Regression Analysis
Justin Lian G. Caballero
12/5/2024
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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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: Each of the three factors varies. Stress levels are mostly normal to mild. Anxiety levels are generally moderate. Respondents use a wide range of coping 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 = Justin10)
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: 0.03584Answer: The results indicate that the model outperforms a model with only the intercept, as at least one coefficient β is significantly different from 0 with a p-value of 0.03584. Additionally, substance use significantly predicts stress, with a p-value of 0.0186. The coefficient for substance use is 3.9883, meaning that higher substance use scores correspond to higher stress levels. On average, a one-unit increase in substance use raises the 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 = Justin10)
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: Justin10$StTotal and Justin$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.