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". 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. At each school, 54 students were randomly selected to participate in the study. Participants completed questionnaires measuring resilience, quality of life, perception of educational environment, depression symptoms, and anxiety symptoms.
The following regression model was fit to analyze the relationship between resilience and depressive symptoms. Resilience was categorized as: very low, low, moderately low, moderately high, high, and very high. Depressive symptoms were measured on a scale of 0 to 63 points, with higher scores indicating either more numerous or more severe depressive symptoms; this questionnaire is called the Beck Depression Inventory (BDI).

In this model, the residual standard error is 5.867, the F-statistic is 118.1 with 5 and 1344 degrees of freedom; P(F_5,1344 > 118:1) < 0.0001.

(a) In terms of the variables in the regression model, state the null hypothesis that corresponds to the F-statistic.
(b) Describe the relationship between the coefficients from the linear model and the usual summary statistics for the six sets of BDI scores.
(c) Explain why the null hypothesis used in this regression model is equivalent to the null hypothesis that would be used if these data were analyzed with an ANOVA approach.
 

Estimate Std. Error t value t value Pr>|t|) (Intercept) 4.9754 0.4118 12.08 0.0000 resHigh 2.2936 0.4987 4.60 0.0000 resModHigh 4.3005 0.5181 8.30 0.0000 resModLow 6.7108 0.5938 11.30 0.0000 resLow 9.6538 0.7458 12.94 0.0000 resVery Low 15.6453 0.7518 20.81 0.0000