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ST2005/MS2019Assignment 3: General Linear Models

Conor Murphy
Due Date:24th February 2025

Recent research has shown that dietary patterns and physical activity levels play a significant role in predicting obesity and metabolic health outcomes. A study by Schnabel et al. (2019) examined how ultra-processed food consumption is associated with body mass index (BMI) and increased mortality risk. Inspired by this research, this assignment explores how dietary habits and physical activity levels influence BMI in adults. The data for this assignment is contained in diet_and_physical.sav and includes:
Variable Description
BMI Body Mass Index (BMI, kg/m²)
Diet_Type (1=Western,2=Mediterranean)
Physical_Activity_Level (1= Low, 2 = Moderate,3= High)

The goal is to determine whether diet type and/or physical activity level significantly predict BMI using a General Linear Model (GLM) and whether the effect of diet type depends on physical activity level. Write a brief report prepared in Microsoft Word which provides the following:

1. Compute appropriate descriptive statistics for BMI across different diet types and physical activity categories.
2. Using an appropriate plot, examine whether the effect of physical activity level on BMI differs across diet types.
3. Conduct an appropriate hypothesis test to determine whether the effect of physical activity level on BMI differs across diet types. State your hypotheses and conclusions.
4. Write out the general linear model equation for predicting BMI using diet type, physical activity level, and their interaction.
5. Use the equation provided in (4) to predict the BMI for a person with a moderate activity level on the Western diet type.
6. What is the coefficient of determination for the fitted model? Interpret this value.
7. Are the assumptions of normality and constant variability satisfied in this case? Justify your answers.

Your brief report should refer to (and contain) appropriate SPSS output. Your answers should be supported by details from your SPSS output. You should submit your report as a word or pdf file. The file should be named using the format ‘First Initial’+ ‘Surname'+ ‘Assignment3'. For example, I would submit a file named‘CMurphyAssignment3’. You are not allowed to collaborate on this assignment and plagiarism will not be tolerated. The completed report should be uploaded to Canvas via the assignment link.

Bibliography

Schnabel, L., Kesse-Guyot, E., Allès, B., Touvier, M., Srour, B., Hercberg, S., & Monteiro, C. A. (2019). Association between ultra-processed food consumption and risk of mortality among middle-aged adults in France.JAMA Internal Medicine, 179(4), 490-498. 

https://doi.org/10.1001/jamainternmed.2018.7289