Liberty University BUSI 230 week 7 exercises 9.1-9.2 complete solutions answers and more!

Liberty University BUSI 230 week 7 exercises 9.1-9.2 complete solutions answers and more!

Question 1

Suppose two variables are positively correlated. Does the response variable increase or decrease as the explanatory variable increases?

Question 2

Suppose two variables are negatively correlated. Does the response variable increase or decrease as the explanatory variable increases?

Question 3

Describe the relationship between two variables when the correlation coefficient r is one of the following.

(a) near –1

Answer

(b) near 0

Answer

(c) near 1

Question 4

Look at the following diagrams. Which diagrams show high linear correlation, moderate or low linear correlation, or no linear correlation?

Question 5

Look at the following diagrams. Which diagrams show high linear correlation, moderate or low linear correlation, or no linear correlation?

Question 6

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).

x

y

(a) Make a scatter diagram of the data and visualize the line you think best fits the data.

(b) Would you say the correlation is low, moderate, or strong?

Would you say the correlation is positive or negative?

Answer

(c) Use a calculator to verify that x = 66, x^2 = 1214, y = 636, y^2 = 90,450, and xy = 10,135.

Compute r. (Round your answer to three decimal places.)

Answer

As x increases from 3 to 25 months, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Question 7

Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? For a random sample of tropical cyclones, 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.

x

y

(a) Make a scatter diagram of the data and visualize the line you think best fits the data.

(b) Would you say the correlation is low, moderate, or strong?

Answer

Would you say the correlation is positive or negative?

Answer

(c) Use a calculator to verify that x = 5803, x^2 = 5617859, y = 577, y^2 = 64859 and xy = 551115.

5803

Compute r. (Round your answer to three decimal places.)

Answer

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

Question 8

Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents.

x

y

(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 = 155.8, Σx2 = 479.50, Σy = 247, Σy2 = 10177 and Σxy = 5663.6.

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.

Question 9

In the least-squares line ŷ = 5 − 7x, what is the value of the slope?

When x changes by 1 unit, by how much does ŷ change?

Question 10

When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?

Question 11

If two variables have a negative linear correlation, is the slope of the least-squares line positive or negative?

Question 12

An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs).

x

y

Complete parts (a) through (e), given Σx = 202, Σy = 29, Σx2 = 7862, Σy2 = 177, Σxy = 1138, and r ≈ 0.818.

(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.)

Σx =

Σy =

Σx^2 =

Σy^2 =

Σxy =

r =

(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.)

x  =

y  =

y hat  =

(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.)

r^2 =

explained

unexplained

(f) For a neighborhood with x = 34 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.)

Question 13

It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game.

x

y

Complete parts (a) through (e), given Σx = 14, Σy = 148, Σx2 = 66, Σy2 = 5750, Σxy = 451, and r ≈ −0.982.

14

(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.)

Σx =

Σy =

Σx^2 =

Σy^2 =

Σxy =

r =

(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.)

x  =

y  =

y hat  =

(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.)

r^2 =

explained

unexplained

(f) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)

Question 14

Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 33% of all fatal accidents of 17-year-olds are due to speeding.

x

y

Complete parts (a) through (e), given Σx = 329, Σy = 111, Σx2 = 18,263, Σy2 = 2425, Σxy = 3907, and r ≈ −0.960.

(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.)

Σx =

Σy =

Σx^2 =

Σy^2 =

Σxy =

r =

(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.)

x  =

y  =

y hat  =

(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.)

r^2 =

explained

unexplained

(f) Predict the percentage of all fatal accidents due to speeding for 45-year-olds. (Round your answer to two decimal places.)

Question 15

Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y.

x

y

Complete parts (a) through (e), given Σx = 52.7, Σy = 83.9, Σx2 = 466.79, Σy2 = 1290.31, Σxy = 756.84, and r ≈ 0.931.

52.7

(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.)

Σx =

Σy =

Σx^2 =

Σy^2 =

Σxy =

r =

(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.)

x  =

y  =

y hat  =

(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.)

r^2 =

explained

unexplained

(f) Suppose a small city in Oregon has a per capita income of 8.3 thousand dollars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.)