3A

Question 1

correlation does not imply causation

Answer 1

Just that there is a correlation between variables, does not mean that one causes the other

Question 2

What is meant by spurious correlation?

Answer 2

Spurrious correlation refers to a connection between two variables that appears to be causal but is not.

Question 3

suppressor variables

Answer 3

a suppressor varriable is a variable that increases the predictie validity of another variable when included in a regression equation.

Question 4

when do we speak of omitted variable bias?

Answer 4

when a regression coefficient is ether overestimated (spurious correlatiom) or underestimated (suppressor variable)

Question 5

what is multiple regression

Answer 5

In multiple regression, there is always one dependent variable (y) but there can be any number of independent variables.

A multiple regression model provides the best possible prediction of Y based on not one but several independent variables

Question 6

Why would you want to do multiple regression analysis?

MR/MRA

Answer 6

MR provides regression coefficients that take into account the role of other variables in the model.

We also say that we estimate the coefficient for an X variable while statistically controlling for the effect of other variables. This means that MR can be used to mitigate the problem of omitted variable bias.

Question 7

interpretation of coefficients MR

Answer 7

Any regression coefficient indicates the predicted increase in Y with every one-unit increase in X while keeping all other variables in the model constant.

The predicted value indicaties the expected value on Y based on all values in the model. The residual indicates the difference between the observerd value on Y an dht expected value on Y based on all X-variables.

Question 8

OLS estimation of multiple regression

Answer 8

It allows to estimate the relation between a dependent variable and a set of explanatory variables.
The OLS estimation of multiple regression coefficients does not follow the exact same formula as for simple linear regression. The principle is very much the same. OLS only analyzes cases with complete observations on all variables in the model.

Question 9

Why should you often include control variables?

Answer 9

We can mitigate omitted variable bias and obtain better estimates of causal relations by including control variables even when our research question is not about these variables.

In addition, you can sometimes also get more precise, by including control variables that are very strong predictors of Y

Question 10

Why you should not include too many control variables

Answer 10

1. interpretation
2. overfitting
3. multicollinaerity
4. risk of including mediators

Question 11

interpretation

Answer 11

The more variables you put in the model, the harder it becomes to interpret and explain your findings.

Question 12

overfitting

Answer 12

overfitting occurs when you include more variables than would be reasonable based on your sample size

Rule of thumb: try to have at least 50 cases, and at least 5-10 cases per X-variable

Question 13

multicollinearity

Answer 13

Multicollinearity refers to the correlation between different X-variables in the model

This is not in itself a problem; in fact it is often the very reason you included a control variable

In the previous example, we controlled for education precisely because we know it is correlated with income and could hence cause omitted variable bias

But if multicollinearity becomes too strong, there is not enough information (especially with a small sample size) to distinguish the effects of different variables (this happens only with very extreme correlations)

If one X variable can be predicted perfectly by another X-variable, or a combination of other X-variables, we speak of perfect multicollinearity. When this occurs, the model cannot be estimated

For example, you cannot include both age and year of birth in one model because these variables have a perfect multicollinearity (in cross-sectional data)

Question 14

risk of including mediators

Answer 14

A mediator is a variable that accounts for the assosciation between X and Y

If you include a mediator in the model, the effect of X on Y will be underestimated or removed, even if there is in fact a causal effect of X on Y

Question 15

include variables in your model when:

Answer 15

1. They are associated with both your X-variable of interest and Y and hence could induce omitted variables bias
2. They are extremely strong predictors of Y and could hence make the model more precise (e.g., smaller standard errors

Question 16

do not include variables in your model when:

Answer 16

1. There is no reason to expect they are relevant and they would just complicate the interpretation
2. Your sample size is so small that it will cause overfitting
3. They are (almost) perfectly correlated with the other X-variables in the model (e.g., perfect multicollinearity)
4. They could be a mediator of the relation between your X-variable of interest and your Y-variable

Question 17

convention

Answer 17

heb jij nog aanvulling hierop?

Question 18

stepwise model specification

first possibility

Question 19

stepwise model specification

second possibility

Question 20

strenghts of multiple regression

Answer 20

Compared to simple regression and bivariate correlations, multiple regression provides us more possibilities to say something about causal relations

By controlling for likely alternative explanations, we can reduce omitted variable bias and we get closer to being able to interpret regression coefficients as causal effects

It is often quite easy to falsify incorrect causal claims with multiple regression by demonstrating how a correlation is spurious

Question 21

Limitations of multiple regression

Answer 21

You can never control for all variables that could theoretically induce omitted variable bias, because:
1. You never know precisely what those variables are
2. Even if you would know, you would never have data on all those variables

Although it is a step in the right direction, the principle “correlation does not imply causation” is still true for multiple regression