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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
- Data level of measurement – what is the level of measurement for the data used in this case study? Ratio
- 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. For BW yes. Skewness = 1.987/.661 = 3.006, kurtosis = 3.797/1.279 = 2. Paste table below:
Descriptives
Statistic Std. Erro Mean_heart_rate_ Mean 132.27 (^) r4. BPM (^) 95% Confidence Lower Interval for Mean Bound Uppe r Boun d
5% Trimmed Mean 132. Median 134. Variance 254. Std. Deviation 15. Minimum 108 Maximum 160 Range 52 Interquartile Range 29
Kurtosis -.639 1. Body_weight_Kg Mean 85.391 4. 95% Confidence Interval for Mean Lower Bound Upper Bound
5% Trimmed Mean
Median 80. Variance 194. Std. Deviation 13. Minimum 73. Maximum 120. Range 46. Interquartile Range
Skewness 1.987. Kurtosis 3.797 1.
- 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 Statisti c df Sig. Statisti c df Sig. Mean_heart_rate .147 11 .200 .966 11.
Body_weight_Kg. 8
*. 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:
Figure 2. Normal Q-Q plot for each variable Paste figure below:
- Were there any outliers; how do you know? HR – no BW – yes They are shown on the box and whiskers plot. Table 3. Box-and-Whiskers plot for each variable Paste table below:
Table 5. Correlations table Paste table below:
Correlations
Mean_hear t rate_BPM Body_weig h t_Kg Mean_heart_rat e BPM Pearson Correlati on
Sig. (2-tailed). N 11 11 Body_weight_Kg Pearson Correlati on
-.705*^1
Sig. (2-tailed). N 11 11 *. Correlation is significant at the 0.05 level (2-tailed). Write-up (8 sentence maximum) Include the following items:
- What is the research question?
- What is the Pearson correlation value, and is it statistically significant (hint: what is the “ p -value”)?
- Is there a positive or negative relationship between the two variables, and how did you come to that conclusion?
- What are your thoughts on the finding of this analysis, and what are the practical application(s) of this finding? The research question is whether or not there is a correlation between mean heart and bowdy weight. The Pearson correlation for this set of data is - .705, (p<.001), which indicates a strong significance level, which is also shown by the sig. of .015. There is a negative relationship between the 2 values because the p value is negative, and the skewness and kurtosis of body weight, was violated because it was too much. The findings are interesting, I’ve always thought
that body weight played a big role in mean heart rate, especially resting, but according to these
Figure 1. Histogram with normal curve for each variable Paste figure below: Figure 2. Normal Q-Q plot for each variable Paste figure below:
SAME AS PREVIOUS
Statistical Analysis Table 4. Descriptives statistics table Paste table below:
Descriptive Statistics
Mean Std. Deviatio n
N
Mean_heart_rat e_ BPM
Body_weight_Kg 85.391 13.9322 11 Table 5. Correlations table Paste table below:
Correlations
Mean_hear t rate_BPM Body_weig h t_Kg Pearson Correlati on Mean_heart_rat e BPM
Body_weight_Kg -.705 1. Sig. (1-tailed) Mean_heart_rat e_ BPM
Body_weight_Kg..
N Mean_heart_rat e_ BPM
Body_weight_Kg 11 11 Table 6. The model summary table Paste table below:
Model Summary
b Model R
R
Squar e Adjusted R Square Std. Error of the Estimate Durbin
Watso n
a
a. Predictors: (Constant), Body_weight_Kg b. Dependent Variable: Mean_heart_rate_BPM Table 7. The ANOVA table Paste table below:
ANOVA
a Sum of Model Squares df Mean Squar e F Sig. 1 Regressi o n
b Residual 1279.094 9 142. Total 2546.182 10
Table 8. The coefficients table Use this table to type out the regression equation for this data. Paste table below: Coefficientsa Model Unstandardized Coefficients Standardized Coefficientst Sig. 95.0% Confidence Interval for B Collinearity Statistics B Std. Error Beta Lower Bound Upper Bound Tolerance VIF 1 (Constant) 201.264 23.384 8.607. 148.366 254. Body_weight_Kg -.808 .271 -.705 -2.986. -1.420 -.196 1.000 1. a. Dependent Variable: Mean_heart_rate_BPM Coefficientsa Unstandardized (^) Standardiz ed 95.0% Co Coefficients Coefficients Mode l B Std. Error Bet a t Sig. Lower Bou 1 (Constant) 201.264 23.384 8.607 .000 148. Body_weight_ K g
a. Dependent Variable: Mean_heart_rate_BPM Y= a + bX Y= 201.264+-.
Write-up (8 sentence maximum) Include the following items:
- What is the research question?
- What is the Pearson correlation value, and is it statistically significant (hint: what is the “ p -value”)?
- Is there a positive or negative relationship between the two variables, and how did you come to that conclusion?
- What is the regression equation for these data?
- What are your thoughts on the finding of this analysis, and what are the practical application(s) of this finding? The research question is whether or not there is a correlation between mean heart and bowdy weight. The Pearson correlation for this set of data is - .705, (p<.001), which indicates a strong significance level, which is also shown by the sig. of .015. There is a negative relationship between the 2 values because the p value is negative, and the skewness and kurtosis of body way was violated because it was too much. The regression equation for this data is Y=201.264+-.808. The findings are interesting, I’ve always thought that body weight played a big role in mean heart rate, but according to these results that is not the case. This can be used practically to help determine why some people have a higher heart rate than others, and how those with higher heart rates can potentially lower theirs.
