Formulas/definitons

Question 1

Rank

Answer 1

How many columns/ rows are linearly independent

Question 2

B

Answer 2

(X’X)^-1(X’Y)

Question 3

Y^

Answer 3

XB^

Question 4

E^

Answer 4

Y-y^

Question 5

Error var

Answer 5

E^’ E^ /(n-k)

Question 6

Var B

Answer 6

Error var (X’X)^-1
E(B^-B)(B^-B)’)

Question 7

fitted y y^

Answer 7

Py
P= X(X’X)-1X’

Question 8

e residual with m

Answer 8

M=I-P
e^=My

Question 9

RSS

Answer 9

e^’ e

Question 10

s^2

Answer 10

RSS/n-k

Question 11

R^2

Answer 11

1-RSS/TSS = 1- e^’e^/sum(y-y_)^2
=TSS-RSS/RSS

Question 12

adjusted R^2

Answer 12

1-RSS/(n-k) / TSS/(n-1)

Question 13

assumptions for multiple linear model

Answer 13

Linear model
errors have 0 mean E(e)=0
Homoskedasticity & no autocorrelation Var(e)= E(e’e)= var x I
no collinearity in x guarantees X is non singular
Normal errors

Question 14

type 1 error

Answer 14

rejecting H0 when its true

Question 15

type 2 error

Answer 15

accepting H0 when its false

Question 16

t or z test

Answer 16

if population error is known do z test - B^-b/s x root var
t test- B^-b/s (sample ) root var

Question 17

calculating confidence intervals

Answer 17

coefficienct of variable +- ttable value x se

Question 18

hypothesis test

Answer 18

make hypothesis
calculate t stat coefficient/se
compare to table value
reject h0 if calculated is bigger than table

Question 19

p value

Answer 19

compare to area (find on table using t value and df) , if value is smaller than eg 5% level, reject h0

Question 20

calculating f stat multiple regression

Answer 20

w= r’B-c/ s x root r’(X’X)-1r
where H0=r’B=c etc

Question 21

H0: B1+B2=1 what’s the t stat

Answer 21

B1+B2-1/se(B1+B2)
se(B1+B2)= root varB1+varB2+2covB1,B2

Question 22

B2=0

Answer 22

(0,1,0,0)B=0

Question 23

B2+B3=0

Answer 23

(0,1,1,0)B=0

Question 24

B2=B3=0

Answer 24

(0,1,0,0)B=(0)
(0,0,1,0) (0)

Question 25

wald test

Answer 25

(RB^-C)’(R(X’X)-1R’)-1(RB^-C)/S^2 (if population mean is known)
(RB^-C)’(R(X’X)-1R’)-1(RB^-C)/J/S^2

Question 26

URSS

Answer 26

E^’E=(Y-XB^)(Y-XB^)

Question 27

RRSS

Answer 27

E‘E=Y-XB(Y-XB)
TSS=sum(y-y_)^2

Question 28

F STAT FOR OMITTED COEFFICIENT

Answer 28

(RRSS-URSS)/J/URSS/(N-K)

Question 29

testing joint significance f stat

Answer 29

TSS-RSS/(k-1) / RSS/(n-k)
R^2/(k-1) / (1-R^2)/(n-k)