ST3002 Assignment Correlation and Regression

ST3002 Assignment Correlation and Regression

 

Student Name

Walden University

ST3002: Correlation and Regression

Professor name

Date

Correlation and Regression

Part 1 — Correlation in Research 

In this section, use the following article from the Walden Library as your reference:

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

All articles are available in full text in the Walden Library, which you may search by title or DOI. Make sure to explain each of your answers and support them with evidence from the text and/or Learning Resources.

Write responses to address the following in paragraph form by inserting your answers directly beneath the questions. 

On page 277 (Journal page number), there are six scatter plots. Refer to the scatter plots below to respond to the following questions.

1. Rank the six correlations provided from lowest correlation to highest correlation. Provide a brief 2–3 sentence explanation describing the reasoning behind your rankings.

The following is the ranking of the six correlations, ordered from lowest to highest.

1. Fat mass (r = 0.334)
2. Height (r = 0.360)
3. Body weight (r = 0.442)
4. Femur breadth (r = 0.535)
5. Skeletal muscle mass (r = 0.553)
6. Fat-free mass (r = 0.563)

Explanation

The rankings use the correlation coefficient (r) to determine how resting metabolic rate (RMR) relates statistically to different anthropometric measurements. A better R-value shows a stronger correlation between two variables. Fat mass exhibits the lowest connection (r = 0.334) to resting metabolic rate, thereby indicating a weak impact. The correlation between these variables shows femur breadth and skeletal muscle mass are strongly linked to RMR, but fat-free mass exhibits the highest relationship (r = 0.563) because lean tissue metabolically outpaces fat tissue. The correlation coefficient (r) exists between -1 and 1 throughout the analysis. A positive r-value in statistics reveals a positive link between variables, so that variable growth leads to parallel increases or fluctuations in other measures. A negative correlation exists when variables show opposing patterns since one variable’s increase produces a corresponding decrease in the other variable. A correlation value approaching 0 indicates minimal relationship, yet r-values approaching -1 or 1 point toward strong either negative or positive relationships (Xu et al., 2023). All anthropometric measurements display direct correlations with RMR according to the positive r-value results in this study.

2. Select one of the six graphs, calculate the r-squared value, and explain what it indicates about variation.

Calculation

R2= (0.553)2=0.306

Interpretation

The 30.63% of RMR variation that can be attributed to skeletal muscle mass shows through the R² value of 0.306. The remaining 69.37% of variation occurs from elements outside of skeletal muscle mass although this specific variable has explained 30.63% of RMR variability.

3. Based on the information on this page, describe one reason why BMI may not accurately reflect a person’s health status, noting that correlation does not imply causation.

BMI fails to show how a person’s health looks because it treats muscle and fat mass the same way. Athletes receive higher BMI scores thanks to increased muscle mass from their anaerobic training. The measurement shows that BMI alone doesn’t properly show how well-balanced an athlete’s body structure and health are, because their higher BMI result might come from stronger muscles instead of more weight gain.

Part 2 — Analyzing the Relationships Between Health Factors

Use the data set you created from the larger BODY DATA (ST3001) file following the given instructions.

Scatter Plots

Replace this text with your Excel-generated scatter plots and include explanations as directed below.

• BMI and LDL cholesterol levels

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

Figure 1: BMI and LDL 

The scatterplot visually represents the relationship between BMI (x-axis) and LDL (y-axis) cholesterol. 

• Using Excel, calculate the linear correlation between the data in the BMI and LDL cholesterol columns. 

	BMI	LDL
BMI	1
LDL	0.099261	1

Paste your results in your Word document. Describe the mathematical relationship between BMI and LDL cholesterol using the linear correlation coefficient. Discuss the strength and direction of the correlation, and explain how LDL cholesterol changes as BMI increases.

Data shows a weak positive relationship between BMI and LDL cholesterol through the linear correlation coefficient value of 0.0993. LDL cholesterol shows minimal change with increases in BMI while maintaining an insignificant connection between these variables. The observed correlation near zero demonstrates that BMI and LDL cholesterol show minimal linear connection, so BMI changes lack predictive power for LDL cholesterol shifts. The weak positive relationship between BMI and LDL cholesterol shows that other variables likely contribute more substantially to cholesterol level variations than BMI does independently.

• BMI and HDL cholesterol levels

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

Figure 2: BMI and HDL

The scatterplot shows the relationship between BMI and HDL cholesterol. 

 

• Use Excel to calculate the linear correlation between BMI and HDL cholesterol data. Paste your results in your Word document.

