EXSC 520
CASE STUDY: CORRELATION AND BIVARIATE REGRESSION TEMPLATE
I. Correlation
Research question: “Is mean heart rate during exercise correlated to body weight?”
Assumptions Testing
1. Data level of measurement – what was the level of measurement for the data used in this case
study (ratio, interval, etc.)? Data level of measurement was the ratio scale for this case
study. The ratio scale is quantitative, with zero as the absence of value and equal values
from point to point. Heart rate and weight are both ratio scales. An example: A person
with a weight of 200 lbs. is twice the weight of someone 100 lbs. It’s the same principle
with a person’s heart rate.
2. Would the amount of skewness and kurtosis in these variables affect the analysis? How do
you know? Give numerical values to support your conclusion. There is 0.714 skewness of
the mean heart rate and -0.523 kurtosis. These are slightly skewed and platykurtic, but
as they ranged between 1.96 and -1.96, the variable was not relevant to the analysis
(Table 1). The skewness of body weight is 2.625 and the kurtosis is 1.633. The skewness
exceeds 1.96, and therefore the variable will influence the analysis (Table 1).
3. Table 1. Table with skewness and kurtosis
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4. Was the assumption of normality met and how do you know? To satisfy the normality
assumption, p0.05 must have been the Sig value of the Shapiro-Wilk test. Normality was
assumed for the average heart rate as the Sig value was p=0.621. But the normative
assumption was not fulfilled for the body weight, since the Sig value was p=0.008 (Table
2).
Table 2. Tests of normality
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Figure 1. Histogram with normal curve for each variable
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Figure 2. Normal Q-Q plot for each variable
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5. Were there any outliers; how do you know?
In the Box-and-Whiskers plot, for heart rate there were no outsiders because there are no
values outside of heart rate. But there was one outside the mean, number 2, for body
weight, by two standard deviations (Table 3).
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160
140
120
100
130.0
120.0
110.0
100.0
90.0
60.0
70.0
Mean_heart_rate_BPM
Body_weight_Kg
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Table 3. Box-and-Whiskers plot for each variable
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Statistical Analysis
Table 4. Descriptives statistics table
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Table 5. Correlations table
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Write-up- Use these questions as a guide to write an abstract (paragraph). Use past tense.
Include the following items:
1. What was the research question?
2. What was the Pearson correlation value (r), and was it statistically significant? (Use “sig”
reported in SPSS. That is the p-value, and compare to alpha to determine significance)
3. Was there a positive or negative relationship between the two variables, and how did you
come to that conclusion? Was this a strong correlation? (use r/Pearson)
4. What are your thoughts on the finding of this analysis, and what are the practical
application(s) of this finding? Elaborate on what the study means, why, how you know,
and relate the findings to exercise physiology knowledge. Use references if needed.
(Hint- does this study “make sense?” What could influence results?)
The case study question was, "Is mean heart rate during exercise related to body weight?"
The Pearson correlation coefficient value was r=-0.411, and sig value was p=0.072 (which is
larger than 0.005 so not statistically significant). They show an inverse relationship between
heart rate and weight. This was not a very high correlation as the number size does not
equal to +1. Their results also revealed body weight skewness. And therefore, more weight
does not imply slower heart rate. In most overweight people, the heart beats faster because
their hearts pump more blood. Larger weight doesn’t in this case necessarily mean that the
subject is overweight (since we don’t know anything else, including height and muscle
mass). Moreover, exercise physiology states that our heart rate rises with exercise and
exertion, but not weight.
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II. Bivariate Regression
Research question: “Can heart rate during exercise be predicted by using body weight as a
predicting variable and creating a linear regression equation?”
(THIS SECTION USES the SAME DATA and will replicate results from above, other than the
REGRESSION Section)
Assumptions Testing
1. Data level of measurement- what was the level of measurement for the data used in this case
study (ratio, scale etc.)?
The data level of measurement used in this case study is ratio.
2. Would the amount of skewness and kurtosis in these variables affect the analysis? How do
you know? Give numerical values to support your conclusion. There is 0.714 skewness of
the mean heart rate and -0.523 kurtosis. These are slightly skewed and platykurtic, but
as they ranged between 1.96 and -1.96, the variable was not relevant to the analysis
(Table 1). The skewness of body weight is 2.625 and the kurtosis is 1.633. The skewness
exceeds 1.96, and therefore the variable will influence the analysis (Table 1).
Table 1. Table with skewness and kurtosis
Paste table below:
3. Was the assumption of normality met and how do you know? To satisfy the normality
assumption, p0.05 must have been the Sig value of the Shapiro-Wilk test. Normality was
assumed for the average heart rate as the Sig value was p=0.621. But the normative assumption
was not fulfilled for the body weight, since the Sig value was p=0.008 (Table 2).
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Table 2. Tests of normality
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Figure 1. Histogram with normal curve for each variable
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Figure 2. Normal Q-Q plot for each variable
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4. Were there any outliers; how do you know?
In the Box-and-Whiskers plot, for heart rate there were no outsiders because there are no
values outside of heart rate. But there was one outside the mean, number 2, for body
weight, by two standard deviations (Table 3).
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Table 3. Box-and-Whiskers plot for each variable
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Statistical Analysis
Table 4. Descriptives statistics table
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Table 5. Correlations table
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Table 6. The model summary table
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Table 7. The ANOVA table
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Table 8. The coefficients table
Use this table to type out the regression equation for this data.
Paste table below:
Write-up- Use these questions as a guide to write an abstract (paragraph). Use past tense.
Use the following questions as a guide:
1. What was the research question?
2. What was the Pearson correlation value (r), and was it statistically significant? (Use “sig”
reported in SPSS. That is the p-value, and compare to alpha to determine significance)
3. Was the relationship positive or negative and what was the (magnitude) strength of the
relationship (use r/Pearson)?
4. What was the regression equation for these data? Consider y=mx + b where y = HR.
5. What are your thoughts on the finding of this analysis, and what are the practical
application(s) of this finding? Elaborate on what the study means, why, how you know,
and relate the findings to exercise physiology knowledge. Use references if needed.
(Hint- does this study “make sense?” What could influence results?)
In this case study, the research question was ""Can you predict heart rate while exercising
by taking body weight as a predicting factor and constructing a linear regression
equation?" Pearson correlation was r=-0.411 and the new sig value is p=0.036 that is higher
than alpha =0.005 and therefore not statistically significant. The correlation between heart
rate and body weight was negative and weak because r doesn’t cross +1.
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HR=-0.521(bodyweight)+177.374 is the regression equation for this data. The Model
Summary for this case reported that an individual’s body weight influenced their exercise
heart rate only 17% of the time. So the above equation alone will not give a 100 percent
accuracy when used to estimate a person’s exercise heart rate because there are many other
variables that could affect a person’s exercise heart rate including their height, fitness and
exercise intensity.
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