What is the minimum age?

Answer: \(30\)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  30.00   43.00   50.00   49.27   57.00   60.00

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

# A tibble: 2 × 3
  Gender count Percentage
  <chr>  <int>      <dbl>
1 female    40       27.6
2 male     105       72.4

Education


      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 
# A tibble: 14 × 3
   Education             count Percentage
   <chr>                 <int>      <dbl>
 1 Colege graduate           1       0.69
 2 College graduate         21      14.5 
 3 College level            16      11.0 
 4 Elementary graduate      17      11.7 
 5 Elementary level         21      14.5 
 6 Ementary level            1       0.69
 7 High School graduate      4       2.76
 8 High chool graduate       1       0.69
 9 High schoo graduate       1       0.69
10 High school graduate     22      15.2 
11 High school level        37      25.5 
12 High scool level          1       0.69
13 High sschool graduate     1       0.69
14 Highschool level          1       0.69
# A tibble: 145 × 84
     No. Gender   age Reappraisal1 Reappraisal2 Reappraisal3 Reappraisal4
   <dbl> <chr>  <dbl>        <dbl>        <dbl>        <dbl>        <dbl>
 1     1 male      43            4            2            2            2
 2     2 male      40            3            2            4            1
 3     3 male      60            3            2            2            2
 4     4 male      50            2            2            4            2
 5     5 male      42            4            4            2            4
 6     6 female    42            2            4            4            3
 7     7 male      54            4            2            3            3
 8     8 male      40            2            2            2            2
 9     9 male      56            2            2            3            2
10    10 male      43            4            2            4            4
# ℹ 135 more rows
# ℹ 77 more variables: Reappraisal5 <dbl>, ReappraisalMean <dbl>,
#   SocialSupport1 <dbl>, SocialSupport2 <dbl>, SocialSupport3 <dbl>,
#   SocialSupportMean <dbl>, ProbSolving1 <dbl>, ProbSolving2 <dbl>,
#   ProbSolving3 <dbl>, ProbSolving4 <dbl>, ProbSolvingMean <dbl>, Rel1 <dbl>,
#   Rel2 <dbl>, Rel3 <dbl>, Rel4 <dbl>, RelMean <dbl>, Tol1 <dbl>, Tol2 <dbl>,
#   TolMean <dbl>, Emo1 <dbl>, Emo2 <dbl>, Emo3 <dbl>, Emo4 <dbl>, …
# A tibble: 6 × 3
  Educationcode        count Percentage
  <fct>                <int>      <dbl>
1 Elementary level        22       15.2
2 Elementary graduate     17       11.7
3 High school level       39       26.9
4 High school graduate    29       20  
5 College level           16       11.0
6 College graduate        22       15.2

Income

# A tibble: 4 × 3
  Income count Percentage
  <fct>  <int>      <dbl>
1 15000    132      91.0 
2 17000      1       0.69
3 18000      2       1.38
4 20000     10       6.9

