ST3002 Assessment Template

Prepared by:

Date: January, 30 2026

Part 1

For this part, you will be making use of the following article from the References

Slavic, D., Jakovljevic, D. K., Zubnar, A., Tapavicki, B., Aleksandric, T., & Drapsin, M. (2019). Effects of different types of training on weight loss. Medicinski Pregled/Medical Review, 72(9/10), 272–279. https://doi.org/10.2298/MPNS1910272S

On page 277 in this journal, there are six scatter plots. Use these scatter plots to answer the following questions:

1. Rank the six correlations provide from lowest correlation to highest correlation. Include a 2- to 3-sentence explanation for why you ranked these the way you did.

Ranked correlations from the lowest to the highest:

0.329, 0.361, 0.535, 0.542, 0.553, 0.563

Variable	R	p-value
Feat mass	0.329	0.034
Height	0.361	0.019
Femur Breadth	0.535	<0.001
Body weight	0.542	<0.001
Skeletal muscle mass	0.553	<0.001
Feat Free Mass	0.563	<0.001

The ranking is based on the magnitude of the correlations. The lower values indicate a weak positive relationship, while the highest values indicate stronger relationships. Generally, correlations that are closer to zero demonstrate a weaker association between variables, while those that are closer to one indicate a stronger relationship.

2. Choose one of the six graphs and compute the r-squared value. Interpret this value as it relates to variation.

The selected graph is the first graph labeled ‘Feat free mass’. The r-squared value is the square of the correlation co-efficient: R² = 0.563² = 0.317 (3 decimal places).

The r-squared value indicates that approximately 31.7% of the variability in the dependent variable (resting metabolic rate) is explained by the independent variable (fat free mass). This also means that the remaining 61.83% of the variation is a result of other factors that are not included in the model.

3. Using the information presented on this page, explain one reason why BMI does not always indicate an individual’s health status (correlation does not imply causation)

BMI does not always indicate an individual’s health status because it only measures weight relative to height and does not account for other important factors such as feet free mass, skeletal muscle mass, feat mass, and femur breadth. Many variables are correlated to BMI, and a change on one of them may not be a major cause for the decrease or increase of BMI.

Part 2

As a medical researcher, you attempt to relate key health factors to each other. Are those with higher BMIs more likely to have higher or lower HDL and LDL cholesterol levels? How are factors such as age, systolic blood pressure, and BMI related to pulse rate? Looking at the correlation between variables will help assess the relationship between key health factors. Once a relationship is established, models can be built to help healthcare professionals assess risk levels for patients based on various factors. While a causal relationship cannot be assumed between factors, regression models can help healthcare practitioners predict key values for patients. To prepare for this Assessment:

Open the data set created in STAT3001, the modified body data set based on your assigned seed number.

Perform the following tasks to complete your data set:

1. Scatter Plots, Correlations, and the Correlation Coefficient

   • BMI and LDL cholesterol levels

     • Create a scatter plot for the data in the BMI and LDL cholesterol columns. Paste it in your report.

     • Using Excel, calculate the linear correlation between the data in the BMI and LDL cholesterol columns. Paste your results in your Word document.

	BMI	LDL
BMI	1
LDL	0.115294	1

The linear correlation co-efficient is 0.1153

• Explain the mathematical relationship between BMI and LDL cholesterol based on the linear correlation coefficient. Be certain to include comments about the magnitude (strength) and the direction (positive or negative) of the correlation. As BMI increases, what happens to LDL cholesterol?

The linear correlation coefficient between BMI and LDL cholesterol is r = 0.115294. This is a positive value, which indicates that there is a weak positive correlation between BMI and LDL cholesterol. As the BMI increases, the LDL cholesterol also increases. However, the correlation coefficient is close to 0 which suggests that BMI explains very little of the variation in LDL cholesterol, and changes in BMI are not strongly associated with changes in LDL levels in this dataset.

• BMI and HDL cholesterol levels

  • Create a scatter plot for the data in the BMI and HDL cholesterol columns. Paste it in your report.

  • Using Excel, calculate the linear correlation between the data in the BMI and HDL cholesterol columns. Paste your results in your Word document.

	BMI	HDL
BMI	1
HDL	-0.20183	1

The correlation coefficient is -0.2018

• Explain the mathematical relationship between BMI and HDL cholesterol based on the linear correlation coefficient. Be certain to include comments about the magnitude (strength) and the direction (positive or negative) of the correlation. As BMI increases, what happens to HDL cholesterol?

