Model Results

            Estimate  Est.Error        Q2.5      Q97.5
Intercept -6.7199203 1.42881141 -9.52273432 -3.8924379
phq_score  0.1258819 0.02627009  0.07482524  0.1773645
gender     0.3707443 0.27005021 -0.13170803  0.9095394
age        0.1505712 0.06656828  0.01883365  0.2832794

0.1 Interpretting the Results:

\[ \text{Log-Odds}(\text{Depression\ Diagnosis}) = \beta_0 + \beta_1 \times \text{PHQ\ score} + \beta_2 \times \text{gender} + \beta_3 \times \text{age} \]

The following interpretations apply to college students aged 18 to 30, assuming all other factors are held constant:

  • Public Health Questionaire Score:
    • Odds Ratio: \[ e^{\beta_1} = e^{0.13} \approx 1.14 \]
    • Explanation: Each 1-point increase in the PHQ score raises the odds of a depression diagnosis by approximately 14%.
  • Gender:
    • Odds Ratio: \[ e^{\beta_2} = e^{0.37} \approx 1.45 \]
    • Explanation: Being female increases the odds of a depression diagnosis by about 45% compared to being male.
  • Age:
    • Odds Ratio: \[ e^{\beta_3} = e^{0.15} \approx 1.16 \]
    • Explanation: Each additional year of age increases the odds of a depression diagnosis by about 16%.
  • Intercept:
    • Odds Ratio: \[ e^{\beta_0} = e^{-6.72} \approx 0.001 \]
    • Explanation: The intercept represents the baseline odds of depression diagnosis when all predictors are zero.