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Algebra 1

3.4.4 Matching Correlation Coefficients

Algebra 13.4.4 Matching Correlation Coefficients
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Activity

Thinking back to the last activity, you learned about the r r -value. Write these characteristics about the r r -value.

The r r -value is called a correlation coefficient. A correlation coefficient is one way to measure the strength of a linear relationship.

  • The sign of r r is the same as the sign of the slope of the best fit line.
  • The values for r r go from –1 to 1 and include –1 and 1.
  • The closer r r is to 1 or –1, the stronger the linear relationship between the variables.
  • The closer r r is to 0, the weaker the linear relationship between the variables.

Take turns with your partner to match a scatter plot with a correlation coefficient. For each match you find, explain to your partner how you know it’s a match. For each match your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.

A

A scatter plot with black dots shows data points forming a straight line trend. A blue line passes through the points, indicating a positive linear relationship between x (0–10) and y (2–9) on labeled axes.

B

Scatter plot with black dots showing data points trending upward, a blue line representing the line of best fit, x-axis labeled from 0 to 90, and y-axis labeled from 0 to 500.

C

A scatter plot with black dots shows a negative correlation between x and y values. A blue trendline slopes downward from left to right, indicating a decreasing linear relationship. The axes are labeled x and y.

D

A scatter plot with black dots showing data points and a blue trend line sloping downward from left to right, indicating a negative correlation between the x and y variables.

E

A scatter plot with black dots showing data points, a blue trend line indicating a positive correlation, and axes labeled x (horizontal) and y (vertical), with x ranging from 0 to 10 and y from 0 to 10.

F

Scatter plot with black data points and a blue line showing a negative linear relationship between x (0 to 10) and y (8 to 2). As x increases, y decreases. Axes are labeled x and y.

G

A scatter plot with black dots showing data points, a light blue line representing the line of best fit, and labeled axes: x (horizontal) and y (vertical). The trend line has a slight negative slope.

H

A scatter plot with black dots showing data points and a blue trend line sloping upward, indicating a positive correlation between x and y values. Axes are labeled x and y.
1.

r = − 1 r = − 1

2.

r = − 0.95 r = − 0.95

3.

r = − 0.74 r = − 0.74

4.

r = − 0.06 r = − 0.06

5.

r = 0.48 r = 0.48

6.

r = 0.65 r = 0.65

7.

r = 0.9 r = 0.9

8.

r = 1 r = 1

Video: Matching Correlation Coefficients

Watch the following video to learn more about the connections of scatter plots to the correlation coefficient.

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Are you ready for more?

Extending Your Thinking

Making a Real-World Connection

Jada wants to know if the speed that people walk is correlated with their texting speed. To investigate this, she measured the distance, in feet, that 5 of her friends walked in 30 seconds and the number of characters they texted during that time. Each of the 5 friends took 4 walks for a total of 20 walks. Here are the results of the first 20 walks.

Scatter plot showing a negative correlation between distance in feet and number of characters texted; as distance increases from 80 to 180 feet, the number of characters texted generally decreases.
Distance (feet) Number of characters texted Distance (feet) Number of characters texted
105 14 95 138
125 110 125 110
115 120 160 80
140 98 175 64
145 102 130 106
160 89 140 95
170 72 150 95
140 100 155 90
130 107 160 74
105 113 135 108

Over the next few days, the same 5 friends practiced walking and texting to see if they could walk faster and text more characters. They did not record any more data while practicing. After practicing, each of the 5 friends took another 4 walks. Here are the results of the final 20 walks.

Scatter plot showing the number of characters texted on the y-axis versus the distance in feet on the x-axis. The data points show a downward trend as distance increases from 120 to 240 feet.
Distance (feet) Number of characters texted Distance (feet) Number of characters texted
140 410 165 151
150 155 170 136
160 151 190 143
155 170 205 132
180 125 205 128
205 130 210 140
225 95 215 109
175 161 220 105
195 108 230 126
155 142 225 138

1. What do you notice about the 2 scatter plots?

2. Jada noticed that her friends walked farther and texted faster during the last 20 walks than they did during the first 20 walks. Since both were faster, she predicts that the correlation coefficient of the line of best fit for the last 20 walks will be closer to –1 than the correlation coefficient of the line of best fit for the first 20 walks. Do you agree with Jada? Be prepared to show your reasoning.

3. Use technology to find an equation of the line of best fit for each data set.

4. The correlation coefficient for the first line of best fit is − 0.95 − 0.95 and the second line of best fit is − 0.68 − 0.68 . Was your answer to question 2 correct? Why do you think the correlation coefficients for the two data sets are so different? Be prepared to show your reasoning.

Self Check

Which correlation coefficient best matches the scatter plot below?

SCATTER PLOT THAT SHOWS A WEAK NEGATIVE CORRELATION.

  1. r = − 0.39
  2. r = 0.26
  3. r = − 0.89
  4. r = 0.95

Additional Resources

Correlation Coefficient

Try matching each scatter plot to one of the following correlation coefficients:

r = − 0.02 r = − 0.02 , r = 0.84 r = 0.84 , r = − 0.72 r = − 0.72 , r = 0.65 r = 0.65

Four scatter plots are labeled A, B, C, D, each with unique data distributions. Plots are on a grid that extend from 0 to 9 on both axes, showing varied clustering.
Scatter plot Correlation coefficient
Scatter plot A

r = − 0.72 r = − 0.72

Scatter plot B

r = 0.84 r = 0.84

Scatter plot C

r = − 0.02 r = − 0.02

Scatter plot D

r = 0.65 r = 0.65

Try it

Try It: Correlation Coefficient

The scatter plot below displays data on the number of defects per 100 cars and a measure of customer satisfaction (on a scale from 1 to 1,000, with higher scores indicating greater satisfaction) for the 33 brands of cars sold in the United States in 2009.

Scatter plot showing the relationship between the number of defects per 100 cars and their satisfaction rating. Points are spread across the grid.

Which of the following is the value of the correlation coefficient for this data set: r = − 0.95 r = − 0.95 , r = − 0.24 r = − 0.24 , r = 0.83 r = 0.83 , or r = 1.00 r = 1.00 ? Explain why you selected this value.

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