Model Fit Comparison

.

Figure S3b.1. Fit of the linear model to the data.

.

Figure S3b.2. Fit of the quadratic model to the data.

.

Quadratic Model

\(y =a+ bx + cx^{2}\), where y is Life Satisfaction and x is Social Time.

Table S3a.1. Linear and quadratic effects of social time.
    Life Satisfaction
    B CI p
(Intercept)   -0.00 -0.15 – 0.15 1.00
Linear   0.24 0.09 – 0.38 .002
Quadratic   -0.08 -0.23 – 0.07 .281
Observations  173
R2 / adj. R2  .063 / .052

.

Figure S3a.3. Linear, quadratic, and piecemeal relationship (all observations).

.

Diagnostics

.

Assumptions

.

Table S3a.2. Omnibus diagnostic statistics for the quadratic model.
Value p-value Decision
Global Stat 1.873 0.76 Assumptions acceptable.
Skewness 1.838 0.17 Assumptions acceptable.
Kurtosis 0.021 0.88 Assumptions acceptable.
Link Function 0.000 1.00 Assumptions acceptable.
Heteroscedasticity 0.014 0.91 Assumptions acceptable.

Notes. Tests are directional test statistic
.

Figure S3a.4. Omnibus diagnostic statistics for the quadratic model.

.

Influential Cases.

.

Figure S3a.5. Most influential cases by leverage (x-axis), std. residual (y-axis), and Cook’s distance (circle size).

.

Table S3a.3. Most influential cases by leverage, studentized residual, and Cook’s distance.
StudRes Hat CookD
22 -3.1 0.01 0.03
74 1.1 0.17 0.09
131 -2.6 0.07 0.17

.

Replottig: Influential Cases Removed

Figure S3a.6. Linear, quadratic, and piecemeal relationship with the most influential cases removed.

.

Figure S3a.7. Is the re-specificied model still a good fit to the data?

.

.

.

Moderation Model

\(y =x + x^{2} + m +mx + mx^{2}\), where y is Life Satisfaction, x is Relatedness, and m is Social Time.

Table S3a.4. Linear and quadratic effects of social time.
    Life Satisfaction
    B CI p
(Intercept)   -0.03 -0.18 – 0.12 .713
Moderation   -0.14 -0.28 – 0.00 .057
Observations  173
R2 / adj. R2  .215 / .192

Plotting: All Observations

Figure S3b.8. Moderation plot.

.

Figure S3b.9. Moderation perspective plot.

.

Figure S3b.10. Moderation interactive plot.

.

Diagnostics

.

Assumptions

.

Table S3b.5. Omnibus diagnostic statistics for the moderation model.
Value p-value Decision
Global Stat 3.45 0.49 Assumptions acceptable.
Skewness 0.41 0.52 Assumptions acceptable.
Kurtosis 0.24 0.62 Assumptions acceptable.
Link Function 2.31 0.13 Assumptions acceptable.
Heteroscedasticity 0.48 0.49 Assumptions acceptable.

.

Figure S3b.11. Omnibus diagnostic statistics for the moderation model.