Simple Linear Regression (2) Flashcards
(18 cards)
What is the simple linear regression model and what does each variable stand for?
y=β0+β1x1+u
y- dependant variable
x1 - independent variable
u - unobserved regression error
What is the assumption of the simple linear regression model?
E[u|x1] = E[u]
conditional mean independence thus:
E[u|x1] does not
depend on the value of x1
E[u] = 0
What is the conditional mean function or the population regression function?
E[y|x1] = β0 + β1x1
What does the population regression function tell us?
a one-unit increase in x1 changes the expected value of y by β1
What are the fitted values?
The estimated coefficients
What are residuals?
The difference between the observed value and fitted values
u^i = yi − y^i ,
What do residuals measure?
how far off the models prediction is
How does the OLS work?
Minimises the sum of squared residuals (SSR)
What are the equations to calculate B^0 and B^1 ?
check ppt 1
What is E[β^0] and E[β^1]
E[β^0]=B0
E[β^1]=B1
What is the assumption “linear in parameters”?
A model is linear in parameters if it can be written as:
y = β0 + β1x1 + u
What is the assumption “random sampling”?
he data {(yi , xi1)}n i=1 consists of a random sample of size n from the population model.
What is the assumption “sample variation in x1”?
The sample outcomes of x1, given by {xi1}n
i=1 are not all the same
What is the assumption “Zero conditional mean”?
The error u and regressor x1 satisfy E[u|x1] = 0.
this implies that Cov(ui, xi1) = 0
What is the assumption of “Homoskedasticity”?
No matter the value of x1 the spread (variance) of the errors remains the same.
Var(u|x1) = σ2
What is it called if the conditional variance Var(u|x1) depends on x1?
heteroskedasticity
What is conditional variance?
The conditional variance of a random variable Y given another variable X is the variance of Y when you know the value of X
What are the SLR assumptions 1-5?
1 -Linear in parameters
2- Random sampling
3- Sample variation in x1
4- Zero conditional mean
5- Homoskedasticity
