Exam Guide for Applied Multivariate Data Analysis – Get yourself a Wonderful Grade!
Summary of Statistics (IBC), Radboud University
Answers assignment 3 business research methods
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Psychologie
ARMS 2020-2021
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Hoorcolleges ARMS 2021
Hoorcollege 1: Multiple regression 10 februari 2021
Het geboorte volgorde effect = mensen die als eerste geboren zijn hebben een hoger IQ – dit
werd aangetoond door de wetenschap, maar is dit wel zo? Het is belangrijk om hier kritisch
naar te kijken.; is er wel een echt effect?
- Hoe is dit eigenlijk onderzocht? – is het een representatieve sample? Werd het op
een betrouwbare manier gemeten? Zijn de resultaten op de juiste manier
geanalyseerd en geïnterpreteerd? = statistische validiteit
Als er een associatie is dan betekent dat
niet dat er sprake is van een oorzaak-
gevolg.
- Het kan zijn dat er een 3e variabele
is. En dit kan je gaan
onderzoeken door een multipele
regressie. Je hebt dan 1 uitkomst
variabele, maar meerdere
voorspellende/ onafhankelijke
variabelen.
Er zijn een aantal dingen belangrijk als het gaat om multipele regressie:
- In hoeverre kan het model van de multipele regressie de variatie (R2) in de data
verklaren. – kan de voorspellende variabele verklaren waarom de ene wel een hoog
IQ heeft en de andere niet.
o Als er veel spreiding is van de punten van je data, dan is je voorspellende
variabele minder goed in staat om de spreiding te verklaren.
o When the R2 is large, the variation is good explained by the predictable
variable.
- The slope of the regression line (B1) – when the B1 is large, the slope is steep, and
when the B1 is 0 the slope is horizontal.
How well does my model fit my data (R2)? AND how important is my predictor on my
outcome variable (B1). – key things for the (multiple) regression model (MLR).
- Observed outcome is the prediction based on the
model and some error in the prediction. – Y-dakje is
the predictor.
- So, the second equation is the shorter version of the
one above; the Y^ is the prediction based on the model.
By the observed part, there is always some residual (error). – when you do the model
prediction Y^, there is no error involved.
,Additive linear model = you add multiple variables to the equation, and you expect that the
multiple variables will be additive on to the outcome variable.
Different types of variables:
- Nominal
- Ordinal
- Interval
- Ratio
When making a decision on which analysis you will use you distinguish between:
Nominal + Ordinal – categorical / qualitative is it about groups?
Interval + Ratio – continuous or quantitative / numerical is it numerical?
In the MLR you will always need continuous outcome and continuous predictors.; it
needs to have a numerical meaning.
- You can include a categorical predictor, but only as a dummy variable.
o If you want to know if gender is a predictor of grade you should make a
dummy variable: it has only two values: 0 & 1.
This works because it has a very clear interpretation. if
you look at B1 now, you will have a clear interpretation
between male and female and the impact on grade.
But what if you have a categorical predictor with
more than 2 categories. – you create multiple dummy
variables. If you have 4 categories; you will need 3
dummy variables. – you score 0 on the other 3 dummies’,
than you must have the colour yellow.
See the grasple lessons!!
The example is about life satisfaction:
o Question 1: Can life Satisfaction (y) be predicted from age (b1) & years of
education (B2)
o Question 2: Are social network factors as measured as child support (b3) and
spouse support (b4) improving the prediction of life satisfaction if the effects of
age and years of education are already accounted for?
Hierarchical MLR = The hierarchical MLR is about:
given that the first two variables are accounted for
(already included), what do these new variables in the
second research questions do. Does this improve
the model?!
So, you have two models! the one with the first
research question and two variables and the
second model with the two variables from the first
question AND the two from the second question.
, R2 = the proportion
of the variation
explained by the
model.; you
compute for you
sample
R = multiple
correlation
coefficient = the
correlation between
the Y (observed)
and Y^ (predicted).
Adjusted R Square = you
compute for the estimated
population. because
the R2 tells only something
about the sample.
- Now it is adjusted for the biases.; R2 is a little to optimistic.
R2 – change: only relevant for the second model, because for the first model there is
nothing to compare it to. it also gives a significance value for the change. (so, the second
hypotheses are correct).
The first table tells you something about ADDING the values tot he first two values and
whether that is significant or not.
The ANOVA table tells you something about the model with just 4 values (so without the
adding thing).
Normally you just pick one of the two
models which one fits the best.
B = is the slope for e.g., age in the model;
you can’t compare them because age and
years of education are different measured.
In a bivariate correlation it tells you how
X is related to Y. In a MLR it tells you
something about the UNIQUE
contribution within a model where there
are other variables as well.; tells nothing
about the relation between Y & X.
- So, for example: you have two persons in your data set with the same age; so, age is
fixed. Then what is the effect on life satisfaction when one person has one more year
of education. you can calculate with model 1. So, 3.035 is the effect of education.
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