Olafson et al$.(2015)$ tested the hypothesis, based on self$-$determination theory, that managerial need support would predict work motivation even when pay, recognition, and other variables were controlled for. They measured managerial need support using the work climate questionnaire. They measured work motivation using the multidimensional work motivation scale $($MWMS$).$ These measures had been validated in previous studies. Their results are shown below:

Predictor

$\backslash$beta

p

Perceived fairness

$\mathrm{.}23$

$\mathrm{.}01$

Managerial need support

$\mathrm{.}46$

$<\mathrm{.}001$

Pay

$\mathrm{.}06$

$\mathrm{.}32$

Recognition

$\mathrm{.}04$

$\mathrm{.}36$

Sex

$-\mathrm{.}01$

$\mathrm{.}59$

Years of work experience

$\mathrm{.}03$

$\mathrm{.}41$

Can the researchers conclude that managerial need support caused an increase in work motivation? Specifically identify each of the three criteria for causation and explain whether or not the researchers fully established, partially established, or failed to establish each criterion and why.