Formulas

Question 1

y-y^

Answer 1

= y-b1-b2x1

Question 2

b1

Answer 2

Constant
y bar - b2 x bar

Question 3

MSE

Answer 3

E(b- beta)^2 = var(b) + (bias(b))^2

Question 4

var(b)

Answer 4

Check notes

Question 5

Cov

Answer 5

Check notes

Question 6

Var(b2)

Answer 6

Sigma squared/ sum (x-x bar)^2

Question 7

Var(b1)

Answer 7

sum x^2/N (b2)

Question 8

cov(b1,b2)

Answer 8

-xbar (b2)

Question 9

Reject or accept h null when p value<sig level

Answer 9

Reject null

Question 10

Reject or accept h null if t value greater than table when looking at h> c

Answer 10

Reject

Question 11

Properties of OLS estimators

Answer 11

Unbiased (estimated value is an accurate value of true parameter)
Variance/ se
Efficiency

Question 12

Se

Answer 12

Seb1 =root varb1
Seb2= root varb2

Question 13

Guass-Markov Theorem

Answer 13

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

Question 14

Central limit theorem

Answer 14

If the slr1-slr5 assumptions hold and N is sufficiently large, then the least squares estimate will have a normal distribution

Question 15

Normalised distribution (Z)

Answer 15

X-u/ sd
b2-B2 / root var B2

Question 16

Type 1 error

Answer 16

Reject the null hypothesis when it’s right

Question 17

Type 2

Answer 17

Accept null when it’s wrong

Question 18

Forecast variance

Answer 18

Compares known values to forecasted values
Var(1 + 1/N + (x0- xbar) squared / sum (xi - xbar) squared )

Question 19

Forecasted variance affected by

Answer 19

Depends on var estimator of x
Var of regressor (sum of (x-xbar) squared

Question 20

SSE

Answer 20

Explained by other variables

Question 21

SSR

Answer 21

Explained by x value

Question 22

MLR1 /SL1

Answer 22

Linearity of population model

Question 23

MLR2 /SLR2

Answer 23

E(e|x) =0
Strict exogeneity

Question 24

MLR3/ SLR3

Answer 24

Var(e|X) = variance
Homoskecasticity, all error terms have same variance

Question 25

Cov(e|x) =0

Answer 25

Autocorrelation / conditionally uncorrelated errors
No covariance between variables or error terms

Question 26

MLR5

Answer 26

No perfect multicollinearity not affected by each other

Question 27

SLR5

Answer 27

Has to have more than 1 variable

Question 28

SLR 6/MLR6

Answer 28

Error normality (normalised)

Question 29

SSR

Answer 29

Sum (y-b1-b2x2-b3x3)^2

Question 30

SSE

Answer 30

Sum of e^ /N-K

Question 31

Steps to hypothesis testing

Answer 31

Defin null &alternative hypothesis
Specify test stat and it’s distribution under null hyp
Decide significance, determine rejection region
State conclusion

Question 32

Pros & cons of R^2

Answer 32

Unit free, concise, bounded measure
Adding a regression won’t reduce R^2 leads to over fitting, model must have an intercept

Question 33

Profit max firm

Answer 33

Marginal benefit= mc

Question 34

Non sample information

Answer 34

Improves estimates information

Question 35

F test

Answer 35

Assesses how big loss of fit is, change in SSE

Question 36

What happens if SSEr> SSEu

Answer 36

If restricted is bigger then the variable does affect the model

Question 37

T test

Answer 37

Differentiated number - cost / sd differentated number

Question 38

Prove bias

Answer 38

E(b2|X) -B2 = B3 gamma if it’s biased, unbiased it’s 0
Violated MLR2

Question 39

Reset test

Answer 39

H0 no omitted variables
H1 omitted variables exist or wrong functional form gamma y squared + gamma y cubed

Question 40

Correlation

Answer 40

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

Question 41

GLS

Answer 41

Hetero turn homo by doing 1/ root x

Question 42

What is the issue with gls model

Answer 42

Biased se
Hetero
Inefficient

Question 43

Properties of GLS

Answer 43

Efficiency is greater
Makes homoskedastic
Reduces variance