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1 Introduction

The research project QUAIL-Mex investigates the relationship between perceived water insecurity, psychological stress, and biological markers of stress among adult women. In this report, we focus on the dependencies between HW_TOTAL, PSS_TOTAL and some predictors of interest. Specifically, we run two linear regression models as follows:

  1. HW_TOTAL ~ D_AGE + D_HH_SIZE + D_CHLD + HLTH_SMK + HLTH_CPAIN_CAT + HLTH_CDIS_CAT + SES_SC_Total

  2. PSS_TOTAL ~ D_AGE + D_HH_SIZE + D_CHLD + HLTH_SMK + HLTH_CPAIN_CAT + HLTH_CDIS_CAT + SES_SC_Total

2 Data preparation

  1. We remove rows with missing data.

  2. HW_TOTAL is calculated by adding up all the HWISE scores; PSS_TOTAL is calculated by adding up PSS 1,2,3, 8, 11, 12, 14, and substracting 4,5,6,7,9,10, and 13.

3 Results

3.1 HW

The regression results for HW is summarized as follows.


Call:
lm(formula = HW_TOTAL ~ D_AGE + D_HH_SIZE + D_CHLD + HLTH_SMK + 
    HLTH_CPAIN_CAT + HLTH_CDIS_CAT + SES_SC_Total, data = reg_dataset)

Residuals:
    Min      1Q  Median      3Q     Max 
-9.6661 -4.4176 -0.7606  3.8845 17.7116 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    14.382856   2.097087   6.858 4.99e-11 ***
D_AGE          -0.107514   0.054957  -1.956   0.0515 .  
D_HH_SIZE      -0.082722   0.103845  -0.797   0.4264    
D_CHLD          0.127345   0.352781   0.361   0.7184    
HLTH_SMK        0.135179   0.983496   0.137   0.8908    
HLTH_CPAIN_CAT  0.783988   0.883577   0.887   0.3757    
HLTH_CDIS_CAT   1.209758   1.091790   1.108   0.2689    
SES_SC_Total   -0.021450   0.008669  -2.474   0.0140 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6.007 on 262 degrees of freedom
Multiple R-squared:  0.04891,   Adjusted R-squared:  0.0235 
F-statistic: 1.925 on 7 and 262 DF,  p-value: 0.06595

The goodness-of-fit for HW regression is given as follow.

Version Author Date
b0e54be Junhui He 2025-03-03

3.2 PSS

The regression results for PSS is summarized as follows.


Call:
lm(formula = PSS_TOTAL ~ D_AGE + D_HH_SIZE + D_CHLD + HLTH_SMK + 
    HLTH_CPAIN_CAT + HLTH_CDIS_CAT + SES_SC_Total, data = reg_dataset)

Residuals:
    Min      1Q  Median      3Q     Max 
-18.302  -4.873  -0.352   5.101  17.827 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)     2.405322   2.579522   0.932   0.3520  
D_AGE          -0.156576   0.067600  -2.316   0.0213 *
D_HH_SIZE      -0.079564   0.127735  -0.623   0.5339  
D_CHLD          0.629308   0.433938   1.450   0.1482  
HLTH_SMK        0.164630   1.209749   0.136   0.8919  
HLTH_CPAIN_CAT  0.597392   1.086844   0.550   0.5830  
HLTH_CDIS_CAT   2.662062   1.342956   1.982   0.0485 *
SES_SC_Total    0.002218   0.010663   0.208   0.8354  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 7.389 on 262 degrees of freedom
Multiple R-squared:  0.03445,   Adjusted R-squared:  0.008653 
F-statistic: 1.335 on 7 and 262 DF,  p-value: 0.2337

The goodness-of-fit for PSS regression is given as follow.

Version Author Date
b0e54be Junhui He 2025-03-03

4 Discussion

4.1 Comments on results

  1. Unfortunately, the coefficient estimates are not significant except for a few predictors. This indicates the linear dependency between the response (HW_TOTAL or PSS_TOTAL) and the predictors are not significant.

  2. Based on the goodness-of-fit figures, the predictive performance is really bad, which is consistent with the last comment.

4.2 Questions

  1. Is it reasonable to use HW_TOTAL or PSS_TOTAL as response variables and other aforementioned variables as predictors? If not, how should I choose response variables and predictors?

  2. Previously, I mentioned feature selection, a method used to identify the most influential variables among a set of predictors. Here, “the most influential variable” refers to one that has a significant impact on the response. However, since your cleaned dataset contains only eight predictors, I believe feature selection is unnecessary. Moreover, feature selection is typically employed to prevent overfitting, whereas our primary problem is underfitting.