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(Solved) Multiple Regression Analysis Assignment – In this assignment, you will explore how different health factors influence healthcare utilization using multiple regression analysis.

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Multiple Regression Analysis Assignment

Overview

In this assignment, you will explore how different health factors influence healthcare utilization using multiple regression analysis. You will work with a dataset containing information about doctor visits, physical health, mental health, and stress levels.

Dataset Information

The file (regress.sav/regress.csv) contains the following variables:

  • timedrs: Number of visits to health professionals
  • phyheal: Number of physical health symptoms
  • menheal: Number of mental health symptoms
  • stress: Stressful life events score
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WEEK 5: Understanding Multiple Regression Analysis

Multiple Regression Analysis Assignment

Overview

In this assignment, you will explore how different health factors influence healthcare utilization using multiple regression analysis. You will work with a dataset containing information about doctor visits, physical health, mental health, and stress levels.

Dataset Information

The file (regress.sav/regress.csv) contains the following variables:

  • timedrs: Number of visits to health professionals
  • phyheal: Number of physical health symptoms
  • menheal: Number of mental health symptoms
  • stress: Stressful life events score

Part 1: Data Exploration (20 points)

Begin by examining relationships in your data:

  1. Create visualizations showing the relationships between doctor visits and each predictor
  2. Examine potential univariate and bivariate outliers
  3. Document any concerning patterns and how you would handle them
    • Note: For consistency, keep all data points in your analysis even if you identify outliers
  4. Calculate and interpret the correlations between variables

Part 2: Standard Multiple Regression (40 points)

Conduct a standard multiple regression analysis using either SPSS or Jamovi:

If Using SPSS:

  1. Navigate to ANALYZE → REGRESSION → LINEAR
  2. Set timedrs as your dependent variable
  3. Enter all other variables as independent variables
  4. Request part and partial correlations in the Statistics menu

If Using Jamovi:

  1. Go to ANALYSES → REGRESSION → LINEAR REGRESSION
  2. Set timedrs as your dependent variable
  3. Move all other variables to the covariates box
  4. Request model fit measures and coefficient statistics
  5. For part and partial correlations:
    • Use REGRESSION → PARTIAL CORRELATION
    • You’ll need separate analyses for each predictor (detailed instructions below)

Required Output:

  • Overall model fit (R, R², adjusted R²)
  • ANOVA results
  • Coefficients with significance tests
  • Part and partial correlations
  • At least one visualization supporting your analysis

Part 3: Hierarchical Regression (40 points)

Conduct a hierarchical regression analysis:

  1. Determine a theoretically-justified order for entering your predictors
  2. Document your reasoning for this order
  3. Enter variables in sequence, examining changes at each step

Required Analysis:

  • R² change at each step
  • Significance of each change
  • Final model coefficients
  • Comparison with standard regression results

Write-up Requirements

Your results section should include:

  1. Data Screening (15%)
    • Description of distributions
    • Discussion of any outliers or patterns
    • Bivariate relationship summaries
  2. Standard Regression Results (40%)
    • Overall model evaluation
    • Individual predictor contributions
    • Effect size interpretations
    • Practical significance discussion
  3. Hierarchical Regression Results (30%)
    • Justification for variable order
    • Changes at each step
    • Final model interpretation
  4. Visual Presentation (15%)
    • Relevant plots/figures
    • Properly formatted tables
    • Clear labeling and titles

Appendix: Understanding Partial and Semi-partial Correlations in Jamovi

Overview

While SPSS provides partial and semi-partial correlations with a single checkbox, Jamovi requires a more detailed approach that can actually deepen your understanding of these concepts.

