EXSC 520
CASE STUDY 1 – CORRELATION AND BIVARIATE REGRESSION TEMPLATE
Instructions: To successfully complete this case study, all of the following instructions must be
adhered to. Only paste tables/figures that contain pertinent information. Only paste tables/
figures where you are instructed to do so. Highlight (in yellow) only relevant data from tables; as
well as your response to each question. In the write-up section, all information must be provided
in paragraph format. When statistical values are discussed, the numerical value must be given
and a reference must be made to the table(s)/figure(s) where the value(s) can be found. An
example of this is “heart rate was statistically greater during running versus cycling (189 vs. 143
bpm) as indicated in Table 1.”
I. Correlation
Research question: “Is mean heart rate during exercise correlated to body weight?”
Assumptions Testing
1. Data level of measurement – what is the level of measurement for the data used in this case
study? __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.
For HR no. Skewness = .015/.661 = .0227, kurtosis = .639/1.279 = -0.499
For BW yes. Skewness = 1.987/.661 = 3.006, kurtosis = 3.797/1.279 = 2.9687
Paste table below:
Descriptives
Std.
Statistic Error
Mean_heart_rate_ Mean 132.27 4.811
BPM 95% Confidence Lower 121.55
Interval for Mean Bound
Upper 142.99
Bound
5% Trimmed Mean 132.08
Median 134.00
Variance 254.618
Std. Deviation 15.957
Minimum 108
Maximum 160
Range 52
Interquartile Range 29
Skewness .015 .661
Page 1 of 17
, EXSC 520
Kurtosis -.639 1.279
Body_weight_Kg Mean 85.391 4.2007
95% Confidence Lower 76.031
Interval for Mean Bound
Upper 94.751
Bound
5% Trimmed Mean 84.079
Median 80.900
Variance 194.105
Std. Deviation 13.9322
Minimum 73.9
Maximum 120.5
Range 46.6
Interquartile Range 9.4
Skewness 1.987 .661
Kurtosis 3.797 1.279
3. Was the assumption of normality met and how do you know?
For mean heart rate yes, because sig is greater than .05 - .842. Body weight no, it is smaller
than .05 - .002.
Table 2. Tests of normality
Paste table below:
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
*
Mean_heart_rate_ .147 11 .200 .966 11 .842
BPM
Page 2 of 17
, EXSC 520
Body_weight_Kg .318 11 .003 .748 11 .002
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
Figure 1. Histogram with normal curve for each variable
Paste figure below:
Page 3 of 17
CASE STUDY 1 – CORRELATION AND BIVARIATE REGRESSION TEMPLATE
Instructions: To successfully complete this case study, all of the following instructions must be
adhered to. Only paste tables/figures that contain pertinent information. Only paste tables/
figures where you are instructed to do so. Highlight (in yellow) only relevant data from tables; as
well as your response to each question. In the write-up section, all information must be provided
in paragraph format. When statistical values are discussed, the numerical value must be given
and a reference must be made to the table(s)/figure(s) where the value(s) can be found. An
example of this is “heart rate was statistically greater during running versus cycling (189 vs. 143
bpm) as indicated in Table 1.”
I. Correlation
Research question: “Is mean heart rate during exercise correlated to body weight?”
Assumptions Testing
1. Data level of measurement – what is the level of measurement for the data used in this case
study? __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.
For HR no. Skewness = .015/.661 = .0227, kurtosis = .639/1.279 = -0.499
For BW yes. Skewness = 1.987/.661 = 3.006, kurtosis = 3.797/1.279 = 2.9687
Paste table below:
Descriptives
Std.
Statistic Error
Mean_heart_rate_ Mean 132.27 4.811
BPM 95% Confidence Lower 121.55
Interval for Mean Bound
Upper 142.99
Bound
5% Trimmed Mean 132.08
Median 134.00
Variance 254.618
Std. Deviation 15.957
Minimum 108
Maximum 160
Range 52
Interquartile Range 29
Skewness .015 .661
Page 1 of 17
, EXSC 520
Kurtosis -.639 1.279
Body_weight_Kg Mean 85.391 4.2007
95% Confidence Lower 76.031
Interval for Mean Bound
Upper 94.751
Bound
5% Trimmed Mean 84.079
Median 80.900
Variance 194.105
Std. Deviation 13.9322
Minimum 73.9
Maximum 120.5
Range 46.6
Interquartile Range 9.4
Skewness 1.987 .661
Kurtosis 3.797 1.279
3. Was the assumption of normality met and how do you know?
For mean heart rate yes, because sig is greater than .05 - .842. Body weight no, it is smaller
than .05 - .002.
Table 2. Tests of normality
Paste table below:
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
*
Mean_heart_rate_ .147 11 .200 .966 11 .842
BPM
Page 2 of 17
, EXSC 520
Body_weight_Kg .318 11 .003 .748 11 .002
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
Figure 1. Histogram with normal curve for each variable
Paste figure below:
Page 3 of 17
