a scatter diagram for the data. Draw the line that best fits the data.

Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. Suppose a random sample of earthquakes gave the following information. x 2.5 4 3.4 4.4 2.4 y 5.2 10.3 10.8 10.3 8.3 Make a scatter diagram for the data.

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 5.50 5.75 6.50 7.25 8.25 y 19 6 53 48 77 Find the equation of the least squares line . $\hat { y } = a + b x$

Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims. Suppose a random sample of employees gave the following information. x 2 8 14 32 73 y 50 45 35 28 16 As x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain.

Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? Let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximum wind speed (in miles per hour) of the cyclone. Suppose a random sample of cyclones gave the following information. x 1014 935 980 955 995 y 50 80 60 135 84 Given that the value of r is -0.556, should y increase as x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain.

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 5.25 5.75 6.50 7.00 7.75 y 38 37 66 80 82 At an archaeological site with elevation 7.5 (thousand feet), what does the least-squares equation forecast for the percentage of culturally unidentified artifacts?

In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player. Let y represent the home run percentage (number of home runs per 100 times at bat). Suppose a random sample of baseball players gave the following information. x 0.251 0.259 0.29 0.265 0.269 y 1.3 3.7 5.8 3.9 3.7 Compute r.