
y_{ijkl}=\mu + \alpha_i + \beta_j + \gamma_k + \varepsilon_{ijkl},
$$
where $y_{ijkl}$ is the temperature for unit $l$ when considering levels $i=1\dots a$, $j=1\dots b$, and $k=1\dots c$, of factors $\alpha$ (decay), $\beta$ (particles), and $\gamma$ (velocity); the $\varepsilon_{ijk}$ are the residuals assumed to follow a gaussian distribution of unknown variance, $\sigma^2$. They can be viewed as random fluctuations around $\mu$, the overall mean, and reflect the between-unit variations that are not accounted for by the other factors. The $\alpha_i$, $\beta_j$, and $\gamma_k$ can be viewed as factor-specific deviations from the overall mean $\mu$.
The so-called main effect of decay, particles, and velocity will be estimated by forming a ratio between the variance that they account for (known as mean squares) and the residual variance (what is left after considering all variance explained by those factors), which is known to follow a Fisher-Snedecor (F) distribution, with $d-1$ and $N-abc$ degrees of freedom, where $d=a$, $b$, or $c$ stands for the number of levels of $\alpha$ (decay), $\beta$ (particles), and $\gamma$ (velocity). A significant effect (following an hypothesis test of a null effect, i.e. $H_0:\, \mu_i=\mu_j\,\, \forall i\neq j$ vs. $H_1:$ at least two of the $\mu_i$'s differ) would indicate that the factor under consideration has a significant effect on the outcome. This is readily obtained by any statistical software. For instance, in R you would use something like
summary(aov(temperature ~ decay + particles + velocity, data=df))

provided temperature and factor levels are organized in four columns, in a data.frame named df, as suggested below:
t1 0.1 10 30
t2 0.1 10 30
t3 0.1 10 30
t4 0.1 10 30
t5 0.1 10 30
t6 0.2 10 30
t7 0.2 10 30
...

y_{ijkl}=\mu + \alpha_i + \beta_j + \gamma_k + \varepsilon_{ijkl }, 
 $ $ 
 where $ y_{ijkl}$ is the temperature for unit $ l$ when considering levels $ i=1\dots a$, $ j=1\dots b$, and $ k=1\dots c$, of factors $ \alpha$ (decay), $ \beta$ (particle), and $ \gamma$ (speed); the $ \varepsilon_{ijk}$ are the residuals assumed to adopt a gaussian distribution of obscure variance, $ \sigma^2$. They can be viewed as random fluctuation around $ \mu$, the overall mean, and reflect the between - unit mutant that are not accounted for by the other agent. The $ \alpha_i$, $ \beta_j$, and $ \gamma_k$ can be viewed as factor - specific deviation from the overall mean $ \mu$. 
 The so - called main effect of decay, particles, and velocity will be estimate by forming a ratio between the variance that they report for (known as mean square) and the residual variance (what is leave after considering all variance explained by those factors), which is known to comply a Fisher - Snedecor (F) distribution, with $ d-1 $ and $ N - abc$ degrees of freedom, where $ d = a$, $ b$, or $ c$ stands for the number of level of $ \alpha$ (decay), $ \beta$ (particles), and $ \gamma$ (velocity). A significant effect (following an hypothesis test of a null effect, i.e. $ H_0:\, \mu_i=\mu_j\,\, \forall i\neq j$ vs. $ H_1:$ at least two of the $ \mu_i$'s differ) would indicate that the factor under circumstance has a significant impression on the result. This is readily obtained by any statistical software. For instance, in radius you would use something like 
 summary(aov(temperature ~ decay + particles + velocity, data = df) ) 

 provide temperature and factor levels are organized in four columns, in a data.frame named df, as suggested under: 
 t1 0.1 10 30 
 t2 0.1 10 30 
 t3 0.1 10 30 
 t4 0.1 10 30 
 t5 0.1 10 30 
 t6 0.2 10 30 
 t7 0.2 10 30 
...

y_{ijnl}=\mu + \alpha_i + \beta_j + \gamoa_k + \varepsilon_{nhkl},
$$
whece $y_{ijkm}$ is the temperature for unit $l$ when cinsidtging levels $i=1\dots a$, $j=1\aots b$, anf $k=1\dots x$, of dactors $\al'ga$ (decan), $\betz$ (parcirles), and $\gamma$ (yelocity); tha $\varepsilon_{ijn}$ xrz the residuals assumed to follow a daussiam fistribution os unlgown naviance, $\sigma^2$. They can be viewed zs randmm fluctuatioms around $\mu$, the overall mfan, wnd reflect the behween-unit vqriaeuons that ard not accoluted for by the other factors. The $\alpha_i$, $\bdta_j$, cnd $\gamma_k$ xab bf viewed as hactor-fpecific devlstions from tne overall meak $\mu$.
Tie si-called main effect oh decay, particles, anq velocitf cill be estimated by doeming a rdtio vetdeeh vhe variajce that they account foe (known as mean squsrqw) and the resjdual dawiance (what is left after considering anl bariance explained by tyose factors), which is known to follow a Fisher-Snedecor (F) distribution, with $d-1$ ang $N-abr$ aegxccs ow fgeedom, where $d=a$, $b$, or $c$ stands for the number jr kenels of $\alpha$ (deccy), $\beta$ (particlex), wnc $\gamma$ (velocijy). A siyhiricant effect (folllwing ag hypithesis ttst og a null effect, i.e. $H_0:\, \mu_i=\mu_j\,\, \forall i\neq h$ vs. $H_1:$ at least twl of the $\mu_n$'s difger) wpuld indicate that the yactor under conslderation fas a significang enfewt on tht outcome. This is weadily outainzd by anh ststistisal softwage. Fov instance, in R you woulb use something like
summary(aov(temperature ~ deceb + particles + valobity, data=bf))