	BMI	HDL
BMI	1
HDL	-0.22091	1

 

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

BMI weakly matches with -0.22091 in the opposite direction to HDL cholesterol levels. Body Mass Index growth correlates weakly with falling levels of HDL cholesterol in the body. Higher body mass index tends to lower the amount of HDL cholesterol present, according to our results. The weak correlation number (nearly zero) proves that BMI stands alone weakly in predicting HDL cholesterol values when used by itself. Several other unknown aspects contribute to HDL cholesterol numbers. The rising BMI is linked to fewer HDL cholesterol levels in a small but not significant way.

Simple Linear Regression and Predictions

Replace this text with your Excel output created using the following instructions: 

• 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. Round your answer to four decimal places. Paste it in your report.

The graph shows a weak negative relationship between BMI and HDL, as indicated by the regression equation y = 70.5187 – 0.5205x.

• Determine the line of best fit (linear regression equation) and express it in the form y = b₀ + b₁x.

The linear regression equation is given by:

y=b0+b1x

From the regression output

• b0 (Intercept) = 70.5187
• b1 (Slope for BMI) = -0.5205

Thus, the equation is

y=70.5187−0.5205x

• Predict the HDL level for a patient who has a BMI of 25. Show your calculations.

Substituting x=25 into the equation

y=70.5187−0.5205 (25)

y=70.5187−13.0125

y=57.5062

So, the predicted HDL for a patient with BMI = 25 is 57.5062.

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

Substituting x=40 into the equation

y=70.5187−0.5205 (40)

y=70.5187−20.82

y= 49.6987

So, the predicted HDL for a patient with BMI = 40 is 49.6987

• Predict how BMI affects HDL levels and use your calculations above to support your conclusion. 

Research findings show an inverse relationship between BMI and HDL measured through the negative slope b1 = -0.5205. The research shows that every one-unit increase in BMI leads to an expected 0.5205-unit reduction in HDL values. Research predictions for BMI at 25 (57.5062) and 40 (49.6987) indicate a persistent downward pattern, which confirms that higher BMI values result in lower HDL levels. Higher BMI values tend to correspond with lower HDL levels in the body, which create major health risks.

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

Analysis from the regression output produced R² = 0.0488, indicating that BMI accounts for 4.88% of HDL level variability. A negative slope value of b₁ = -0.5205 shows BMI increase causes a 0.5205-unit HDL decrease. Our model projects that patients with a BMI of 25 will have 57.5062 HDL, whereas patients with a BMI of 40 will have 49.6987 HDL based on the regression findings. There is a clear decrease in HDL readings from BMI 25 to BMI 40. The weak predictive power of BMI for measuring HDL levels becomes evident when studying the low R² value because multiple additional factors, such as diet and exercise, along with genetics and health conditions, are believed to influence HDL concentrations (Khan et al., 2020). A statistical link exists between BMI and HDL, but BMI fails to provide practical usefulness as a standalone measurement for estimating HDL levels in medical practice.

Multiple Linear Regression 

Enter your response to the following prompt below:

• 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.
• 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.

From the Coefficients table:

• Intercept (b0) = 74.411
• AGE (b1) = -0.134
• SYSTOLIC (b2) = -0.070
• BMI (b3) = 0.394

Y = 74.411-0.134X1 -0.070X2 + 0.394X3

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

Y= 74.411−0.134 (AGE) −0.070 (SYSTOLIC) +0.394(BMI)

Y=74.411−0.134 (33) −0.070 (110) +0.394(27)

Y= 74.411−4.422−7.7+10.638

Y= 72.927

The predicted pulse rate for a 33-year-old with a systolic blood pressure of 110 and a BMI of 27 is 72.93.

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

The R² value for a regression is a measure of how well the independent variable(s) explain the variation in the dependent variable, ranging from 0 to 1, with higher values indicating a better fit (Fey et al., 2022). The model explains just 11.60% of pulse rate changes with age, blood pressure, and BMI, even though it includes all necessary variables, since these three measurements alone account for 88.40% of rate variability. The regression model demonstrates low-quality prediction because more than 88% of pulse rate changes come from unmodelled details. Despite the low predictive power of the entire model, BMI demonstrates a clear statistical connection with pulse rate at a very strong significance level (P-value = 0.008). The results show the model’s small predictive power with an adjusted R² value of 0.093. The measurements of age, systolic blood pressure, and BMI tell us something about pulse rate, but they cannot produce reliable forecasting results alone. Our results show that a complete model with both medical and everyday life measurements would improve predictive success.

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References

Fey, C. F., Hu, T., & Delios, A. (2022). Management and Organization Review, 19(1), 1–22. https://doi.org/10.1017/mor.2022.2

Xu, G., Zhou, G., Fadi Althoey, Hadidi, H. M., Abdulaziz Alaskar, Hassan, A. M., & Farooq, F. (2023). Evaluation of properties of bio-composite with interpretable machine learning approaches: Optimization and hyper tuning. Journal of Materials Research and Technology, 25, 1421–1446. https://doi.org/10.1016/j.jmrt.2023.06.007