For years scholars have wondered what produces happiness and well-being. A substantial range of recent studies have provided answers to such questions. In this regard, two concepts of well-being, subjective and psychological were introduced. Subjective well-being lays emphasis on a positive evaluation of life, and the balance between positive affect and negative affect (Diener et al. 1997). Psychological well-being is defined by parameters such as living based on self-development, personal growth and purposeful engagement (Ryff et al. 2004). According to Ryff and Singer (2006). psychological well-being is beyond mental well-being, and is an appropriate indicator when considering health. Moreover, psychological well-being is one of the important factors in personal and social growth. When individuals take advantage of mental health and well-being, they are able to take action towards problems that may arise, and choose solutions accordingly.

Researchers have highlighted the significance of various contributing factors in psychological well-being. Deci and Ryan (2000) suggest well-being as a function of contextual factors and individuals’ self-determination level. Kaplan et al. (1977) considers social support as attachments by which abilities are developed, guidelines are provided, and confirmatory feedback on behaviors are performed. The results of studies (Tian et al. 2013; Ratelle et al. 2013 revealed that taking advantage of an appropriate social support, understanding of adequacy, availability, and satisfaction with its perception are highly important and they provide capacity needed for adolescent for psychological well-being in adulthood. Tian et al. (2013) and Ratelle et al. (2013) suggested that social support is closely related to juvenile well-being. Moradi et al. (2014) and Hosseinzadeh et al. (2012) conducted a study in Iran, which showed that there is a positive significant relationship between social support and psychological well-being.

On the other hand, the impact of external and internal factors on psychological well-being also have been studied. On this basis, motivation as a reinforcement, leading, and supportive factor of behavior takes on great importance (Pintrich and Schunk 2002). Many studies have shown that independent orientation or intrinsic motivation is positively correlated with psychological health indicators, whereas controlled orientation or extrinsic motivation is negatively correlated with indicators of mental health. For example, findings of Deci (2004). Ryan and Deci (2000, 2001, 2006, 2008). Black and Deci (2000). Burton et al. (2006). and Van Petegem et al. (2008) showed that intrinsic motivation is associated with positive mood, vitality, personal growth, positive coping strategies, and self-development. In another study, Miquelon and Vallerand (2008) introduced a model where the relationship of goal motivators, well-being, and physical health are discussed. The results showed that intrinsic motivation predicted well-being, however, extrinsic motivation negatively predicted well-being.

A review of previous studies suggests that interest in psychological well-being and its contributing components has increased in recent years, but a study on the contribution of social support (as a contextual variable) and academic motivation (as a personal variable) in psychological well-being of students is lacking.

This research intended to examine the relationship between perceived social support and psychological well-being among students as well as investigating the mediating role of academic motivation.

Methodology

Population and Sample

The population of the present research consisted of all female high school students from second and third grade students in public schools of Tehran city in Iran during the school period between 2013 and 2014. The statistics for the population were obtained from an educational planning center in Tehran, which reported 49 919 students.

According to Cochran’s sample size formula, a sample size equal to 371 was selected based on a random multistage cluster sampling technique. Given the fact that the design of the present research is non-experimental (descriptive) and sample individuals were randomly selected from a normal student group, no exclusion criteria were used. However, regarding control variables, the inclusion criteria’s were grade, field of study, and gender.

Data Collection Tools

In order to gather data we used the following tools:

  1. (a).

    Psychological well-being questionnaire (Ryff 1989). in this study, a short 18-item form was used, which consisted of 6 components; self-acceptance, positive relations with others, autonomy, personal growth, purpose in life, and environmental mastery.

  2. (b).

    Social Support Appraisals scale (Vaux et al. 1986: the questionnaire contains 23 items and three important scopes, family, friends, and significant others.

  3. (c).

    Questionnaire of Academic motivation (Harter 1981). Harter’s questionnaire is widely used to measure individual differences in educational contexts with respect to aspects of motivation (intrinsic and extrinsic).

