# Using the Correlation Coefficient

# Using the Correlation Coefficient

##### Problem 1

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

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

$\begin{array}{|c|c|} \hline \\[-1em] x & y \\[-1em] \\ \hline \\[-1em] 5 & 2 \\[-1em] \\ \hline \\[-1em] 6 & 4.6 \\[-1em] \\ \hline \\[-1em] 7.5 & 7.2 \\[-1em] \\ \hline \\[-1em] 8 & 8.4 \\[-1em] \\ \hline \\[-1em] 8.3 & 8.2 \\[-1em] \\ \hline \\[-1em] 9 & 9.1 \\[-1em] \\ \hline \\[-1em] 10.2 & 10.3 \\[-1em] \\ \hline \\[-1em] 11.4 & 9.9 \\[-1em] \\ \hline \\[-1em] 11.4 & 11 \\[-1em] \\ \hline \\[-1em] 12 & 12.5 \\[-1em] \\ \hline \end{array}$

3) What is an equation of the line of best fit? Round numbers to two decimal places.

4) What is the value of the correlation coefficient?

##### Problem 4

5) 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?

##### 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 finds the residuals for the companies that have been in business for 3 years,

Find the residuals for the two points representing companies that have been in business for 3 years, (3, 0.42) and (3, 0.3).

6) (3, 0.42)

7) (3, 0.3)

Compare the residuals for the two companies who have been in business for 3 years.

8) How are they different?

9) How are they similar?

10) What does the information about the residuals for the two companies tell you about their fair trade business?

##### Problem 6

11) The correlation coefficient, $r$, is given for several different linear models for a data set. Which value for $r$ indicates the worst fit for the data?

##### Problem 7

12) Which of the following is the best estimate of the correlation coefficient for the line of best fit shown in the scatter plot?