The linear correlation coefficient between BMI and LDL cholesterol is r = -0.2018. This is a negative value, which indicates that there is a weak inverse relationship between BMI and HDL cholesterol. As the BMI increases, the HDL cholesterol decreases. However, the correlation coefficient is close to 0 which suggests that changes in BMI are not strongly associated with changes in HDL levels in this dataset.

2. Linear Regression and Prediction

   • Let’s say that we wanted to be able to predict the HDL cholesterol level of a patient based on their BMI.

     • Using this sample data, perform a linear regression to determine the line of best fit. Use BMI as your x (independent) variable and HDL as your y (response) variable. Use four (4) places after the decimal in your answer. Paste it in your report.

Regression Statistics
Multiple R	0.201828
R Square	0.040734
Adjusted R Square	0.032741
Standard Error	16.91133
Observations	122

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1457.333	1457.333	5.095696	0.025794
Residual	120	34319.16	285.993
Total	121	35776.49

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	68.55387	6.40776	10.69857	3.63E-19	55.86695	81.24078	55.86695	81.24078
BMI	-0.47948	0.212408	-2.25736	0.025794	-0.90003	-0.05893	-0.90003	-0.05893

• What is the equation of the line of best fit (linear regression equation)? Present your answer in y = bo + b1x form.

The equation of the line is y = 68.5539 - 0.4795x

• What would you predict the HDL would be for a patient with a BMI of 25? Show your calculations.

y = 68.5539  − 0.4795 * 25 = 56.5664

The predicted HDL for a patient with a BMI of 25 would be 56.5664.

• What would you predict the HDL would be for a patient with a BMI of 40? Show your calculations.

y = 68.5539  − 0.4795 * 40 = 49.3739

The predicted HDL for a patient with a BMI of 25 would be 49.3739.

• What effect would you predict BMI would have on HDL levels? Use your computations above to justify your reasoning.

The regression has a negative slope (-0.4795) which indicates that HDL levels decrease as BMI increases. The calculations support the trend because when the BMI increased from 25 to 40, the predicted HDL reduced from 56.5664 to 49.3739.

• Calculate the coefficient of determination (R2 value) for this data. What does this tell you about this relationship?

R² = r²

R² = (−0.20183)² = 0.0407

The R² value demonstrates that approximately 4.07% of the variation in HDL can be explained by BMI in the model. This also means that 95.93% of the variation in the data is unexplained by the model. The findings indicate that BMI is a weak predictor of HDL levels even though the two variables have a negative correlation.

3. Multiple Regression

   • Let’s say that we wanted to be able to predict a patient’s pulse using age, systolic blood pressure, and BMI. Using this sample data, perform a multiple-regression line of best fit using age, systolic blood pressure, and BMI as predictor variables and pulse rate as the response variable. Paste your Excel work in your report.

Regression Statistics
Multiple R	0.31147
R Square	0.097014
Adjusted R Square	0.074056
Standard Error	10.9779
Observations	122

ANOVA
	df	SS	MS	F	Significance F
Regression	3	1527.818	509.2727	4.225832	0.007074
Residual	118	14220.67	120.5142
Total	121	15748.49

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	71.68535	8.777265	8.167162	3.97E-13	54.30397	89.06672	54.30397	89.06672
AGE	-0.10481	0.067159	-1.56062	0.121292	-0.2378	0.028183	-0.2378	0.028183
SYSTOLIC	-0.06389	0.080425	-0.79435	0.428584	-0.22315	0.095377	-0.22315	0.095377
BMI	0.39877	0.1412	2.824155	0.005567	0.119156	0.678385	0.119156	0.678385

• What is the equation of the line of best fit? The form of the equation is: Y = bo + b1X1 + b2X2 + b3X3 (fill in values for bo, b1, b2, and b3). Round coefficients to three (3) decimal places.

The equation of the line of best fit is: y = 71.685 − 0.105b1 − 0.064b2 + 0.399b3, where y is pulse rate, b1 is age, b2 is systolic blood pressure, and b3 is BMI.

• What would you predict the pulse rate would be for a patient with who is 33 years old with a systolic blood pressure of 110 and BMI of 27?

The predicted pulse rate would be:

y = 71.685 − 0.105 * 33 − 0.064 * 110 + 0.399 * 27

Pulse rate = 71.953

• What is the R2 value for this regression? What does it tell you about the regression?

The R² value for the regression, based on the excel output is 0.097. This means that approximately 9.7% of the variability in pulse rate can be explained by age, systolic blood pressure, and BMI in the model. This also means that 90.3% of the variation in the data is unexplained by the model. The findings indicate that the regression model has weak predictive power.