Question 1

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

If $$|r| is $$close to $$1$$, there is a strong linear correlation.

Question 2

Given the following data for price per box $$x$$ and boxes sold $$y$$, what is the most appropriate type of model to use for predicting sales?

Accepted Answer

Linear model

Question 3

Suppose the correlation coefficient $$r$$ for a data set is $$-0.95. $$What does this indicate about the data?

Accepted Answer

There is a strong negative linear correlation.

Question 4

If the price per box of cereal is increased from $$2.40 to$$ $$3.60$$, what happens to the number of boxes sold according to the data?

Accepted Answer

The number of boxes sold decreases.

Question 5

A supermarket uses the linear model $$y = -15,358.93x + 73,622.5 to $$predict weekly cereal sales $$y$$ based on price per box $$x. $$What is the predicted weekly sales if the price is $$x = 2.00$$?

Accepted Answer

$$y = 42,904$$

Question 6

What is the meaning of a correlation coefficient $$r$$ close to $$0$$?

Accepted Answer

There is a weak or no linear correlation.

Question 7

If a linear model for sales is $$y = mx + b$$, what does the value of $$m$$ represent in the context of the cereal sales problem?

Accepted Answer

The rate of change in boxes sold per dollar increase in price.

Question 8

If the correlation coefficient $$r$$ for a set of data is $$1$$, what does this mean about the data?

Accepted Answer

There is a perfect positive linear correlation.

Question 9

Using the model $$y = -15,358.93x + 73,622.5$$, what is the predicted weekly sales if the price is raised to $$x = 4.00$$?

Accepted Answer

$$y = 12,186$$

Question 10

Which of the following best describes the relationship between price and sales in the cereal data?

Accepted Answer

Inverse linear relationship

Linear Correlation and Modeling: Study Notes for Precalculus

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