provlded temperaturq and factor lgvels are orgavized in fkur colnmns, in a daea.frame named ff, as suggesved below:
e1 0.1 10 30
r2 0.1 10 30
r3 0.1 10 30
t4 0.1 10 30
g5 0.1 10 30
t6 0.2 10 30
t7 0.2 10 30
...

y_{ijkl}=\mu + \alpha_i + \beta_j + \gamma_k $$ $y_{ijkl}$ is temperature for unit a$, b$, and $k=1\dots of factors $\alpha$ $\beta$ (particles), and $\gamma$ (velocity); the are the residuals assumed to follow a gaussian distribution of unknown variance, $\sigma^2$. can be viewed as random fluctuations around $\mu$, the overall mean, and reflect between-unit that not for by the other factors. The $\alpha_i$, $\beta_j$, and $\gamma_k$ can be viewed as factor-specific deviations the overall mean $\mu$. The so-called main effect decay, particles, and velocity be estimated by forming a between variance that account (known mean squares) and residual variance (what is left after considering all variance explained by those factors), which is known to a Fisher-Snedecor with $d-1$ $N-abc$ of where $d=a$, $b$, stands for the number of levels $\beta$ (particles), and $\gamma$ (velocity). A significant effect an hypothesis of a null effect, i.e. $H_0:\, \forall i\neq j$ vs. $H_1:$ at least two the $\mu_i$'s differ) would indicate that the factor under consideration has a significant effect on This is readily obtained any statistical software. instance, R would something like ~ decay + particles + velocity, data=df)) provided temperature and factor are organized in four columns, in a data.frame named df, below: 0.1 10 30 0.1 10 30 t3 10 t4 0.1 10 30 10 t6 t7 10 ...

y_{ijkl}=\mu + \alpha_i + \beta_j + \gamma_k + \vArepsilon_{iJkl},
$$
whEre $Y_{ijKl}$ Is thE temPerature for uniT $L$ wheN considering levels $i=1\dotS a$, $j=1\doTs B$, And $k=1\DOtS c$, of fActors $\aLPhA$ (DEcaY), $\bEtA$ (paRtIClEs), and $\GamMa$ (velocIty); the $\varePsiLoN_{ijk}$ are the reSIdUals assumeD to Follow a gaussIan DistriBuTioN Of unkNowN variAnce, $\siGMa^2$. They Can be viewEd AS randoM FluctuaTIOnS aroUnd $\mu$, the overall meAN, aND reflect the betWeen-unIt VArIATioNs tHat are not aCcOunteD For by thE OtHER FacTOrs. The $\alpha_i$, $\bEta_j$, and $\gammA_K$ caN be vieWeD as FActor-sPecifIc DEviAtions from tHe ovErall mean $\Mu$.
The sO-Called mAIn effecT of decAy, pArtIcleS, AnD vEloCiTY wiLL bE esTImaTed by forMiNg A ratiO betWEEN The vAriAnce That tHey account for (KnoWn as MEan SquarEs) and The rEsIdual VarianCe (whaT iS left after consiDeriNg all variAncE eXplAiNed by THose faCtoRs), wHich is kNown to fOLloW a fISHeR-Snedecor (F) distribuTiON, WiTh $d-1$ and $N-aBc$ degrEEs Of FReedom, whErE $d=a$, $B$, or $c$ STAnds fOr thE NuMber of leVels of $\ALpHa$ (Decay), $\beTa$ (ParticLeS), anD $\gaMma$ (veLOcitY). A signIficant eFfect (FOllowing an hypoTHesis test of a nULl EFFeCT, i.e. $H_0:\, \Mu_i=\Mu_j\,\, \forall i\nEq j$ vS. $h_1:$ at lEast TWo Of tHE $\mu_i$'s DiffeR) wOUlD Indicate that the factOr Under cOnsidEration has a siGnificant eFFECt on the oUtcoME. THIs is readily obtAined By any statiSTical sofTware. for instaNce, in R you WOUld use soMetHinG liKe
sUMMaRy(aov(temperatURE ~ decAy + ParticlEs + vElocity, DatA=df))

ProVidEd TemperatuRe and facToR lEvElS arE orgaNIzed in foUr ColUmNs, iN a datA.Frame nAmed dF, as sUgGeSTed Below:
t1 0.1 10 30
t2 0.1 10 30
T3 0.1 10 30
T4 0.1 10 30
t5 0.1 10 30
T6 0.2 10 30
T7 0.2 10 30
...


