Question 1

Which of the following best describes the correlation coefficient $$r$$ when $$r = -0.95$$ for a data set relating two variables?

Accepted Answer

There is a strong negative linear correlation.

Question 2

Given the following weekly sales data for a cereal brand, what is the most appropriate type of model to use for predicting sales as a function of price?

Accepted Answer

A linear model

Question 3

Suppose the correlation coefficient $$r$$ for a set of data is $$0.02. $$What does this indicate about the relationship between the variables?

Accepted Answer

There is a weak or no linear correlation.

Question 4

If the price per box of cereal is $$2.00$$ and the linear model for weekly sales is $$y = -15358.93x + 73622.5$$, what is the predicted number of boxes sold per week? (Round to the nearest whole number)

Accepted Answer

$$42,904$$

Question 5

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

Accepted Answer

If $$r = 0$$, there is a strong linear correlation.

Question 6

A supermarket uses a linear model to predict weekly cereal sales based on price. If the price increases from $$2.40 to$$ $$3.00$$, what is the average rate of change in boxes sold per dollar increase in price, using the data: $$38,320$$ boxes at $$2.40$$ and $$26,550$$ boxes at $$3.00$$?

Accepted Answer

$$\displaystyle \frac{26,550 - 38,320}{3.00 - 2.40} = -19,583.33$$ boxes per dollar

Question 7

If the correlation coefficient $$r$$ for a data set is $$-0.8$$, which of the following best describes the relationship?

Accepted Answer

Strong negative linear correlation

Question 8

A company finds that the weekly revenue $$R$$ from cereal sales can be modeled by $$R(x) = x(-15358.93x + 73622.5)$$, where $$x is $$the price per box. What type of function is $$R(x)$$?

Accepted Answer

A quadratic function

Question 9

If the price per box is raised to $$4.00$$, use the model $$y = -15358.93x + 73622.5 to $$predict the weekly cereal sales. (Round to the nearest whole number)

Accepted Answer

$$12,187$$

Question 10

Which of the following is NOT a property of the correlation coefficient $$r$$?

Accepted Answer

If $$|r| \u003e 1$$, the correlation is undefined.

Linear Correlation and Modeling in Precalculus

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