# Lesson 8

Using the Correlation Coefficient

### Problem 1

The number of hours worked, $$x$$, and the total dollars earned, $$y$$, have a strong positive relationship.

Explain what it means to have a strong positive relationship in this situation.

### Problem 2

The number of minutes on the phone and the customer satisfaction rating have a weak negative relationship.

Explain what it means to have a weak negative relationship in this context.

### Problem 3

Technology required. Use a graphing calculator to answer the questions.

$$x$$ $$y$$
5 2
6 4.6
7.5 7.2
8 8.4
8.3 8.2
9 9.1
10.2 10.3
11.4 9.9
11.4 11
12 12.5
1. What is an equation of the line of best fit?
2. What is the value of the correlation coefficient?

### Problem 4

Elena collects data to investigate the relationship between the number of bananas she buys at the store, $$x$$, and the total cost of the bananas, $$y$$. Which value for the correlation coefficient is most likely to match a line of best fit of the form $$y = mx + b$$ for this situation?

A:

-0.9

B:

-0.4

C:

0.4

D:

0.9

### Problem 5

A researcher creates a scatter plot that displays the relationship between the number of years in business, $$x$$, and the percentage of company business that is fair trade, $$y$$. The researcher creates a line of best fit, $$y=0.091x+0.060$$, and wants to find the residuals for the companies that have been in business for 3 years.

1. Find the residuals for the two points representing companies that have been in business for 3 years, $$(3, 0.42)$$ and $$(3, 0.3)$$.
2. Compare the residuals for the two companies who have been in business for 3 years. How are they different? How are they similar? What does the information about the residuals for the two companies tell you about their fair trade business?

### Solution

(From Unit 3, Lesson 6.)

### Problem 6

The correlation coefficient, $$r$$, is given for several different data sets. Which value for $$r$$ indicates the weakest correlation?

A:

0.01

B:

0.5

C:

-0.99

D:

1

### Solution

(From Unit 3, Lesson 7.)

### Problem 7

Which of the following is the best estimate of the correlation coefficient for the data shown in the scatter plot?

A:

-0.9

B:

-0.4

C:

0.4

D:

0.9