Question 1

Which of the following best describes the relationship between advertising expenditures and total sales in the brewery example, as shown by the scatterplot?

Accepted Answer

There is a positive linear relationship between advertising expenditures and total sales.

Question 2

What is the range of possible values for the correlation coefficient $$r$$?

Accepted Answer

$$-1 \leq r \leq 1$$

Question 3

If all points in a scatterplot fall perfectly on a straight line with a downward trend, what is the value of the correlation coefficient $$r$$?

Accepted Answer

$$r = -1$$

Question 4

A car manufacturer finds that as horsepower increases, gas mileage decreases. What type of correlation is this?

Accepted Answer

Negative linear correlation

Question 5

Which statement about the sign of the correlation coefficient $$r is $$correct?

Accepted Answer

If $$Y$$ tends to increase as $$X$$ increases, $$r is $$positive.

Question 6

Given the least squares prediction equation $$Y = a + bX$$, what does the slope $$b$$ represent in the context of predicting sales from advertising expenditures?

Accepted Answer

The change in sales for each unit increase in advertising expenditure.

Question 7

If the correlation coefficient $$r$$ between advertising and sales is $$0.9475$$, what does this indicate about the relationship?

Accepted Answer

There is a strong positive linear relationship.

Question 8

What is the coefficient of determination $$r^2$$ used to measure?

Accepted Answer

The fraction of variability in $$Y$$ explained by a linear relationship with $$X.$$

Question 9

If $$r^2 = 0.8977$ for the relationship between sales and advertising, what percentage of the variation in sales is explained by advertising?

Accepted Answer

89.77%

Question 10

Which hypothesis is tested when examining the correlation between two quantitative variables?

Accepted Answer

$$H_0$$: $$X$$ and $$Y$$ are not correlated

Question 11

A brewery spends $$2000 on advertising. Using the prediction equation $$Sales = 25.051529 + 1.446853 	imes Advertising$, what is the predicted sales?

Accepted Answer

$$27.945236$$

Question 12

Which interval is used to estimate the mean value of $$Y$$ for a particular value of $$X$$?

Accepted Answer

Confidence interval

Question 13

Which interval is used to predict a single value of $$Y$$ for a particular value of $$X$$?

Accepted Answer

Prediction interval

Question 14

If the p-value for the correlation test is less than $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 15

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

Accepted Answer

The value of $$r$$ can be greater than $$1$$ for strong relationships.

Question 16

In the least squares regression equation $$Y = a + bX$$, what does the intercept $$a$$ represent?

Accepted Answer

The predicted value of $$Y$$ when $$X = 0$$

Question 17

A scatterplot shows no apparent pattern as $$X$$ increases. What is the likely value of the correlation coefficient $$r$$?

Accepted Answer

$$r is $$close to $$0$$

Question 18

Which of the following best describes what $$1 - r^2$ represents in regression analysis?

Accepted Answer

The fraction of variability in $$Y$$ not explained by $$X$$

Question 19

A researcher finds $$r = 0$$ for the relationship between two variables. What does this mean?

Accepted Answer

There is no linear relationship.

Question 20

Which of the following scenarios would most likely result in a strong positive correlation coefficient?

Accepted Answer

As the number of hours studied increases, exam scores increase.

Exploring Relationships Between Variables: Scatterplots, Correlation, and Linear Regression

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