## (CORRECT ANSWER) MATH225N Week 8 Assignment : Correlation and Causation

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**Question**

Which of the following situations could produce data sets or plots that could have a regression line with a negative y-intercept? Select all that apply

- The net profit of a company as a function of the number of months since it was founded, where net income is gross income minus expenses.
- The number of employees of a company as a function of the number of months since it was founded.
- The cost of a company’s flagship product as a function of the number of months since it was founded.
- The number of franchises of a company as a function of the number of months since it was founded.

**Question**

True or False: The more mangoes you eat, the more rashes you get.

Select the correct answer below:

True

False

** ****Question**

A retail store uses sales data to make a regression line. The independent variable x represents time and the dependent variable y represents sales.

Which of the following situations could produce data sets or plots that have a regression line with a negative slope? Select all that apply.

Select all that apply:

- The percent change in the total sales is so good that everyone is talking about it.

- The company’s supplier is experiencing a shortage of materials to manufacture the items that the store sells.

- The sales staff decreased in size when some members transferred to a new store that opened across town.

- Because of company growth, the human resources department hired more store employees.

** ****Question**

True or False: The more samples taken in a scientific study, the longer the amount of time it will take to complete the research on the samples.

Select the correct answer below:

True

False

**Question**

Which of the following situations could have a regression line with a negative y-intercept?

Select all that apply:

- The present value of an insurance policy as a function of the age of the ensured person if the person purchases the policy when he or she is 50 years old

- The number of millions of barrels of oil in an oil field as a function of the number of years the oil field has been in production.

- The value of a Fortune-500 company, founded in the year 1990, as a function of the number of years after the year 2010

- The value of a rail locomotive as a function of the number of years since it was put into service.

**Question**

Which of the following data sets or plots could have a regression line with a negative slope? Select all that apply.

Select all that apply:

- The number of tons of trash in a landfill as a function of the number of years since the landfill was built.
- The number of loads of trash a dump truck hauls per month as a function of the number of years since the dump truck was built.
- The number of tons of trash produced in a city as a function of the population.
- The number of tons of trash hauled to a landfill and a function of the number of tons of recycling that is processed.

**Question**

Suppose that data collected from police reports of motor vehicle crashes show a moderate positive correlation between the speed of the motor vehicle at the time of the crash and the severity of injuries to the driver. Answer the following question based only on this information.

True or false: It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are.

Select the correct answer below:

True

False

** ****Question**

The scatter plot below shows data for the number of babies (y) born in a certain city in a given year, where x is the year. The least squares regression line is given by yˆ=28,450−344x.

Interpret the y-intercept of the least squares regression line.

Select the correct answer below:

The predicted number of babies born in the year 0 is 28,450.

The predicted number of babies born in the year 2000 is −344.

The predicted number of babies born in the year 2002 is 28,450.

**Question**

Which of the following data sets or plots could have a regression line with a negative slope? Select all that apply.

Select all that apply:

The number of tons of trash in a landfill as a function of the number of years since it was built.

The number of loads of trash a dump truck hauls per month as a function of the number of years since it was built.

The number of tons of trash produced in a city as a function of the population

The number of tons of trash hauled to a landfill and a function of the number of tons of recycling that is processed.

**Question**

A business finds that sales increase when the outdoor temperature decreases.

Identify the relation between sales and temperature.

Select the correct answer below:

Sales and temperature are positively correlated.

An increase in sales causes an increase in temperature.

Sales and temperature are negatively correlated.

An increase in temperature causes an increase in sales.

**Question**

Suppose that a large controlled experiment tests whether caffeine improves reaction times. A very large number of randomly selected participants are randomly given identical-seeming pills with varying doses of caffeine (including none) and then given tests of reaction times under the same conditions. The experiment finds a strong negative correlation between caffeine dose and reaction time. (Note that lower reaction times are better.)

Identify what can be concluded based on this information.

Select the correct answer below:

There is evidence that caffeine causes lower (better) reaction times.

People with lower (better) reaction times generally choose to consume more caffeine.

Lower reaction times are associated with higher caffeine doses, but this study provides no evidence that caffeine causes lower reaction times.

There is no relationship between reaction time and caffeine.

**Question**

Which of the following situations would have data sets or plots that could have a regression line with a positive slope? Select all that apply.

Select all that apply:

- The cumulative number of ships launched by ship builders as a function of the number of months since the start of the year

- The number of cars produced as a function of the number of days since the end of the last strike.

- The total shipping orders that are backlogged as a function of the number of ships in drydock.

- The number of backorders as a function of the number of assembly workers in a manufacturing company that makes the product

**Question**

Which of the following situations could produce data sets or plots would have a regression line with a negative slope? Select all that apply.

Select all that apply:

- The number of miles a ship has traveled as a function of the number of years since it was launched.

- The number of miles a ship travels each year as a function of the number of years since it was launched.

- The number of times a ship needs repairs as a function of the number of years since the ship was initially launched.

- The number of voyages a ship can make per year as a function of the length (in days) of each voyage.

** ****Question**

A large observational study asks participants about caffeine consumption and sleep duration. The study finds that people with the largest caffeine intake have the shortest sleep duration.

Identify the relation between caffeine consumption and sleep duration.

Select the correct answer below:

Caffeine consumption and sleep duration are correlated.

An increase in caffeine consumption causes a decrease in sleep duration.

A decrease in sleep duration causes an increase in caffeine consumption.

There is no relation between caffeine consumption and sleep duration.

**Question**

True or false: Increases in height cause increases in shoe size.

Select the correct answer below:

True

False

**Question**

True or False: The longer a road, the greater the amount of time it will take to travel its length. Assume speed is constant.

Select the correct answer below:

True

False

**Question**

An experiment finds that runners with the longest legs complete a mile run in less time.

Identify the relation between leg length and time of a mile run.

Select the correct answer below:

Leg length and time of a mile run are positively correlated.

Leg length and time of a mile run are negatively correlated.

An increase in leg length causes a decrease in the time of a mile run.

A decrease in the time of a mile run causes a decrease in leg length.

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