Estimation

Question 1

Sum of squares of errors

Answer 1

Question 2

Find LSE

Answer 2

NEED TO FIND MIN OF sum of squares of errors
- partial deriv w respect to β0, β1;
-equate to zero (obtain normal eqs)
-calc 2nd deriv
-form hessian

Question 3

For lse of sum of squares errors

Answer 3

Question 4

For Lse,

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

Terms of c_i

Answer 7

Question 8

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

Answer 11

Question 12

Normal equations obtained from lsm given by (matrix form)

Answer 12

Question 13

Unique solution to normal equations obtained from lsm (vector)

Answer 13

Question 14

Lsm β^ is?

Answer 14

Unbiased

Question 15

Variance matrix of β^ (vector)

Answer 15

Question 16

Prove that β^- is unbiased

Answer 16

Question 17

Prove var matrix of β^

Answer 17

Question 18

Vector of null model

Answer 18

Question 19

β^ in null model

Answer 19

Question 20

Var[β^] in null model?

Answer 20

Question 21

β^ in no intercept model?

Answer 21

Question 22

Var[β^] in no intercept model?

Answer 22

Question 23

LSE β^- (vector) given by?

Answer 23

Question 24

Limitation of β^- vector estimator?

Answer 24

Question 25

Estimation of β by least squares; S=?

Answer 25

Sum of squares, which then needs to be minimised

Question 26

Estimation of β; normal equations?

Answer 26

Question 27

Estimation of β; unique solution to normal equations?

Answer 27

Question 28

Then β^ ~?

Answer 28

Question 29

Gauss Markov Theorem

Answer 29

Question 30

BLUE

Answer 30

Best Linear Unbiased Estimator . Estimator, among all unbiased estimators of form (image) that has smaller variance

Question 31

Answer 31

Question 32

Answer 32

Question 33

c_i

Answer 33