# Liberty BUSI 230 Week 8 Review and Exam Answers Complete Solutions

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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.

(a) Make a scatter diagram of the data.

Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σx = 24.6, Σx2 = 89.86, Σy = 52.6, Σy2 = 444.72 and Σxy = 191.18.

Compute r. (Round to 3 decimal places.)

Answer

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

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, and let y represent the player’s home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information.

(a) Make a scatter diagram of the data.

Then visualize the line you think best fits the data.

(b) Use a calculator to verify that Σx = 1.957, Σx2 = .553, Σy = 30.3, Σy2 = 152.67 and Σxy = 8.774.

Compute r. (Round to 3 decimal places.)

As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms).

## STATUS

Complete parts (a) through (e), given Σx = 97, Σy = 623, Σx2 = 2383, Σy2 = 83,181, Σxy = 13,951, and r ≈ 0.999.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r^2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r^2 to three decimal places. Round your answers for the percentages to one decimal place.)

(f) The calves you want to buy are 16 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)

Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way.

Complete parts (a) through (e), given Σx = 372, Σy = 115, Σx2 = 24814, Σy2 = 3375, Σxy = 8485, and r ≈ 0.947.