# Liberty BUSI 230 Week 7 Exercises 9.1-9.2 Answers Complete Solutions

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### 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?

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

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?

Would you say the correlation is positive or negative?

(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.)

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.)

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