The sample is described using four structural variables: gender, age, study level, and academic discipline.

The sample consists of students with a mixed gender distribution, with 60.6% identifying as female, 38.7% as male, and 0.7% in other categories. The majority of respondents are in the age group 21-30 years old. Regarding study level, most participants are enrolled in Bachelor studies, followed by Master Students. In terms of field of study, respondents are distributed across several disciplines, with the highest proportions in “other” fields.

In addition to Digital Behaviour (D) and Mental Health (M), a Physical Health (P) scale was constructed based on three items: sleep quality, junk food consumption, and sport frequency

The Digital Behavior (DigiAddict) scale, shows a moderate distribution among the student sample. The sample mean stands at 3.57 (SD = 1.35).The median value of 3.33 suggests that at least half of the respondents report relatively low to moderate levels of digital interference in their daily lives. Only two cases (NA’s) were missing from this calculation, ensuring a robust representation of the total sample (N=273 valid cases).

The Mental Health (M) scale is a composite score derived from five items measuring positive emotional states (feeling good, relaxed, active, fresh, and fulfilled). The distribution of mental health scores in this sample is notably symmetric, with both the mean and median standing at 3.80 (SD = 0.89). With a mean of 3.80 on a typical 1–6 scale, the average student reports experiencing positive psychological states slightly more than half of the time. However, the scores range from a minimum of 1.40 to a maximum of 6.00, reflecting a wide diversity in well-being across the participant group. Compared to the Physical Health scale, the higher standard deviation (0.89) suggest that mental health varies significantly more between individual students than their physical habits do.

The Physical Health (P) sample shows a highly concentrated distribution with a mean of 2.82 (SD = 0.52) and a median of 2.67.Visually, the distribution (as seen in the histogram) is relatively narrow, with most students scoring between 2.5 and 3.5. This indicates a high level of homogeneity in the sample’s physical habits.

cor(df[,c("phys_health", "mentalhealth")], use="complete.obs")
##              phys_health mentalhealth
## phys_health    1.0000000    0.2054415
## mentalhealth   0.2054415    1.0000000
cor.test(df$phys_health, df$mentalhealth)
## 
##  Pearson's product-moment correlation
## 
## data:  df$phys_health and df$mentalhealth
## t = 3.4365, df = 268, p-value = 0.0006828
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.08822942 0.31704201
## sample estimates:
##       cor 
## 0.2054415
#####
cor(df[,c("mentalhealth", "digiaddict", "phys_health")], use="complete.obs")
##              mentalhealth  digiaddict phys_health
## mentalhealth    1.0000000 -0.23213301  0.18792052
## digiaddict     -0.2321330  1.00000000 -0.09654841
## phys_health     0.1879205 -0.09654841  1.00000000
# REGRESSION MODEL
model = lm(mentalhealth ~ digiaddict + use_marijuana + phys_health, data=df)
summary(model)
## 
## Call:
## lm(formula = mentalhealth ~ digiaddict + use_marijuana + phys_health, 
##     data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.22389 -0.53388  0.02975  0.53550  2.22927 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3.00221    0.35737   8.401  5.7e-15 ***
## digiaddict      -0.09955    0.04102  -2.427  0.01604 *  
## use_marijuana.L  0.01482    0.17446   0.085  0.93239    
## use_marijuana.Q  0.20684    0.19316   1.071  0.28543    
## phys_health      0.42000    0.10723   3.917  0.00012 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7834 on 218 degrees of freedom
##   (52 Beobachtungen als fehlend gelöscht)
## Multiple R-squared:  0.1007, Adjusted R-squared:  0.0842 
## F-statistic: 6.103 on 4 and 218 DF,  p-value: 0.0001133

Hypotesis: Physical Health (P) has a significant positive effect on Mental Health (M), meaning that students with better physical habits will report higher psychological well-being, even when controlling for digital behavior and marijuana use.

The correlation between Physical Health and Mental Health is r 0.2.This is a positive correlation. As students report better physical habits (sleep, food, sport), their mental health scores tend to rise. The p-value is 0.00068. Since this is well below 0.05, the relationship is statistically significant. The correlation matrix shows that DigiAddict and Mental Health have a negative correlation (r = -0.23), meaning higher smartphone addiction is linked to lower mental well-being.

Regression Analysis: Digital Addiction (beta = -0.099): This has a significant negative effect (p = 0.016). Increased digital addiction is a “drain” on mental health. Marijuana Use is not significant (p = 0.93). In this specific model, once sleep, sport, and phone use is taking into account, marijuana consumption doesn’t uniquely predict mental health levels. The results provide strong support for the role of physical habits. Physical Health was the most powerful predictor of Mental Health (B = 0.42, p < .001), suggesting that improvements in sleep and exercise are heavily tied to emotional resilience.Conversely, Digital Addiction showed a significant negative impact (B = -0.10, p = .016), confirming that problematic smartphone use acts as a risk factor for diminished well-being. Marijuana use did not reach statistical significance in this model.