The American Psychological Association defines resilience as "the process of adapting well in the face of adversity, trauma, tragedy, threats or even significant sources of stress". Resilience refers to a person's capacity to resist adversity and is closely related to qualities such as self-confidence and persistence. Studies have suggested that resilience is an important factor in contributing to how medical students perceive their quality of life and educational environment. Survey data were collected from 1,350 students across 25 medical schools in the United States as part of a study examining the life of students and residents in healthcare professions. At each school, 54 students were randomly selected to participate in the study. Participants completed assessments measuring resilience, quality of life, perception of the educational environment, depression symptoms, and anxiety symptoms. - Resilience. Higher scores on the resilience assessment are indicative of greater resilience; possible scores range from 14 to 98. 

The scores are reported according to a standardized scale: very low (14 to 56 points), low (57 to 64 points), moderately low (65 to 73 points), moderately high (74 to 81 points), high (82 to 90 points), and very high (91 to 98 points). - 

Quality of Life. 

Quality of life was assessed via three measures: overall quality of life (overall QoL), medical school quality of life (MSQOL), and a questionnaire from the World Health Organization (WHOQOL). For the overall QoL and MSQOL, students were asked to rate, on a scale from 0 to 10 with a higher score indicating better QoL, their overall quality of life and their quality of life in medical school. The WHOQOL is a 26-question survey measuring quality of life in four domains (environment, psychological health, social relationships, and physical health); participant responses to questions such as "Do you have enough energy for everyday life?" and "How well are you able to concentrate?" are converted to a 0 to 100 point score for each domain, with higher scores representing better quality of life. - 

Educational Environment. 

Perception of educational environment was assessed via the DREEM questionnaire; possible scores range from 0 to 200, with higher scores representing a more positive perception about educational environment. Questions include "I feel I am being well prepared for my profession" and "The atmosphere motivates me as a learner". Depression Symptoms. The Beck's Depression Inventory(BDI) 

Depression Symptoms. 

The Beck's Depression Inventory(BDI) questionnaire was used to assess depressive symptoms. Possible scores vary from 0 to 63, with higher scores indicating either more numerous or more severe depressive symptoms: no depressive symptoms (0 to 9 points), mild depressive symptoms (10 to 17 points), moderate depressive symptoms (18 to 29 points), severe depressive symptoms (30 to 63 points).  

Anxiety Symptoms. 

Anxiety symptoms were assessed based on two dimensions of anxiety: state anxiety (feelings of anxiety arising specifically when faced with a stressful event) and trait anxiety (feelings of anxiety on a daily basis). Possible scores range from 20 to 80 points. A score of 50 or higher for either state anxiety or trait anxiety (or both) is considered indicative of an anxiety disorder. Information was also collected on participants' age and sex. Year in medical school was recorded as the current level of training. The first two years of medical school are focused on basic science education (pre-clinical curriculum) and the last two years consist of rotations in clinical settings (clinical curriculum). After medical school, students undergo residency training in which they work as practicing physicians under the supervision of a senior clinician. Data from the study are in the file resilience.xlsx. The following table provides a list of the variables in the dataset and their descriptions. 

Use the data to answer the following questions. 

a) Does the perception of the educational environment(dream) change with respect to gender? Conduct a formal statistical comparison using independent samples t-test. Reference appropriate graphical and numerical summaries as needed. Interpret your findings? ANSWER 

b)  Does the perception of the educational environment change with respect to resilience? Conduct a formal statistical comparison using the ANOVA test. Reference appropriate graphical and numerical summaries as needed. Interpret your findings. (Hint: Follow the test with post-hoc if you find statistical significance) 

c) (10 pts.) Create a plot illustrating the association between age and perception of the educational environment. Describe what you see. (Hint: Scatter plot and correlation) 

d)  Fit a simple regression model where the independent variable is age and the dependent variable is the perception of the educational environment. ANSWER 

e) Is there evidence that age is a useful variable for predicting DREEM score? Explain your answer. 

f)  Report and interpret the model R2 for the model fit in part e. 

g) Explain why we use regression models briefly and explain the limitation of the simple linear regression model in part d. 

h) Fit a model estimating the association between resilience and perception of the educational environment, after adjusting for age. In no more than three sentences, summarize the main finding(s). (In other words, fit a multiple regression model to see the effect of resilience on the perception of the educational environment controlling for age) (Hint: dreem= resilience+age) 

i)  Explain briefly why we use the multiple linear regression model in part h. 

h) Fit a model estimating the association between resilience and perception of the educational environment, after adjusting for age. In no more than three sentences, summarize the main finding(s). (In other words, fit a multiple regression model to see the effect of resilience on the perception of the educational environment controlling for age ) (Hint: dreem= resilience+age)

i) Explain briefly why we use a multiple linear regression model in part h. 

Evaluate the following assumptions of the model from part i. 

Linearity Homoscedasticity Normality ANSWER 

k) A New York Times reporter is potentially interested in writing a piece about the research you have conducted. They have requested that you prepare a short statement, no more than ten sentences long. Selectively drawing from the results of your analyses, summarize the main conclusions about the relationship between resilience and perceptions of quality of life, bdi, and educational environment for medical students and residents. Be sure to use language accessible to a general audience.