Question 1

Which of the following best describes the difference between the explanatory variable and the response variable in a scatter diagram?

Accepted Answer

The explanatory variable is plotted on the horizontal axis, and the response variable is plotted on the vertical axis.

Question 2

A researcher finds a correlation coefficient $$r = 0.773$$ between drilling depth and drilling time, with a critical value of $$0.576$$ for $$n = 12. $$What can be concluded?

Accepted Answer

There is a positive linear relation between drilling depth and drilling time.

Question 3

Which formula correctly represents the sample linear correlation coefficient $$r$$?

Accepted Answer

$$r = \frac{\sum \left( \frac{x_i - \overline{x}}{s_x} \right) \left( \frac{y_i - \overline{y}}{s_y} \right)}{n-1}$$

Question 4

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

Accepted Answer

$$r is $$resistant to outliers.

Question 5

A scatter diagram shows that as the number of colas consumed per week increases, bone mineral density decreases. The correlation coefficient is $$-0.806. $$What type of association is this?

Accepted Answer

Strong negative linear association

Question 6

Which of the following best explains why correlation does not imply causation?

Accepted Answer

Correlation can be caused by lurking variables or confounding factors.

Question 7

Given the regression equation $$\hat{y} = 0.0116x + 5.5273$$, what is the predicted drilling time when drilling starts at $$x = 130$$ feet?

Accepted Answer

$$\hat{y} = 0.0116(130) + 5.5273 = 7.035$$

Question 8

What does the slope of the least-squares regression line represent in the context of drilling data?

Accepted Answer

The average increase in drilling time for each additional foot of depth.

Question 9

Which of the following is the correct formula for the least-squares regression line?

Accepted Answer

$$\hat{y} = b_1$ x + b_0$

Question 10

If the observed value of $$y is 5.2 $$and the predicted value from the regression line is 4.75, what is the residual?

Accepted Answer

$$0.45$$

Question 11

Which of the following best describes the coefficient of determination $$R^2$$?

Accepted Answer

$$R^2$$ measures the proportion of total variation in the response variable explained by the regression line.

Question 12

Suppose $$r = 0.773$$ for a regression model. What is the value of $$R^2$$ and how should it be interpreted?

Accepted Answer

$$R^2 = 0.5975$, meaning 59.75% of the variability in the response variable is explained by the regression line.

Question 13

Which of the following is a lurking variable in the study of cola consumption and bone mineral density?

Accepted Answer

Calcium intake

Question 14

Why should you avoid making predictions using a regression line for values of the explanatory variable far outside the observed data range?

Accepted Answer

Because the linear relation may not continue to exist outside the observed range.

Question 15

Which scenario best illustrates a positive association between two variables?

Accepted Answer

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

Question 16

Which of the following is NOT a property of the least-squares regression line?

Accepted Answer

It is resistant to extreme values.

Question 17

If the correlation between two variables is close to zero, what does this imply?

Accepted Answer

There is no linear relation between the variables.

Question 18

Which of the following best describes the total deviation in regression analysis?

Accepted Answer

The difference between the observed value and the mean value of the response variable.

Question 19

Which equation correctly relates total variation, explained variation, and unexplained variation?

Accepted Answer

$$	ext{Total Variation} = 	ext{Explained Variation} + 	ext{Unexplained Variation}$$

Ch 4 part 1 Scatter Diagrams, Correlation, and Regression

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