PROBLEM SET #7

What is the minimum age?

Answer:

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

Minimum age is:  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:

Count of individuals aged at least 50 is:  69 

Socio-Demographic Profile

Gender

Education

Income

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

Interpretation:

• Stress levels appear to vary, with a majority falling into the Normal and Mild categories.

• Anxiety levels also vary, with a significant portion falls within the Moderate range.

• Coping mechanisms can vary, and it seems respondents use a mix of coping strategies, with varying mean scores across different strategies.

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 = D1)

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

Interpretation:

• 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 \(\beta\) is significantly different from 0 with a p -value = \(0.03584\).

• Using \(\alpha=0.05\), it also shows that substance-use (Subsmean) 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 \(3.9883\).

• Thus, there seems to be a potential relationship between the respondent’s level of stress and the coping mechanism Subsmean.

Checking of Assumptions

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

Call:
lm(formula = AnTotal ~ ReappraisalMean + SocialSupportMean + 
    ProbSolvingMean + RelMean + TolMean + Emomean + OveracMean + 
    RelaxMean + Subsmean, data = D1)

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

Interpretation:

• 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 \(\beta\) is significantly different from 0 with a p -value = \(0.01223\).

• Using \(\alpha=0.05\), it also shows that substance-use (Subsmean) significantly predict anxiety or considered a statistically significant predictor of the respondent’s level of 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 \(4.47935\).

• Thus, there seems to be a potential relationship between the respondent’s level of anxiety and the coping mechanism Subsmean.

Checking of Assumptions

3.3 Is there a significant relationship between stress and anxiety?

    Pearson's product-moment correlation

data:  D1$StTotal and D$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 

Interpretation:

• 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 statistically significant relationship between anxiety and stress with a p-value result of \(2.2e-16\), that is, \(0.00000000000000022\). This positive correlation suggests that as one variable increases, the other tends to increase as well.