lecture 7 Flashcards
what is the sum of squared deviations
TSS = ESS + RSS
how do you define R suared
π ^2=πΈππ/πππ=1βπ ππ/πππ
how is r squared displayed on a graph
when it is close to 1, all observations will be on the regression line
what are the 5 properties of R suared
R-squared always lies in the range zero to one.
If R-squared equals one then the regression is a perfect fit to the data (this almost always indicates that there is something wrong with it!).
If R-squared is equal to zero then the regression has no explanatory power.
In multivariate regressions the R-squared will always increase when we add an extra variable (even if that variable is completely irrelevant).
Tells us how much we have explained using our regression!
what is the market model?
let Pk = share price of company K Pm = index for the market as a whole
returns from holding equity will be:
π π‘π=Ξ lnβ‘ππ‘π and π π‘π=Ξ lnβ‘ππ‘π
what would be the relationship established in the market model
estimate of Ξ² will indicate
how the share price moves with the market and the R-squared for
the regression will indicate how much of the variance of the share
price is due to market movements. π
_π‘^π expected return of the
market and π
_π‘^πexpected return on a security
what is the tole of beta in CAPM
Relevant measure of a stockβs risk (or companyβs risk)
Measures volatility, (i.e. how much the price of a particular stock jumps up and down compared with how much the entire stock market jumps up and down.
If a share price moves:
Exactly in line with the market, then the stockβs beta is 1.
how do you test if an equation has explantory power?
you test if the conditional variable is the same as the unconditional variable.
against the hypothesis that the conditional variance is greater than the unconditional vairance
this is done using the F test
what is the relationship between F-statistic and R squared
multivariate models we can think of the F-test as a test of
the joint hypothesis that all the slope coefficients are equal
to zero.
what is the relationship between a F-test and T-RATIO
F = (Bhat/SE(Bhat))^2
only holds for bivariate regression equations.
Things become more complicated when we move to multivariate
regressions.
what is the difference between conditional and unconditional variances of Y defined in the model?
both are unknown population parameters
conditioned: explanatory variables are adding information onto the variables you want to estimate (varience of U0
unconditioned: independent variables are not adding information to the variables you want to estimate (vairence pf u)
how is the unconditional varience of Y calcualted?
TSS 1/N-1
how is the conditional varience of Y calculated?
TSS 1/N-2
what is the F test used to test the explanatory power of a model
(TSS-RSS)/RSS * (N-2)/1
why should you look at the relationship between F test and R squared
F test looks at whether your regression model provides a better fit comapred to one with no independant variables
R squared: this looks at how well your model fits the data
