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Flashcards in lecture 8 Deck (11)
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1
Q

how are matrices used to explain power

A

let X be a matrix whose columns contain the data for
the explanatory variables and let y be a vector containing the data
for the dependent variable. The multivariate OLS estimator can be
calculated as:

2
Q

what would happen if 2 variables are correlated

A

least-squares method will not allow us
to estimate separate coefficients for the two right-hand side
variables.

generally we might have less than perfect collinearity:

If this is the case then it is possible to estimate separate effects
using least-squares but the estimates may be very inaccurate

3
Q

if an equation is loglinear what does the co-efficients measure

A

the elasticities

4
Q

what does Rsquare measure

A

measure the the fraction of the variance of the endogenous variable –> explained by the model

5
Q

in order to caculate the OLS estimator using the matrix form (multi varieate) , what are the 2 most important assumption

A
    1. k
6
Q

what is perfect collinearity

A

Perfect multicollinearity occurs when two or more independent variables in a regression model exhibit a deterministic (perfectly predictable or containing no randomness) linear relationship

7
Q

whats the difference between a bivariate and a multivariate regression

A

bivariate has 2 unknown, whilst multivariate has more than 3 unknowns

8
Q

in terms of a matric regression what is the slope parameter

A

Bhat

9
Q

in a multivariate regression what is the form of a 3 variable matrix regression line

A

Bhat = 𝛽+(𝑋^t * 𝑋)^(−1) * X^t*Y

10
Q

how are able to have a matrix form of the multivariate regression (2)

A

only possible because (𝑋^t * 𝑋)^(−1) is invertiable

  • number of columns is less than the number of rows
  • columns of X must be linearly independant
11
Q

what are the 2 most important assumptions of OLS in terms of a multivariate regression

A
  1. k less than N, where N is the number of observations

2. The X variables are linearly independent.