Conceptual Understanding

  • Partial correlation: Shows the relationship between two variables after controlling for other variables
  • Semi-partial (part) correlation: Shows the unique contribution of a predictor to the dependent variable

Getting These Values in Jamovi

  1. For each predictor, you’ll need to run a separate analysis:
    • Go to ANALYSES → REGRESSION → PARTIAL CORRELATION
    • Under “Correlation Type” select “Semipartial”
    • You don’t need to check “Report significance”
  2. For each analysis:
    • Variables box: Put timedrs and one predictor
    • Control Variables box: Put the other two predictors
  3. Running Three Analyses: Example for phyheal:
    • Variables: timedrs and phyheal
    • Control Variables: menheal and stress

Repeat this process for menheal and stress.

Interpreting Results

  • The coefficient in the output is your semi-partial correlation
  • Square this value to get the unique variance explained
  • Compare these values to understand each predictor’s unique contribution

Example Interpretation

“The semi-partial correlation between physical health and doctor visits, controlling for mental health and

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stress, was .25, indicating that physical health uniquely explains 6.25% (.25²) of the variance in doctor visits.”

Multiple Regression Analysis Template

Part 1: Data Exploration (20 points)

Correlations between Variables

[Insert correlation matrix for timedrs, phyheal, menheal, and stress]

Outlier Analysis

  • Univariate outliers: _____
  • Bivariate outliers: _____
  • Concerning patterns identified: _____
  • Decision regarding outliers: _____

[Insert visualizations showing relationships between doctor visits and each predictor]

Part 2: Standard Multiple Regression (40 points)

Model Fit

  • R = _____
  • R² = _____
  • Adjusted R² = _____

ANOVA Results

F(___, ___) = _____, p = _____

Coefficients and Correlations

Variable B SE B t p Part correlation Partial correlation
phyheal
menheal
stress

[Insert visualization supporting analysis]

Practical Significance

[Discussion of effect sizes and practical significance of findings]

Part 3: Hierarchical Regression (40 points)

Order of Entry Justification

  1. First variable: _____ because _____
  2. Second variable: _____ because _____
  3. Third variable: _____ because _____

Results by Step

Step 1

  • R² = _____
  • R² change = _____
  • Significance of change: p = _____

Step 2

  • R² = _____
  • R² change = _____
  • Significance of change: p = _____

Step 3

  • R² = _____
  • R² change = _____
  • Significance of change: p = _____

Final Model Coefficients

[Insert final model coefficients table]

Comparison with Standard Regression

[Compare these results with the standard regression findings]

APA Write-up Template

Results

Data Screening

Preliminary analyses were conducted to examine the relationships between doctor visits and three predictors: physical health symptoms, mental health symptoms, and stress levels. Data screening revealed [describe any outliers, distributions, or notable patterns]. The relationships between variables were [linear/nonlinear], and examination of bivariate scatterplots indicated [describe any notable patterns]. Correlations between all variables are presented in Table 1.

[Table 1: Correlation Matrix]

Standard Multiple Regression

A standard multiple regression was conducted to determine how well physical health symptoms, mental health symptoms, and stress predicted the number of doctor visits. The linear combination of the three predictors was significantly related to doctor visits, R² = ___, adjusted R² = , F(, ___) = ___, p = ___. The model explains approximately ___% of the variance in doctor visits.

Analysis of individual predictors revealed that [describe which predictors were significant, include B weights, partial and part correlations]. For example, [interpret one notable finding in practical terms]. Table 2 presents the coefficients and correlations for each predictor.

[Table 2: Standard Regression Results]

Hierarchical Multiple Regression

A hierarchical multiple regression was performed to examine how well [later variables] predicted doctor visits after controlling for [earlier variables]. Variables were entered in the following order: [explain order and rationale].

At Step 1, [first variable(s)] accounted for ___% of the variance in doctor visits (R² = , F(, ___) = ___, p = ___). At Step 2, [describe what was added and results]. The addition of [variables] to the model resulted in a significant increase in R² of , F change(, ___) = ___, p = ___. [Continue for Step 3 if applicable].

The final model was significant, R² = , F(, ___) = ___, p = ___. [Interpret final model and compare to standard regression results]. Table 3 presents the coefficients for each step of the model.

[Table 3: Hierarchical Regression Results]

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