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The Effect - - Regression

Q: 13.1.1 Error terms, what is an error term?

T he error is the difference between the true best fit-line and the actual value.

Q: How can we interpret the binary variable's coefficient (the effect of that binary variable on our model)?

It’s the difference in the dependent variable between the trues and the falses. for example, if we ran the regression Sales=β0+β1Winter+ε, where Winter is a binary variable that’s 1 whenever it’s winter and 0 when it’s not, then β1 would be how much higher sales are on average in Winter than in Not Winter. Also, we only include one side of the yes/no equation.

Q: How do you figure out wheter a categorical variable has a significant effect as a whole?

Don't look at the individual coefficients, but at all the category coefficients. This takes the form of a 'joint F-test'.

9 important questions on The Effect - - Regression

13.1.1 Error terms, what is an error term?

The error is the difference between the true best fit-line and the actual value.

13.1.2 Regression Assumptions and Sampling Variation, what are the assumptions?

Exogeneity Assumption

Assumption that ε is uncorrelated with any variable we want to know the causal effect of

There is no perfect multicollinearity

You can’t make a perfect linear prediction of any of the variables in the model with any of the other variables

13.2 Getting Fancier with Regression, what does this section entail?

It introduces how we can also work with different variables rather that continuous variables, for example, discrete variables (often binary variables, ie yes/no, or categorial variables)
It introduces how we can transform variables.
It introduces how the relationships themselves might be affected by other variables, through interaction.

How can we interpret the binary variable's coefficient (the effect of that binary variable on our model)?

It’s the difference in the dependent variable between the trues and the falses.
for example, if we ran the regression Sales=β0+β1Winter+ε, where Winter is a binary variable that’s 1 whenever it’s winter and 0 when it’s not, then β1 would be how much higher sales are on average in Winter than in Not Winter.

Also, we only include one side of the yes/no equation.

How do you handle categorial variables?

Give each of the categories its own binary variable.

What do you do when you want to interpret the coefficient of one of the categorial variables you made binary?

Make a reference category, meaning that all the coefficients are relative to that category.

You do this by dropping one of the categorial variables, this will be the reference variable.

With binary variables, the coefficient gave you the difference between yes and no, now with the categorial variables and reference variable, the difference will be between this category and the reference category.

Ie. The means average income in Gambia is .5 higher than average income in France.

How do you figure out wheter a categorical variable has a significant effect as a whole?

Don't look at the individual coefficients, but at all the category coefficients.
This takes the form of a 'joint F-test'.

What are the two ways to make regression work if there is not linear relation?

Add Polynomial Terms
Transform the Data

How can you interpret the regression model when you have polynomial terms?

As you square you X, you must interpret every square of X, so interpet all the X's together.

You do this by using the derivative.

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Quantitative Research Methods

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The Effect - - Regression

9 important questions on The Effect - - Regression

13.1.1 Error terms, what is an error term?

13.1.2 Regression Assumptions and Sampling Variation, what are the assumptions?

13.2 Getting Fancier with Regression, what does this section entail?

How can we interpret the binary variable's coefficient (the effect of that binary variable on our model)?

How do you handle categorial variables?

What do you do when you want to interpret the coefficient of one of the categorial variables you made binary?

How do you figure out wheter a categorical variable has a significant effect as a whole?

What are the two ways to make regression work if there is not linear relation?

How can you interpret the regression model when you have polynomial terms?

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