Formulas Flashcards
y-y^
= y-b1-b2x1
b1
Constant
y bar - b2 x bar
MSE
E(b- beta)^2 = var(b) + (bias(b))^2
var(b)
Check notes
Cov
Check notes
Var(b2)
Sigma squared/ sum (x-x bar)^2
Var(b1)
sum x^2/N (b2)
cov(b1,b2)
-xbar (b2)
Reject or accept h null when p value<sig level
Reject null
Reject or accept h null if t value greater than table when looking at h> c
Reject
Properties of OLS estimators
Unbiased (estimated value is an accurate value of true parameter)
Variance/ se
Efficiency
Se
Seb1 =root varb1
Seb2= root varb2
Guass-Markov Theorem
Under the assumptions of slr1-5, the estimators b1 and b2 have the smallest variance among all other values
Bet Linear Unbiased Estimator of B1 &B2
Central limit theorem
If the slr1-slr5 assumptions hold and N is sufficiently large, then the least squares estimate will have a normal distribution
Normalised distribution (Z)
X-u/ sd
b2-B2 / root var B2
Type 1 error
Reject the null hypothesis when it’s right
Type 2
Accept null when it’s wrong
Forecast variance
Compares known values to forecasted values
Var(1 + 1/N + (x0- xbar) squared / sum (xi - xbar) squared )
Forecasted variance affected by
Depends on var estimator of x
Var of regressor (sum of (x-xbar) squared
SSE
Explained by other variables
SSR
Explained by x value
MLR1 /SL1
Linearity of population model
MLR2 /SLR2
E(e|x) =0
Strict exogeneity
MLR3/ SLR3
Var(e|X) = variance
Homoskecasticity, all error terms have same variance
Cov(e|x) =0
Autocorrelation / conditionally uncorrelated errors
No covariance between variables or error terms
MLR5
No perfect multicollinearity not affected by each other
SLR5
Has to have more than 1 variable
SLR 6/MLR6
Error normality (normalised)
SSR
Sum (y-b1-b2x2-b3x3)^2
SSE
Sum of e^ /N-K
Steps to hypothesis testing
Defin null &alternative hypothesis
Specify test stat and it’s distribution under null hyp
Decide significance, determine rejection region
State conclusion
Pros & cons of R^2
Unit free, concise, bounded measure
Adding a regression won’t reduce R^2 leads to over fitting, model must have an intercept
Profit max firm
Marginal benefit= mc
Non sample information
Improves estimates information
F test
Assesses how big loss of fit is, change in SSE
What happens if SSEr> SSEu
If restricted is bigger then the variable does affect the model
T test
Differentiated number - cost / sd differentated number
Prove bias
E(b2|X) -B2 = B3 gamma if it’s biased, unbiased it’s 0
Violated MLR2
Reset test
H0 no omitted variables
H1 omitted variables exist or wrong functional form gamma y squared + gamma y cubed
Correlation
When related the variance and correlation goes bigger, you don’t want them to be related or to use bad data, having a little correlation isn’t an issue
If you take on a bad variable, your correlation still increases but variance would fall compared to before
GLS
Hetero turn homo by doing 1/ root x
What is the issue with gls model
Biased se
Hetero
Inefficient
Properties of GLS
Efficiency is greater
Makes homoskedastic
Reduces variance