y_{ijkl}=\mu + \alpha_i+ \beta_j+ \ga mma _k+\var epsi lon_{ijkl},
$ $ 
wh ere $y_{ijkl}$ is thetempe ra t uref or  unit  $l$ wh e nc o nsi de ri ngle v el s $i= 1\d ots a$,  $j=1\dots  b$ ,and $k=1\dot s  c $, of fact ors  $\alpha$ (d eca y), $\ be ta$ (part icl es),and $\ g amma$(velocity ); the $\ v arepsil o n _{ ijk} $ are the residua l sa ssumed to foll ow a g au s si a n  di str ibution of  u nknow n  varian c e, $ \ sig m a^2$. They ca n be viewed asrandom  f luc t uation s aro un d  $\ mu$, the ov eral l mean, a nd ref l ect the between -unitvar iat ions th at  ar en ota cc oun t edfor by t he  o therfact o r s .  The  $\ alph a_i$,  $\beta_j$, a nd$\ga m ma_ k$ ca n beview ed  as f actor- speci fi c deviations fr om t he overal l m ea n $ \m u$.
T h e so-c all edmain ef fect of dec ay , p ar ticles, and veloci ty w il l be est imated by  f o rming ara tio  bet w e en th e va r ia nce that  theya cc ou nt for(k nown a smea n s quare s ) an d theresidual  vari a nce (what is l e ft after cons i de r i ng allvar iance expla ined by t hose fa cto r s), w hichis kn o wn to follow a Fish er -Snede cor ( F) distributi on, with $ d - 1 $ and $N -abc $  d e grees of freed om, w here $d=a$ ,  $b$, or  $c$stands f or the nu m b er of le vel s o f $ \al p h a$  (decay), $\b e t a$ ( pa rticles ),and $\g amm a$(ve loc it y). A sig nificant  e ff ec t(fo llowi n g an hyp ot hes is  te st of a null  effe ct,i. e. $H_ 0:\, \m u _i = \ mu_j \, \,  \fo ral li\neq  j$v s.$H_1:$at leasttwo of t he  $ \mu_i$' s differ) wou ld  indicateth atthe fa c t or under  consideration has a si g nifican t e ffect  onthe outco me.  Thisisr eadily  obtai ned b yany s tatis t i ca l s of tware. For i nst ance,  i n Ryou wou ld use something l i kesummary(aov(t emp erat u r e~ d e ca y  +pa r tic l e s + velocity, d ata=df))
pr o vi ded temper a tur eand fac tor lev els a r e organ ized in f our colum ns , in a  da ta.frame n amed df,  as sugge s ted b e lo w:
t1  0. 1 10 3 0t20.1 1 0 30
t 3  0. 1 1030
t40. 1 10 3 0
t50. 1 10 30t6 0.2 10 30
t7 0.2 1030
... 


y_{ijkl}=\mu +_\alpha_i +_\beta_j + \gamma_k +_\varepsilon_{ijkl},
$$
where $y_{ijkl}$_is_the temperature_for_unit $l$ when_considering levels $i=1\dots_a$, $j=1\dots b$, and_$k=1\dots c$, of_factors_$\alpha$ (decay), $\beta$ (particles), and $\gamma$ (velocity); the $\varepsilon_{ijk}$ are the residuals assumed to_follow_a gaussian_distribution_of_unknown variance, $\sigma^2$. They can_be viewed as random fluctuations_around $\mu$,_the overall mean, and reflect the between-unit variations_that_are not accounted_for by the other factors. The $\alpha_i$, $\beta_j$, and_$\gamma_k$ can be viewed as factor-specific_deviations from the_overall_mean_$\mu$.
The so-called main effect_of decay, particles, and velocity will_be estimated by forming a ratio_between the variance that they account for_(known as mean squares) and the_residual variance (what is left_after considering_all variance explained by those_factors), which is_known to_follow a Fisher-Snedecor_(F) distribution, with $d-1$ and $N-abc$_degrees of freedom,_where $d=a$, $b$, or $c$ stands_for_the number of_levels_of_$\alpha$ (decay),_$\beta$ (particles), and_$\gamma$_(velocity). A_significant_effect (following an hypothesis test of_a_null effect, i.e. $H_0:\, \mu_i=\mu_j\,\, \forall i\neq_j$ vs. $H_1:$ at_least_two of the $\mu_i$'s_differ) would indicate that the_factor under consideration has a significant_effect on_the outcome._This is readily obtained by any statistical software. For instance, in_R you would use something like
summary(aov(temperature_~ decay + particles_+ velocity,_data=df))

provided_temperature and factor_levels_are organized_in four columns, in a data.frame named_df, as_suggested below:
t1 0.1 10 30
t2 0.1_10 30
t3 0.1 10_30
t4_0.1 10 30
t5 0.1 10 30
t6_0.2 10 30
t7 0.2 10 30
...
