 4.4 Stats at Erasmus University Rotterdam | Flashcards & Summaries

# Lernmaterialien für 4.4 stats an der Erasmus University Rotterdam

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Regression formula
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Y(pred.) = intercept(called b0) + coefficient of x1(called b1) * x1 + coefficient of x2(called b2) * x2 ... etc.
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Regression - Creating a straight line.

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y = b0 + b1xi +ei
b1 = Rxy * Sy/Sx
b1 - Regression coefficient, slope of the line
b0 - Intercept where Regression line crosses the y axis where x = 0
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Quantitative Variables

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Variables whose values result from counting or measuring something.

Examples: height, weight, time in the 100 yard dash, number of items sold to a shopper

- continuous

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Qualitative Variables

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Variables that are not measurement variables. Their values do not result from measuring or counting.

Examples: hair color, religion, political party, profession

- categorical

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Regression - what is it?

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Hypothetical, linear model that predicts the value of one variable from another. The relationship is described using the equation of a straight line.
Simple - one predictor
Multiple - more than one predictor
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regression with dummies

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Y = b0 + b1dummy1 + b2dummy2
Y = b0+ (b1xD1)+( b2xD2 )

lecture example:

b0 = mean of the no training group
b1 = difference between the mean of training A and the no training group
b2 = difference between the mean of training B and the no training group

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GLM hypothesis

null hypothesis

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GLM hypotheses:

•General hypothesis:
•H0: R2= 0 (in the population) OR:
•H0: β1= β2= 0 (H0: μnotraining= μtrainingA= μtrainingB)

•Specific hypotheses:
•H0: β1= 0 (μnotraining= μtrainingA)
•H0: β2= 0 (μnotraining= μtrainingB)

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dummie scores

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Dummies have only two scores:
0 and 1

✓E.g. Gender →males= 0; females= 1

Youhave to choose one groupas a reference group (e.g. males), this group has a score of 0 on each dummy
•The remaining group sare each defined by one dummy: females 1 or if more groups then :

Dummy1: people who got training A have a score of 1, all others a 0.
Dummy2: people who got training B have a score of 1, all others a 0.

0 -> no traning - as reference group in this case

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Moderation

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Definition moderation: the effect of predictor X on dependent variable Y depends on the value of third variable M, where M is the moderator.
Moderation analysis: test for external validity: how universal (generalizable) is the relationship between Xand Y?

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Regression notation of a moderation-effect

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Yi=b0+b1Xi+b2Mi+b3XMi+εi

The interaction XM, and thus coefficient b3, indicates the moderation-effect.
Coeffient b1 indicates the simple effect of X on Y. This is the effect of X on Y when M is 0.
Coeffient b2 indicates the simple effect of M on Y. This is the effect of M on Y when Xis 0.

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Mediation

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Definition mediation:  effect of a predictor variable X on outcome variable Y can be (partly-> partial mediation) explained by a third variable M. Variable M is the mediator.
a= direct effect of X on M
b= direct effect of M on Y
c= total effect of X on Y
c’=direct effect of X on Y

The mediation model is a causal model. Thus it is assumed that the mediator causes Y and not vice versa. If this assumption is false, than the interpretation is disputable.

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How does bootstrapping work?

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1.We draw a large number (here: 1000) of bootstrap samples of Ncases, from the original sample. We sample with replacement (this means cases can be drawn more than once or not once) In each sample we compute indirect effect ab

2.We make a histogram of all values of ab. Thisis the bootstrap sampling distribution of ab. It will be positively skewed.
3.We determine the 95% CI by reading of the 2.5th and 97.5th percentile in the distribution. NB. Het CI of ab is also skewed (asymmetrical).
4.This interval is corrected towards the right tail and the upper limit is streched out towards the right tail: Bias corrected and accelerated.

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Q:
Regression formula
A:
Y(pred.) = intercept(called b0) + coefficient of x1(called b1) * x1 + coefficient of x2(called b2) * x2 ... etc.
Q:
Regression - Creating a straight line.

A:
y = b0 + b1xi +ei
b1 = Rxy * Sy/Sx
b1 - Regression coefficient, slope of the line
b0 - Intercept where Regression line crosses the y axis where x = 0
Q:

Quantitative Variables

A:

Variables whose values result from counting or measuring something.

Examples: height, weight, time in the 100 yard dash, number of items sold to a shopper

- continuous

Q:

Qualitative Variables

A:

Variables that are not measurement variables. Their values do not result from measuring or counting.

Examples: hair color, religion, political party, profession

- categorical

Q:
Regression - what is it?

A:
Hypothetical, linear model that predicts the value of one variable from another. The relationship is described using the equation of a straight line.
Simple - one predictor
Multiple - more than one predictor
Q:

regression with dummies

A:

Y = b0 + b1dummy1 + b2dummy2
Y = b0+ (b1xD1)+( b2xD2 )

lecture example:

b0 = mean of the no training group
b1 = difference between the mean of training A and the no training group
b2 = difference between the mean of training B and the no training group

Q:

GLM hypothesis

null hypothesis

A:

GLM hypotheses:

•General hypothesis:
•H0: R2= 0 (in the population) OR:
•H0: β1= β2= 0 (H0: μnotraining= μtrainingA= μtrainingB)

•Specific hypotheses:
•H0: β1= 0 (μnotraining= μtrainingA)
•H0: β2= 0 (μnotraining= μtrainingB)

Q:

dummie scores

A:

Dummies have only two scores:
0 and 1

✓E.g. Gender →males= 0; females= 1

Youhave to choose one groupas a reference group (e.g. males), this group has a score of 0 on each dummy
•The remaining group sare each defined by one dummy: females 1 or if more groups then :

Dummy1: people who got training A have a score of 1, all others a 0.
Dummy2: people who got training B have a score of 1, all others a 0.

0 -> no traning - as reference group in this case

Q:

Moderation

A:

Definition moderation: the effect of predictor X on dependent variable Y depends on the value of third variable M, where M is the moderator.
Moderation analysis: test for external validity: how universal (generalizable) is the relationship between Xand Y?

Q:

Regression notation of a moderation-effect

A:

Yi=b0+b1Xi+b2Mi+b3XMi+εi

The interaction XM, and thus coefficient b3, indicates the moderation-effect.
Coeffient b1 indicates the simple effect of X on Y. This is the effect of X on Y when M is 0.
Coeffient b2 indicates the simple effect of M on Y. This is the effect of M on Y when Xis 0.

Q:

Mediation

A:

Definition mediation:  effect of a predictor variable X on outcome variable Y can be (partly-> partial mediation) explained by a third variable M. Variable M is the mediator.
a= direct effect of X on M
b= direct effect of M on Y
c= total effect of X on Y
c’=direct effect of X on Y

The mediation model is a causal model. Thus it is assumed that the mediator causes Y and not vice versa. If this assumption is false, than the interpretation is disputable.

Q:

How does bootstrapping work?

A:

1.We draw a large number (here: 1000) of bootstrap samples of Ncases, from the original sample. We sample with replacement (this means cases can be drawn more than once or not once) In each sample we compute indirect effect ab

2.We make a histogram of all values of ab. Thisis the bootstrap sampling distribution of ab. It will be positively skewed.
3.We determine the 95% CI by reading of the 2.5th and 97.5th percentile in the distribution. NB. Het CI of ab is also skewed (asymmetrical).
4.This interval is corrected towards the right tail and the upper limit is streched out towards the right tail: Bias corrected and accelerated. ### Erstelle und finde Lernmaterialien auf StudySmarter.

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