Linear regression model: module 2 Flashcards

1
Q

How is the LRM formulated?
What does all of the components stand for?

What is is we try to do with the LRM?

A

Formula: y(i)= β(1) + (2)*x(i) + ε(i)

β(1) and beta 2 are unkown parameters that are intercept and slope
x(i) is the independent/explanatoyu vriable
y(i) is the dependent/ explained variable
ε is the error term. It is an unobserved random variable

LRMs mainpoints:
observe data x and y (the only variables that are observable)
Make LRM assumptions
Find ESTIMATES of the two betas!

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2
Q

What is an important assumption about ε?

Hint: it’s relation to x

A

ε and x can not be correlated! In other words: the x-varible is exogenous if E(ε|x)=0
Note: in whole it is =0

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3
Q

What result of E(y|x) do we get if E(ε|x)=0?

A

Then E(y(i)|x(i))= β(1) + β(2)*x(i)

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4
Q

What formula can we write error term epsilon as?

hint: expected value

A

Since we know that E(y(i) | x(i))= β(1) + β(2)*x(i)
We can write the LRM as: y(i) = E(y(i)|x(i)) + ε(i)
Which means that we can write
ε= y(i) - E(y(i)|x(i))

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5
Q

If we have LRM + exogeneity, what can we estimate the LRM values to?

A

We can then use the OLS trendline
We estimate beta(1) to b(1) and beta(2) to b(2)
We estimate ε to e (residuals)
We estimate E(y | x) to the fitted values

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6
Q

When is an estimator unbiased and cosistent? (both x-bar and b1, b2))

A

x-bar is unbiased estimator of μ (mean) if E(x-bar)=μ
x-bar is consistent if x-bar goes closer to μ when n goes to infinity

b is unbiased if E(b)= β
consistent if b becomes equal to as n goes to infinity

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7
Q

When is an error term homoscedastic?

A
If Var(εi | xi) = σ (sqrd)
All error terms have the same variance (conditional on xi)
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8
Q

When is an error term heteroscedastic? (ingen matte)

A

When each error term has its own variance which is contitional to xi

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9
Q

Waht are the Gauss-Markov assumptions?

A

We have an LRM with random variables where the explanatory variable (x) is exogenous and the error terms are homoscedastic

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10
Q

What are our OLS estimators?

A

b1,b2, fitted values, e

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11
Q

Waht is the Gauss-markov theorem?

A

We have LRM with r. variables
OLS estimates are linear
In the LRM under GM-assumptions, the OLS estiamtes will be BLUE

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12
Q

What does efficiency mean?

A

The smaller the variance - the more efficient

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13
Q

What does BLUE mean?

A

Best linear unbiased estimator

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