Question 1

Which of the following best describes the relationship shown in a scatter diagram where the points form a pattern that rises from left to right in a straight line?

Accepted Answer

A strong positive linear association

Question 2

Given the formula for the sample linear correlation coefficient $$r$$:

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

What does a value of $$r = -1$$ indicate about the relationship between two variables?

Accepted Answer

A perfect negative linear relationship

Question 3

Suppose you calculate a correlation coefficient $$r = 0.78$$ for two variables. Which of the following is the best interpretation?

Accepted Answer

There is a strong positive linear association between the variables.

Question 4

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

Accepted Answer

It is always between $$-1$$ and $$1$$, inclusive.

Question 5

A researcher finds a correlation of $$r = 0$$ between two variables. Which of the following is the most accurate conclusion?

Accepted Answer

There is no linear relationship between the variables.

Question 6

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

Accepted Answer

Correlation can be affected by lurking variables that influence both variables.

Question 7

Given the regression equation $$ \hat{y} = 5.5273 + 0.0116x $$, what does the slope $$0.0116$$ represent in the context of drilling depth and time to drill five feet?

Accepted Answer

For each additional foot of depth, the time to drill five feet increases by 0.0116 minutes, on average.

Question 8

If the correlation coefficient between two variables is $$r = 0.6$$, what is the coefficient of determination $$R^2$$?

Accepted Answer

$$R^2 = 0.36$

Question 9

Which of the following is a property of the least-squares regression line?

Accepted Answer

It minimizes the sum of the squared residuals.

Question 10

A contingency table is used to:

Accepted Answer

Display the relationship between two categorical variables.

Question 11

What is Simpson’s Paradox?

Accepted Answer

A situation where the association between two variables reverses or disappears when a third variable is considered.

Question 12

Which of the following is NOT a reason to use a scatter diagram when analyzing two variables?

Accepted Answer

To determine the exact value of the correlation coefficient

Question 13

Suppose you have a regression equation $$ \hat{y} = b_0$ + b_1$ x . If $$you use this equation to predict $$y$$ for values of $$x$$ far outside the range of your data, what is this practice called?

Accepted Answer

Extrapolation, which is not recommended because the linear relationship may not hold.

Question 14

Which of the following best describes a lurking variable?

Accepted Answer

A variable that is not measured but affects both the explanatory and response variables.

Question 15

In the context of regression, what is a residual?

Accepted Answer

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

Question 16

Which of the following is TRUE about the coefficient of determination $$R^2$$?

Accepted Answer

It measures the proportion of variation in the response variable explained by the regression line.

Question 17

A conditional distribution in a contingency table is used to:

Accepted Answer

List the relative frequency of each category of the response variable, given a specific value of the explanatory variable.

Question 18

Which of the following scenarios is most likely to result in a correlation coefficient that is not resistant?

Accepted Answer

A data set with an outlier that does not follow the overall pattern.

Question 19

If the sum of squared residuals for a regression line is minimized, what does this imply about the line?

Accepted Answer

It is the least-squares regression line.

Question 20

Which of the following is a correct interpretation of an $$R^2$$ value of $$0.57 in a $$regression analysis?

Accepted Answer

57% of the variation in the response variable is explained by the regression model.

Describing the Relation Between Two Variables: Scatter Diagrams, Correlation, Regression, and Association

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