Distributions overview
1. Normal distribution and T-Distribution
Look like each other, but the normal distribution is the distribution of a population
(used for one-sample Z test, and proportion test).
The T-distribution is more accurate for samples, with an exact form depending on the
number of degrees of freedom (usually, 1 or 2 degrees of freedom).
2. 𝛘2-distribution and F-distribution
Both are asymmetrical right-skewed distributions with only positive values (W and F).
The exact shape of 𝛘2-distribution depends on 1 degree of freedom: v. Here, you look
up W-values based on 𝛂 and v.
The exact shape of F-distribution depends on 2 degrees of freedom: v1 and v2. Here,
you look up F-values based on 𝛂, v1 and v2.
Multiple Linear Regression Model
= There is one dependent variable (Y), and multiple independent variables (X1, X2, etc.).
- Basic assumption multiple regression:
Y = 𝛃0 + 𝛃1X1 + 𝛃2X2 + … + 𝛃kXk + 𝛆
With E(𝛆) = 0
It could also be written as E(Y) = 𝛃0 + … + 𝛃kXk
Reminder: you always have to write one E in the formula; either at the end (+𝛆) or at
the beginning (E(Y)).
→ Here, the interpretation of the slope b1 = the average change in the statistics
when a student studies 1 hour more, ceteris paribus (=everything else remaining the
same, meaning in this case: one IV changes with +1, and the other IVs are constant).
Quantitative variables: can take all kinds of values
Qualitative variables: can only indicate if an option is valid (e.g. gender = ‘man’). → In
regression:
- Dummy variables: can only take value 0 or 1.
Always displayed in regression model: ‘the number of options – 1’.
→ you add the dummy variables in the basic assumption multiple regression, after
the IVs as: … + 𝛃5D1 + 𝛃6D2
→ The ‘slope’ is then the difference between the dummy in the model and the
omitted dummy:
Slope of D1 = average of D1 – average of omitted dummy
Slope of D2 = average of D2 – average of omitted dummy
1
, → The omitted options ‘disappear’ into the intercept b0. The slope b1 of the
remaining options are now the mean difference from the omitted option.
→ Interpretation of dummy slope: If someone has “dummy variable”, it means that
it will have/score “slope” higher/lower than the omitted dummy, ceteris paribus.
Second-order 𝛃k
A regression model measures linear coherence. Still, it is possible to include a second-order
(squared) relationship in the model.
→ In the basic assumption: you note the normal, linear slope 𝛃4 of the independent
variable X4, and at the end, you also note the slope 𝛃8 of the squared independent
variable X42.
- So: there are 2 slope coefficients of the same variable: the normal and the non-linear
(second-order, squared).
Interaction 𝛃x
Additionally, it is also possible to create an interaction slope. This means that the magnitude
of the effect of Xk on Y, depends on another X.
- Xk * the other X = ‘the interaction between Xk in … and X’
→ In the basic assumption: you note the normal slopes of both independent
variables 𝛃1X1 + … + 𝛃4X4, and at the end, you also note the slope of the interaction
effect 𝛃9X1_ X4.
- You can make an interaction with quantitative and qualitative (dummy) variables.
Then:
When value of dummy = 0 → interaction effect is ‘not active’.
When value of dummy = 1 → interaction effect is ‘active’.
SPSS output multiple regression
(Don’t look at the numbers in this example, they don’t make any sense):
→ Std. Error of the Estimate = S𝛆
2
, → look at df (=degrees of
freedom):
Regression df = k
Residual df = n-(k+1)
Total df = n-1
→ left dark-grey column
Shows the independent variables k=5
1.constant shows 𝛃0.
a.Mentions dependent variable below.
- Know how to calculate everything related SPSS. Here already the calculation of MSE:
MSE = SSE / dfe or MSE = S𝛆2 or MSE = MSR / F
r2 = SSR/SST or 1 – SSE/SST
Example question to find r2:
Solve: F = (r2/dfr) / (1 - r2 /dfe)
Or: solve regression test complete model
3
Voordelen van het kopen van samenvattingen bij Stuvia op een rij:
Verzekerd van kwaliteit door reviews
Stuvia-klanten hebben meer dan 700.000 samenvattingen beoordeeld. Zo weet je zeker dat je de beste documenten koopt!
Snel en makkelijk kopen
Je betaalt supersnel en eenmalig met iDeal, creditcard of Stuvia-tegoed voor de samenvatting. Zonder lidmaatschap.
Focus op de essentie
Samenvattingen worden geschreven voor en door anderen. Daarom zijn de samenvattingen altijd betrouwbaar en actueel. Zo kom je snel tot de kern!
Veelgestelde vragen
Wat krijg ik als ik dit document koop?
Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.
Tevredenheidsgarantie: hoe werkt dat?
Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.
Van wie koop ik deze samenvatting?
Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper kellymonka. Stuvia faciliteert de betaling aan de verkoper.
Zit ik meteen vast aan een abonnement?
Nee, je koopt alleen deze samenvatting voor €7,16. Je zit daarna nergens aan vast.