New names:
• `Relax3` -> `Relax3...40`
• `Relax3` -> `Relax3...41`
• `Education` -> `Education...50`
• `` -> `...51`
• `Income` -> `Income...52`
• `` -> `...71`
• `Education` -> `Education...72`
• `` -> `...73`
• `` -> `...74`
• `` -> `...75`
• `Income` -> `Income...76`
• `` -> `...77`
• `` -> `...79`
• `` -> `...80`
• `` -> `...81`
• `` -> `...82`

What is the minimum age?

Answer: 30_

In the variable “age”, group the “age” variable into two groups, with atmost 50 years and more than 50 years old.

How many of them with at least 50 years old?

Answer: _____69____

Socio-Demographic Profile

Gender

   Length     Class      Mode 
      145 character character

Education

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    filter

      Colege graduate      College graduate         College level 
                    1                    21                    16 
  Elementary graduate      Elementary level        Ementary level 
                   17                    21                     1 
  High chool graduate   High schoo graduate  High school graduate 
                    1                     1                    22 
 High School graduate     High school level      High scool level 
                    4                    37                     1 
High sschool graduate      Highschool level 
                    1                     1

Income

1. What is the respondent’s level of stress and anxiety as measured by Depression, Anxiety, and Stress Scale (DASS-21)?


Extremely severe             mild             Mild         Moderate 
               2                1               41               24 
          Normal           Severe 
              75                2

#Answer: All of the three factors varies. In terms of stress, the majority of it falls under normal and mild. In terms of anxiety, the majority of it falls under Moderate. And in coping mechanism, respondents use wide variety of coping strategies.

3.1 Is there a significant relationship between respondent’s level of stress and coping mechanisms?

Warning: package 'performance' was built under R version 4.3.2

Call:
lm(formula = StTotal ~ ReappraisalMean + SocialSupportMean + 
    ProbSolvingMean + RelMean + TolMean + Emomean + OveracMean + 
    RelaxMean + Subsmean, data = Bienuel1)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.2452  -4.1688   0.1868   3.0768  20.7605 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)  
(Intercept)         7.6781     4.8332   1.589   0.1145  
ReappraisalMean     0.5264     1.1958   0.440   0.6605  
SocialSupportMean   1.1563     1.0585   1.092   0.2766  
ProbSolvingMean    -2.5310     1.3180  -1.920   0.0569 .
RelMean             0.8649     1.2815   0.675   0.5009  
TolMean            -0.3901     0.9907  -0.394   0.6943  
Emomean             1.9311     1.3611   1.419   0.1583  
OveracMean          0.8203     1.3734   0.597   0.5513  
RelaxMean          -1.2134     1.2422  -0.977   0.3304  
Subsmean            3.9883     1.6741   2.382   0.0186 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.868 on 135 degrees of freedom
Multiple R-squared:  0.1216,    Adjusted R-squared:  0.063 
F-statistic: 2.076 on 9 and 135 DF,  p-value: 0.03584

Answer: As shown in the above results, it shows that the model is better than a model with only the intercept because at least one coefficient β is significantly different from 0 with a p -value = 0.03584. It also shows that substance-use significantly predict stress with a p-value results of 0.0186. The coefficient of substance-use is 3.9883, this means that higher substance-use score indicates higher stress level. On, the average, a one unit increase in substance-use increases its stress level by 3.9883.

3.2 Is there a significant relationship between respondent’s level of stress and coping mechanisms?


Call:
lm(formula = AnTotal ~ ReappraisalMean + SocialSupportMean + 
    ProbSolvingMean + RelMean + TolMean + Emomean + OveracMean + 
    RelaxMean + Subsmean, data = Bienuel1)

Residuals:
   Min     1Q Median     3Q    Max 
-8.640 -3.572 -1.267  2.766 20.594 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)   
(Intercept)       -0.79897    4.46615  -0.179  0.85829   
ReappraisalMean    1.60382    1.10498   1.451  0.14897   
SocialSupportMean  1.31082    0.97808   1.340  0.18243   
ProbSolvingMean   -1.97803    1.21791  -1.624  0.10668   
RelMean           -0.32183    1.18417  -0.272  0.78621   
TolMean            0.24674    0.91544   0.270  0.78793   
Emomean            0.77602    1.25779   0.617  0.53829   
OveracMean         1.75879    1.26915   1.386  0.16809   
RelaxMean         -0.05083    1.14784  -0.044  0.96475   
Subsmean           4.47935    1.54695   2.896  0.00442 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.423 on 135 degrees of freedom
Multiple R-squared:  0.1414,    Adjusted R-squared:  0.08411 
F-statistic: 2.469 on 9 and 135 DF,  p-value: 0.01223

#Answer: As shown in the above results, it shows that the model is better than a model with only the intercept because at least one coefficient β is significantly different from 0 with a p -value = 0.006703. It also shows that substance-use significantly predict anxiety with a p-value result of 0.00387. The coefficient of substance-use is 4.4680, this means that higher substance-use score indicates higher anxiety level. On, the average, a one unit increase in substance-use increases its anxiety level by 4.680.

Checking of Assumptions

Explain each assumptions in using multiple regression.

Answer:

In Posterior Predictive Check, the model predicted data resembles the observed data line, hence, it is suggested that the model is a good fit for data.

3. Is there a significant relationship between stress and anxiety?


    Pearson's product-moment correlation

data:  Bienuel1$StTotal and Bienuel$AnTotal
t = 9.743, df = 143, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.5224234 0.7204693
sample estimates:
      cor 
0.6316421

Answer Based on the results above, it shows that there is a positive correlation between stress and anxiety with a correlation value of 0.6316421. It further shows that there is a signification relationship between anxiety and stress with a p-value result of 2.2e-16, that is, 0.00000000000000022.