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 
# A tibble: 145 × 84
     No. Gender   age Reappraisal1 Reappraisal2 Reappraisal3 Reappraisal4
   <dbl> <chr>  <dbl>        <dbl>        <dbl>        <dbl>        <dbl>
 1     1 male      43            4            2            2            2
 2     2 male      40            3            2            4            1
 3     3 male      60            3            2            2            2
 4     4 male      50            2            2            4            2
 5     5 male      42            4            4            2            4
 6     6 female    42            2            4            4            3
 7     7 male      54            4            2            3            3
 8     8 male      40            2            2            2            2
 9     9 male      56            2            2            3            2
10    10 male      43            4            2            4            4
# ℹ 135 more rows
# ℹ 77 more variables: Reappraisal5 <dbl>, ReappraisalMean <dbl>,
#   SocialSupport1 <dbl>, SocialSupport2 <dbl>, SocialSupport3 <dbl>,
#   SocialSupportMean <dbl>, ProbSolving1 <dbl>, ProbSolving2 <dbl>,
#   ProbSolving3 <dbl>, ProbSolving4 <dbl>, ProbSolvingMean <dbl>, Rel1 <dbl>,
#   Rel2 <dbl>, Rel3 <dbl>, Rel4 <dbl>, RelMean <dbl>, Tol1 <dbl>, Tol2 <dbl>,
#   TolMean <dbl>, Emo1 <dbl>, Emo2 <dbl>, Emo3 <dbl>, Emo4 <dbl>, …
# A tibble: 5 × 3
  Stress1          count Percentage
  <fct>            <int>      <dbl>
1 Normal              75      51.7 
2 Mild                42      29.0 
3 Moderate            24      16.6 
4 Severe               2       1.38
5 Extremely severe     2       1.38
# A tibble: 5 × 3
  Anxiety1         count Percentage
  <fct>            <int>      <dbl>
1 Normal              37       25.5
2 Mild                26       17.9
3 Moderate            52       35.9
4 Severe              20       13.8
5 Extremely severe    10        6.9
# A tibble: 1,305 × 77
     No. Gender   age Reappraisal1 Reappraisal2 Reappraisal3 Reappraisal4
   <dbl> <chr>  <dbl>        <dbl>        <dbl>        <dbl>        <dbl>
 1     1 male      43            4            2            2            2
 2     2 male      40            3            2            4            1
 3     3 male      60            3            2            2            2
 4     4 male      50            2            2            4            2
 5     5 male      42            4            4            2            4
 6     6 female    42            2            4            4            3
 7     7 male      54            4            2            3            3
 8     8 male      40            2            2            2            2
 9     9 male      56            2            2            3            2
10    10 male      43            4            2            4            4
# ℹ 1,295 more rows
# ℹ 70 more variables: Reappraisal5 <dbl>, SocialSupport1 <dbl>,
#   SocialSupport2 <dbl>, SocialSupport3 <dbl>, ProbSolving1 <dbl>,
#   ProbSolving2 <dbl>, ProbSolving3 <dbl>, ProbSolving4 <dbl>, Rel1 <dbl>,
#   Rel2 <dbl>, Rel3 <dbl>, Rel4 <dbl>, Tol1 <dbl>, Tol2 <dbl>, Emo1 <dbl>,
#   Emo2 <dbl>, Emo3 <dbl>, Emo4 <dbl>, Overac1 <dbl>, Overac2 <dbl>,
#   Overac3 <dbl>, Overac4 <dbl>, Overac5 <dbl>, Relax1 <dbl>, Relax2 <dbl>, …
# A tibble: 9 × 5
  Coping            variable     n  mean    sd
  <fct>             <fct>    <dbl> <dbl> <dbl>
1 Emomean           Score      145  1.95 0.424
2 OveracMean        Score      145  2.25 0.439
3 ProbSolvingMean   Score      145  3.04 0.575
4 ReappraisalMean   Score      145  2.70 0.559
5 RelaxMean         Score      145  2.54 0.511
6 RelMean           Score      145  3.64 0.438
7 SocialSupportMean Score      145  2.54 0.519
8 Subsmean          Score      145  1.23 0.315
9 TolMean           Score      145  2.20 0.605

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


Call:
lm(formula = StTotal ~ ReappraisalMean + SocialSupportMean + 
    ProbSolvingMean + RelMean + TolMean + Emomean + OveracMean + 
    RelaxMean + Subsmean, data = Durias1)

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

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 = Durias1)

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

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 = 0.01223. It also shows that substance-use significantly predict anxiety with a p-value result of 0.00442. The coefficient of substance-use is 4.47935, 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 4.47935.

Checking of Assumptions

Explain each assumptions in using multiple regression.

Answer: Posterior Predictive Check is model predictions for new data points should closely match actual observed data. This requires generating simulated data from the model and comparing it to the real observed data, ensuring the model accurately reflects the uncertainty in predicting new observations. Linearity, independent and dependent variables should exhibit a linear relationship, indicating that a straight line can effectively fit the data. Homogeneity of Variance, error term variance should be constant across all independent variable levels, implying consistent scatter of points around the regression line for every independent variable value. Influential Observations, outliers or high leverage points could distort parameter estimation and require identification and potential handling and that points should be inside the reasonable line. Colinearity, independent variables should be minimally correlated with each other to allow for accurate estimation of their individual effects on the dependent variable. Normality of Residuals, error terms should be normally distributed. This means that the histogram of the error terms should be bell-shaped.

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


    Pearson's product-moment correlation

data:  Durias1$StTotal and Durias$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

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.