Introduction to Multiple Regression

Question 1

Are there always omitted variables in a regression model

Answer 1

Yes because reality is interconnected and not entirely causal

Question 2

When are omitted variables a problem for regression functions

Answer 2

When they are not unbiased aka they fail to fulfill the E(u|X=x) = 0 requirement

Question 3

What is omitted variable bias

Answer 3

Bias in the OLM estimator that is a result of some variable being omitted. For the bias to uccur the omitted variable Z must be at least a little correlated with X and also be a determinant of Y

Question 4

If room temperature is a determinant of test scores but is not correlated at all with the amount of teachers in the class will the admission of room temperature lead to a omitted variable bias in the regression model of grades based on teachers in class

Answer 4

No, both the requirements of correlation and determinants must be fulfilled by the third factor for its omission to result in a omitted variable bias.

Question 5

What is P a sign fore in statistics

Answer 5

correlation

Question 6

Is there a formulaic way to determine if the slope is biased due to an omitted variable

Answer 6

If there is correlation between the independent variable X and the residual u

Question 7

What is reverse causality

Answer 7

when effects causes the cause because of an expected effect. For example when patients choose a treatment because they believe it will cure them

Question 8

How do you avoid omitted variable bias

Answer 8

You ither use a randomized and controlled sample that compensates for the bias or you use multiple regression aka include the omitted variable in the regression function

Question 9

How is the standard error of the regression SER effected by multiple regression

Answer 9

the denominator it is divided by is subtracted by 1 in addition to the number of independent variables.

Question 10

R² always increases when you add another regressor

Answer 10

Yes because the method gets more to work with, that is why the adjusted -R² penalizes you for using another regressor.

Question 11

How do you calculate adjusted -R² from R²

Answer 11

You multiply the regression with the sample size subtracted by one divided by the sample size subtracted by one and the amount of regressors

Question 12

What is perfect multicollinearity

Answer 12

When one of the regressors is an
exact linear function of the other regressors

Question 13

Explain why the dummy variable trap leads to perfect multicillinearity

Answer 13

Becouse if the variables are muturally exclusive and exhaustive you can re write one variable as a linear function of the other.

Question 13

What is the dummy variable trap

Answer 13

That when you have a group of dummy varables that are mutually exclusive and exhaustive aka a few classes buch each datapoint falls withing one of them they achive perfect multicollinerity if you add a constant to the regression.

Question 14

How do you escape the dummy variable trap

Answer 14

Omit one of the variables

Question 15

imperfect multicillinearity breaks the OLS estimator

Answer 15

false, when the multicillinearity is imperfect the two variables are highly corelated but not perfectly which will not break the function but might result in large standard errors and a failure to estimate what happens when one of the regressors change and the correlated one does not.