Model Checking

Question 1

Var[e_i]=?

Answer 1

Question 2

Cov[e_i,e_j]=

Answer 2

Question 3

Standardize residuals

Answer 3

Question 4

Studentise residuals

Answer 4

Replace σ^2 in Standardized residual with S^2

Question 5

Constant varíance?

Answer 5

Homoscedasticity

Question 6

To check linearity of model

Answer 6

Plot r_i against x_i

Question 7

To check homoscedasticity

Answer 7

Plot r_i against y^^_i (fitted valúes)

Question 8

h_ii =

Answer 8

Question 9

Rule of thumb for outlier observations when standardised

Answer 9

If abs value >2, outlier

Question 10

Answer 10

Question 11

Large leverage?

Answer 11

Question 12

Very large leverage

Answer 12

Question 13

Cook’s distance?

Answer 13

Statistic to measure influence of an observation

Question 14

Determine if cook’s stat is unusually large?

Answer 14

If D_i is bigger than 50th percentile of(where p is #parameters):

Question 15

Pure error?

Answer 15

Question 16

Replications

Answer 16

More than one observation for some valúes of an explanatory variable;
Y_ij for x_i

Question 17

Answer 17

When múltiple observations at single x_i

Question 18

Sum of squares for residuals (Y_ij for x_i)

Answer 18

Question 19

Puré error sum of squares

Answer 19

Question 20

Lack of fit sum of squares

Answer 20

Question 21

In SLRM SS_E =

Answer 21

SS_LoF + SS_PE

Question 22

ANOVA table columns

Answer 22

Source of variation, d.f., SS, MS, VR

Question 23

E(SS_PE) =

Answer 23

(N-m)σ^2

Question 24

If SLRM is true then E(SS_LoF) =

Answer 24

Question 25

MS_PE and MS_LoF give estimators?

Answer 25

Both give unbiased estimators of var
But latter only if SLRM is true

Question 26

F test for lack of fit:
-H_0?

Answer 26

SLRM is true

Question 27

F test for lack of fit:
H_1?

Answer 27

Question 28

F test for lack of fit:
-2Stats?

Answer 28

Question 29

F test for lack of fit:
-F stat under H_0

Answer 29

Question 30

Can only ro F test for LoF if

Answer 30

We have replications (not repeated measurements of same sampling unit)

Question 31

Answer 31

0 vector

Question 32

Answer 32

Question 33

h_ii is?

Answer 33

ite diagonal element of Hat matrix

Question 34

Answer 34

Question 35

ith mean response? (Matrix)

Answer 35

Question 36

Estimator of ith mean response

Answer 36

Question 37

Varíance of estimator of ith mean response

Answer 37

Question 38

Estimator of varíance of estimator of ith mean response

Answer 38

Question 39

Answer 39

Question 40

Answer 40

Question 41

Varíance of estimator of beta zero

Answer 41

Question 42

Answer 42

Question 43

Answer 43

Question 44

Vector of residuals

Answer 44

Question 45

Múltiple regression model written in vectors

Answer 45

Question 46

Vector of fitted valúes

Answer 46

Question 47

ith fitted valúe? (Vector)

Answer 47

Question 48

h_ii indicates?

Answer 48

Question 49

Properties of h_ii:
As var(e_i) = σ^2 (1-h_ii)

Answer 49

Question 50

Properties of h_ii:
h_ii is usually small/large when?

Answer 50

Question 51

Centroid?

Answer 51

The vector of means of each feature across all data points

Question 52

Properties of h_ii:
When p=2?

Answer 52

SLRM,

Question 53

Properties of h_ii:
Range of value for h_ii

Answer 53

1/n < h_ii < 1

Question 54

Properties of h_ii:
Sum of h_ii

Answer 54

Question 55

Average leverage

Answer 55

p/n

Question 56

High leverage

Answer 56

h_ii > 2p/n

Question 57

Very high leverage

Answer 57

h_ii > 3p/n

Question 58

Cooks distance in vectors

Answer 58

Question 59

Answer 59

Question 60

Cooks distance in vectors (reduced)

Answer 60

Question 61

PRESS residuals

Answer 61

PRediction Error Sum of Squares

Question 62

PRESS

Answer 62

Sum of squares of press residuals

Question 63

PRESS residuals simplified

Answer 63

Question 64

What does PRESS assess?

Answer 64

The model’s predictive ability
-used for calculating predicted R^2

Question 65

Predicted R^2 defined?

Answer 65

Question 66

When is Predicted R^2 used?

Answer 66

In MLRM to indicate how well the model predicts responses to new observations

Question 67

A Good modele ould have R^2

Answer 67

And R^2(pred) both high and close to each other

Question 68

Large discrepancy in R^2 and R^2(pred)

Answer 68

Means model May b over fitted

Question 69

If (below) is singular, then?

Answer 69

No uni que least square estimators exist

Question 70

Singularity of below caused by

Answer 70

Linear dependence among explanatory variables

Question 71

Problems of Multicollinearity

Answer 71

-some or all estimators will have large variances
-very different models May fit equally well therefore variable selection may b difficult
- some params May have wrong sign

Question 72

What is use of varíance inflación factor?

Answer 72

Used to indicate when multi collinearity May b a problem

Question 73

VIF_j=?

Answer 73

For regression w p-1 predictors, model with X_j as function of remaining p-2 exp variables, R^2_j coefficient of determination (not as a %)

Question 74

The scatterplot of the residuals vs fitted values is useful to check if

Answer 74

-the variance of the error is constant
- if there is any trend in the residuals (thus some term is missing in the regression model)
- if there is any outlier