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Algebra 1

3.4.3 Finding the Correlation Coefficient with Technology

Algebra 13.4.3 Finding the Correlation Coefficient with Technology

3.4.3 Finding the Correlation Coefficient with Technology

3.4.3 • Finding the Correlation Coefficient with Technology

Activity

1. Click on the " + + " sign in the Desmos graphing tool. Choose table from the drop down menu. This will generate a table for entering a data set.

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2. Enter the data set shown in the table below into the corresponding x 1 x 1 and y 1 y 1 columns.

(If preferred, the data can be copied and pasted into Desmos from a spreadsheet using keyboard shortcuts. Windows: Ctrl+C for copy and Ctrl+V for paste. Mac: Command+C for copy and Command+V for paste.)

x 1 x 1 y 1 y 1
2 12
9 11
15 6
21 3
22 -1

Hint: The window should be appropriately set to display the points in the table, but sometimes it will be necessary to adjust the window of the graph in order to properly view your data set. Use the mouse to drag and change the viewing window. To zoom in or out, use the buttons in the top right or the scrolling wheel on the mouse.

3. In the Desmos window, click in the entry box #2 below the table from Question 1 and enter the command c o r r ( x 1 , y 1 ) c o r r ( x 1 , y 1 ) . (You can just type x 1 x 1 and y 1 y 1 . The subscripts will appear automatically.)

4. A number between -1 and 1 will appear after an equal sign in the bottom right-hand corner of the same box. What is the number rounded to the thousandths place?

5. What does this number tell you about the strength of the linear relationship?

Self Check

Use the Desmos graphing tool below to find the correlation coefficient for this data.

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Additional Resources

Finding The Correlation Coefficient Using Technology

Let’s find the correlation coefficient for a given data set.

Step 1 - Click on the " + + " sign in the Desmos graphing tool. Choose table from the drop down menu. This will generate a table for entering a data set.

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Step 2 - Enter the data into the corresponding x 1 x 1 and y 1 y 1 columns in the table you created in Step 1. Press Enter or use arrow keys to enter a new data value in the table.

(If preferred, the data can be copied and pasted into Desmos from a spreadsheet using keyboard shortcuts. Windows: Ctrl+C for copy and Ctrl+V for paste. Mac: Command+C for copy and Command+V for paste.)

x 1 x 1 y 1 y 1
-6 -1
-4 1
0 -2
1 -3
3 0

Hint: The window should be appropriately set to display the points in the table, but sometimes it will be necessary to adjust the window of the graph in order to properly view your data set. Use the mouse to drag and change the viewing window. To zoom in or out, use the buttons in the top right or the scrolling wheel on the mouse.

You should have created the following table and scatter plot:

Step 3 - In the Desmos window, click in the entry box #2 below the table from Question 1 and enter the command c o r r ( x 1 , y 1 ) c o r r ( x 1 , y 1 ) . (You can just type x 1 x 1 and y 1 y 1 . The subscripts will appear automatically.)

As soon as you enter the correlation command, Desmos will display the correlation coefficient after an equal sign in the bottom right corner of the same box.

Step 4 - Round to the nearest thousandth. The correlation coefficient is -0.299.

Step 5 - Determine the strength of the linear relationship. This correlation coefficient shows a weak negative linear relationship.

Try it

Try It: Finding the Correlation Coefficient with Technology

1.

Find the correlation coefficient of the data set. Round the answer to the nearest thousandth.

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x 1 x 1 y 1 y 1
-1 4
0 9
3 14
5 -3
6 1
2.

What is the strength of the linear relationship?

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