# Relationships between variables | MA320-statistics | Herzing University–Madison

In this lesson, you will run a correlation between the resting and after-exercising heart rates to determine if a linear relationship exists between the two variables and how strong the relationship is.

Steps

1. Open the Heart Rate Data Set in Excel and identify the X-variable (resting heart rates for all 200 participants) and the Y-variable (after-exercise heart rates for all 200 participants).
2. Use the Scatter Plot function in the Insert Charts section of Excel to create a scatter plot of the X and Y variables.
3. Add a trendline to the scatter plot.
4. Use the Data Analysis tools in Excel to find the regression equation.
5. In a Word document, describe the relationship between the X-variable (resting heart rate)and the Y-variable (after exercise heart rate).
• Graph the scatter plot with a trend line. Does it appear there is a linear relationship?  What does this mean?
• Calculate the correlation coefficient r using excel. Is this r (value) high compared to +1?  Based on the correlation coefficient is the relationship strong?
• Use excel to find the regression equation. Identify the slope.  What does it tell us in terms of our heart rate data?

Heart rate before and after exercise
M=0 F=1 Resting After Exercise
0 55.0 65.0
0 67.7 79.4
0 80.3 93.4
0 85.2 97.7
0 86.3 99.7
0 76.6 83.7
0 94.4 101.9
0 86.4 100.6
0 83.4 97.4
0 89.8 97.4
0 88.7 97.1
0 78.4 87.2
0 67.0 79.9
0 85.0 100.0
0 86.2 95.9
0 83.9 93.9
0 78.1 87.2
0 64.0 70.7
0 72.8 86.7
0 65.0 75.0
0 80.2 83.3
0 78.2 86.0
0 62.0 88.0
0 75.5 84.4
0 82.7 89.1
0 87.7 95.1
0 76.0 88.7
0 73.4 82.7
0 80.1 94.6
0 77.6 84.6
0 76.6 86.4
0 85.6 96.2
0 74.2 82.1
0 79.0 91.6
0 74.6 86.7
0 88.8 98.8
0 82.1 85.6
0 77.6 80.6
0 77.9 83.8
0 72.0 93.9
0 81.6 90.3
0 91.2 100.6
0 80.3 88.0
0 76.7 91.8
0 88.4 103.0
0 75.2 86.5
0 75.2 84.9
0 73.1 71.9
0 77.0 84.7
0 59.0 68.2
0 84.9 96.0
0 87.5 105.9
0 75.6 84.3
0 84.0 90.4
0 78.2 94.0
0 86.6 90.6
0 84.9 95.1
0 78.8 90.4
0 69.4 82.6
0 78.3 91.1
0 76.9 92.3
0 84.2 87.9
0 76.3 85.9
0 86.3 99.7
0 72.3 80.9
0 81.8 93.8
0 92.8 99.8
0 74.8 90.2
0 91.7 99.2
0 71.0 87.0
0 96.1 100.2
0 82.5 95.1
0 81.9 97.5
0 89.7 94.8
0 81.4 100.9
0 74.8 94.0
0 88.1 102.1
0 69.2 81.4
0 78.8 90.9
0 85.3 94.2
0 74.8 81.3
0 77.7 89.9
0 78.0 89.8
0 80.5 95.3
0 75.4 84.8
0 81.5 84.2
0 73.9 85.2
0 69.4 74.1
0 89.4 96.7
0 70.9 82.0
0 82.9 90.2
0 60.1 79.0
0 74.5 75.6
0 92.3 102.2
0 87.7 98.0
0 78.9 89.7
0 79.8 81.5
0 85.5 97.4
0 87.3 94.1
0 77.8 97.8
0 71.0 80.1
0 70.0 90.7
0 74.8 83.7
0 69.2 79.4
0 80.5 87.4
0 89.4 99.2
0 74.5 88.0
0 70.0 100.0
1 60.0 78.1
1 79.2 90.4
1 80.5 101.3
1 75.4 93.1
1 83.7 90.5
1 73.9 89.1
1 76.0 90.8
1 85.2 93.5
1 82.1 93.5
1 76.3 87.0
1 97.0 104.5
1 81.5 86.5
1 65.3 86.3
1 60.8 86.7
1 78.5 89.9
1 60.4 97.6
1 89.8 92.9
1 87.8 98.5
1 76.2 89.9
1 74.2 88.8
1 67.4 78.8
1 75.5 80.2
1 80.0 90.2
1 76.4 88.0
1 60.0 95.7
1 89.2 96.9
1 83.3 87.7
1 85.8 90.4
1 75.3 84.1
1 77.9 99.0
1 70.0 83.0
1 88.0 94.2
1 86.9 95.0
1 87.1 95.9
1 60.3 82.7
1 81.2 90.7
1 82.9 91.9
1 87.4 103.6
1 83.0 90.0
1 76.8 83.3
1 76.9 87.7
1 79.8 88.2
1 83.2 93.0
1 79.5 88.6
1 82.4 89.3
1 80.8 84.2
1 83.2 94.5
1 71.6 81.5
1 82.8 93.1
1 76.8 92.8
1 93.2 89.4
1 91.4 100.9
1 97.3 103.3
1 88.3 90.1
1 80.6 85.2
1 87.4 91.7
1 96.5 99.3
1 77.9 91.6
1 76.1 84.1
1 85.2 89.7
1 68.6 72.8
1 79.4 91.0
1 85.2 99.1
1 74.3 85.6
1 74.3 89.2
1 78.5 98.5
1 80.4 90.8
1 82.9 85.9
1 78.9 90.7
1 78.6 87.0
1 87.5 93.9
1 78.9 91.4
1 80.0 89.1
1 80.4 89.2
1 88.3 90.5
1 80.6 95.9
1 85.8 90.5
1 84.6 93.0
1 90.5 101.2
1 92.4 101.2
1 84.4 96.7
1 82.3 86.9
1 77.2 85.8
1 83.3 82.1
1 86.2 98.9
1 81.3 97.7
1 90.2 96.4
1 78.4 85.5
1 84.7 90.9
1 89.7 94.3
1 78.4 88.0
1 70.0 80.0