# Using the Correlation Coefficient

ID: mohob-haruv Illustrative Math
Subject: Algebra, Algebra 2

# Using the Correlation Coefficient

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##### 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?

a) $\text{-0.9}$b) $\text{-0.4}$c) $\text{0.4}$d) $\text{0.9}$
##### 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 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)

Show Work

7) (3, 0.3)

Show Work

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?

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?
a) $\text{0.01}$b) $\text{0.5}$c) $\text{-0.99}$d) $\text{1}$ a) $\text{-0.9}$b) $\text{-0.4}$c) $\text{0.4}$d) $\text{0.9}$