Linear Regression Analysis
Junhui He
2025-03-03
Last updated: 2025-03-03
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Knit directory: QUAIL-Mex/
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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:
HW_TOTAL ~ D_AGE + D_HH_SIZE + D_CHLD + HLTH_SMK + HLTH_CPAIN_CAT + HLTH_CDIS_CAT + SES_SC_Total
PSS_TOTAL ~ D_AGE + D_HH_SIZE + D_CHLD + HLTH_SMK + HLTH_CPAIN_CAT + HLTH_CDIS_CAT + SES_SC_Total
2 Data preparation
We remove rows with missing data.
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: 0.06595The goodness-of-fit for HW regression is given as follow.
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: 0.2337The goodness-of-fit for PSS regression is given as follow.
4 Discussion
4.2 Questions
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?
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.
4.1 Comments on results
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.
Based on the goodness-of-fit figures, the predictive performance is really bad, which is consistent with the last comment.