Samenvatting
MVDA Full Summary
- Instelling
- Universiteit Leiden (UL)
MVDA summary from weeks 1-7, guaranteed pass
[Meer zien]Voorbeeld 4 van de 52 pagina's
Voorbeeld 4 van de 52 pagina's
In winkelwagengesponsord bericht van onze partner
1 beoordeling
Door: lilly-nije-2003 • 6 maanden geleden
Voorbeeld van de inhoud
MVDA. Athena SummaryWeek 1: Multiple Regression Analysis (MRA)
- Two sets of variables, Y and X, where there is only one Y variable and multiple X
variables (simple regression = only 1 X variable)
- All variables are interval
- When 2 or more predictors are highly correlated
Simple Regression Analysis
Y = b0 + b1X + e
- b0 = intercept
- b1 = regression weight
- X = score of a person (independent variable)
- Y = dependent variable
- e = error
Parameters need to be estimated from data, we choose b0 and b1 in a way that sum of
squares error is as small as possible (least squares estimation)
Standard Regression Formula:
- ez = error term but in standard deviation units
Regression towards the mean: Predicted value of Y is always closer to the mean than the
value of X
Multiple Regression Analysis
Goal: predict one Y variable (dependent) with multiple X variables (independent)
predict score of Y variable based on X variables
---> Asymmetric question: we go from X to Y, not other way around
---> we assume a kind of causality (X causes Y), but can’t test this with regression (remains
a correlational test)
---> WE CANNOT TEST WHETHER X IS THE CAUSE
Multiple Regression Equation:
, - Y = dependent variable predicted by X variables
- Ŷ = predicted Y
- b0 = constant / intercept. Outcome of Y when all X variables are 0
- bk = regression weights per variable (coefficient)
- e = error term
Multiple Correlation
Used to define pearson correlation between the predicted and observed values of Y:
R = ryŷ
Multiple regression gives optimal prediction of Y, which can sometimes be our ultimate goal.
Explained variance: We can use regression to see how well our X variable actually predicts
Y variable and how well each individual X variable does so.
Multiple correlation, R, indicates the correlation between the predicted values of Y and the
actual values of Y.
R is always between 0 and 1.
If we square this correlation, we have proportion of shared variance between Ŷ and Y =
proportion of explained variance (VAF).
---> VAF = how much variance is accounted for
The higher the R², the better our prediction is as a whole.
R² is the value of the sample, but we can also calculate adjusted R², which we then apply to
the population.
- N = number of people (sample size)
- k = number of predictors
SPSS: R2 and Adjusted R2 in Model Summary
,R² change = shows if change in R² (explained variance) from first model to second model is
significant
Regression Weights
Regression weights indicate how much the predicted value of Y changes when the X
variable increases with 1 unit. Our predicted value is never entirely correct, so there is
always error.
Residual = Difference between predicted value of Y and the actual value of Y
Regression line is chosen in such a way that these residuals are as small as possible so that
we can make the most accurate prediction of the population based on the sample
= AS SMALL AS POSSIBLE
Least squares method = Making differences as small as possible. Draw regression line in
such a way that if you add up all individual differences (vertical lines) you get smallest
number as possible
Standardised regression weights = indicated by β (Beta in SPSS).
Value of the weight indicates how many standard deviations Y changes when X increases by
1 standard deviation. The constant disappears when standardising.
Advantage of β’s instead of normal b’s: we can compare them directly with each other. A
higher value compared to another predictor also means more influence than that predictor.
Unstandardised b’s can’t be compared to each other because they depend on the unit with
which X is measured
Disadvantage of β’s instead of b’s: they depend on the standard deviation of our sample.
If we would then use the same formula for a different sample, it could be problematic if this
sample has a different standard deviation.
Regression equation = fill in names for variables at Y and X, look at unstandardised
coefficients B column and use the number at the constant for b0, write down values under
Unstandardised coefficients B for each bw. Also possible to write down the standardised
regression equation by using values in standardized coefficients beta column.
, - Zero-order = pearson r correlation between predictor and dependent variable or
regression coefficient between dependent variable
(Squared) Semi-Partial correlation
Semi-partial correlation = how much does a predictor uniquely add to dependent variable
(squared)
Evaluate individual predictors
Correlation between X and Y with the overlapping correlation removed.
If we square those values, we get the uniquely explained variance of the predictor = how
much variance is explained uniquely by that predictor and not by any other predictor.
---> the higher the value, the more influential the predictor is when predicting Y
---> value between 1 and -1
SPSS: part correlation
Using Venn diagram, formula for uniquely explained variance of X1 (squared semipartial
correlation):
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 gaiaantico. Stuvia faciliteert de betaling aan de verkoper.
Zit ik meteen vast aan een abonnement?
Nee, je koopt alleen deze samenvatting voor €4,99. Je zit daarna nergens aan vast.
Is Stuvia te vertrouwen?
4,6 sterren op Google & Trustpilot (+1000 reviews)
Afgelopen 30 dagen zijn er 52510 samenvattingen verkocht
Opgericht in 2010, al 14 jaar dé plek om samenvattingen te kopen