Question 1

Which of the following best describes the relationship shown in the first scatter diagram from left to right in the provided image?

Accepted Answer

A positive linear relationship

Question 2

In a study investigating whether eating a yogurt a day causes people to lose weight, which is the explanatory variable and which is the response variable?

Accepted Answer

Explanatory: Eating yogurt; Response: Weight loss

Question 3

Given the data set: $$x = [2, 6, 6, 7, 9]$$, $$y = [8, 7, 6, 9, 5]$$, what is the value of the sample correlation coefficient $$r ($$rounded to two decimal places)?

Accepted Answer

$$r = -0.71$$

Question 4

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

Accepted Answer

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

Question 5

If the correlation coefficient $$r$$ for a data set with $$n = 10 is$$ $$0.65$$, and the critical value from Table II is $$0.632$$, what can you conclude?

Accepted Answer

There is evidence of a linear relationship between the variables.

Question 6

Which of the following best describes a situation where $$r = -1$$?

Accepted Answer

A perfect negative linear relationship exists between the variables.

Question 7

A scatter diagram shows points that form a clear upward slant from left to right. What does this indicate about the association between the two variables?

Accepted Answer

There is a positive linear association.

Question 8

Why is the linear correlation coefficient considered 'unitless'?

Accepted Answer

Because it is a ratio of deviations and the units cancel out.

Question 9

Suppose you have a data set with $$n = 7$$ and you calculate $$r = 0.70. $$According to Table II, is this sufficient evidence of a linear relationship?

Accepted Answer

No, because $$|r| = 0.70 \u003c 0.754 ($$the critical value for $$n=7)$$

Question 10

Which of the following is a correct interpretation if $$r is $$close to $$0$$?

Accepted Answer

There is little or no evidence of a linear relationship.

Question 11

A researcher finds $$r = 0.95$$ for the relationship between hours studied and exam score. What does this suggest?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam score.

Question 12

If an outlier is present in your data, what effect can it have on the linear correlation coefficient $$r$$?

Accepted Answer

It can significantly change the value of $$r.$$

Question 13

Which of the following is NOT a property of the linear correlation coefficient?

Accepted Answer

It is resistant to outliers.

Question 14

Given the following data: $$x = [2, 6, 6, 7, 9]$$, $$y = [8, 7, 6, 9, 5]$$, and using Table II, does a linear relationship exist at $$n=5$$?

Accepted Answer

No, because $$|r| = 0.71 \u003c 0.878 ($$the critical value for $$n=5)$$

Question 15

Which scenario best illustrates a negative association between two variables?

Accepted Answer

As the number of cigarettes smoked increases, lung capacity decreases.

Question 16

If a scatter diagram shows no discernible pattern, what can you conclude about the relationship between the variables?

Accepted Answer

There is no linear relationship between the variables.

Question 17

Which of the following is the correct formula for the sample linear correlation coefficient $$r$$?

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}}$$

Question 18

A data set has $$r = 0.05. $$Which of the following is the best interpretation?

Accepted Answer

There is little or no evidence of a linear relationship.

Question 19

If the value of $$r is $$close to $$-1$$, what does this indicate about the relationship between the two variables?

Accepted Answer

There is a strong negative linear relationship.

Question 20

Which of the following is a correct step in determining whether a linear relation exists between two variables?

Accepted Answer

Compare the absolute value of $$r to $$the critical value for the sample size.

Scatter Diagrams and Correlation: Understanding Relationships Between Two Variables

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