Data Analysis

Descriptive statistics and inferential statistics (Pearson correlation coefficients and path analysis to check the mediating variable) were employed to analyze data in this study. Data analysis was done by calculating correlation coefficients and path analysis.

Results and Discussion

Prior to main analysis, descriptive statistics for research variables are reported in Table 1.

Table 1 Descriptive statistics for research variables
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A correlation analysis was used to examine the relationship between perceived social support and psychological well-being (Table 2).

Table 2 Correlation coefficients for the components of perceived social support and psychological well-being (P < 0.01)
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As shown in Table 2, components of social support (family, friend, and significant other) are positively and significantly correlated with the whole components of psychological well-being (self-acceptance, positive relations with others, autonomy, environmental mastery, purpose in life, and personal growth).

In order to explore the mediating role of academic motivation in the relationship between perceived social support and psychological well-being, the proposed model was depicted in such a way that perceived social support was considered as exogenous variable, academic motivation as mediating variable, and psychological well-being as endogenous variable. In Fig. 1, structural equation model diagram and standardized coefficients of paths are presented.

Fig. 1
figure 1

Structural equation model diagram

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As demonstrated in Table 3, chi-square (x2), chi-square relative to its degree of freedom (X2/df), the comparative fit index (CFI), goodness of fit index (GFI), adjusted goodness of fit index (AGFI), and Root Mean Square Error of Approximation (RMSEA) provided a good fit. According to standardized path coefficients, perceived social support directly has a positive significant effect on psychological well-being (regression slope coefficient = 0.53, P < 0.01), and academic motivation (regression slope coefficient = 0.35, P < 0.01). The direct effect of academic motivation on psychological well-being (regression slope coefficient = 0.24, P < 0.01) is statistically considerable. Perceived social support could indirectly influence psychological well-being (regression slope coefficient = 0.08, P < 0.01) with the help of the mediating role of academic motivation.

Table 3 Indexes of structural equation model for psychological well-being
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Discussion

As demonstrated in this study, the direct effect of social support on psychological well-being is positive and significant. In line with this, other studies (Siedlecki et al. 2013; Ratelle et al. 2013; Yalçın 2011; Zimmer and Chen 2012; Moradi et al. 2014) also indicated that benefitting from a desirable social support can lead the individual into physical and psychological well-being (Siedlecki et al. 2013; Ratelle et al. 2013; Yalçın 2011; Zimmer and Chen 2012; Moradi et al. 2014). Through explaining results, it can be suggested that social support seemingly includes ‘love,’ ‘care,’ and ‘esteem,’ all of which can be obtained from family, friends, and other groups (Cobb 1976). which would affect the psychological well-being of individuals (Yang and Farn, 2005. Thus, the more often students perceive social support, the more frequently psychological well-being will influence them. This is also consistent with findings of Deci and Ryan (2000).

Perceived social support indirectly has an effect on psychological well-being with the help of academic motivation. Perceived social support could explain 13 % of academic motivation, and both predicted 37 % of psychological well-being variations. In explaining the mediating role of academic motivation, we can point to Deci and Ryan (2000)which suggested that desirable performance and well-being, in addition to contextual-social conditions, are influenced by self-motivation (Hamdan-Mansour and Dawani 2008). Similarly, if an individual’s relationship with family, friends, and/or significant others are based solely on supporting their independent behaviors, satisfaction of basic psychological needs is facilitated, which leads to the establishment of intrinsic motivation and eventually, psychological adjustment.

Deci and Ryan (2000) believe that intrinsic motivation is a determining factor in well-being. Researchers maintain that intrinsic motivation is facilitated when environmental conditions are supportive enough to satisfy psychological needs (Hamdan-Mansour and Dawani 2008). Similarly, motivation is reduced when environmental conditions hinder the satisfaction of personal needs. The result of the current study shows consistency between our data and the self-determination theory.